This post is a followup to the original ladder analysis post, which shall go into further detail regarding the system. Please note that much of the content contained within this post is of a more speculative nature, and if a detail here is wrong it should not reflect poorly on the original analysis. I will be delving deeper into the mathematical underpinnings, though it should not be excessively complex and I will try to make it easy to follow.
Overview
To start with, we assumed that Blizzard used a system quite similar to their WoW Arena matchmaking system, albeit with refinements. The Arena system uses a Bayesian inference model to create its ladder and do its matchmaking. What this means in essence is that the rating used to represent your skill is easily updated after each match. For more details, see: http://en.wikipedia.org/wiki/Bayesian_analysis
In conjunction with this, the MMR is actually one part of the skill probability distribution. Blizzard also uses an “uncertainty” factor. That is, when you first start in Arena there is a lot of uncertainty in your rating. As you play more games, that uncertainty decreases and the system is more “confident” in the rating it has assigned to you. I will be referring to this uncertainty factor as sigma, and it is the inverse of the system's confidence. This forms a bell curve, also known as a Gaussian, or normal, distribution. For more details, see: http://en.wikipedia.org/wiki/Gaussian_distribution . The curve represents a couple related ideas: the range in which your skill may truly fall, as well as the fact that you do not play at exactly the same skill level every game. A more consistent player would have a narrower curve, for example.
This class of ladder and matchmaking is not new. The first system using a method similar to this is the Glicko system, used to rank chess players, and is arguably better than the famous ELO system which encourages some strange behavior (e.g. it is better to draw in ELO than risk a loss in many cases). Another well-known system is Microsoft TrueSkill, used in every Xbox 360 game for matchmaking and ranking, as well as PC games such as Dawn of War 2.
The short version of what the links above show is that it is possible (and computationally efficient) to take the MMR and uncertainty factor (also known as sigma, or standard deviation) for both players. The MMR and sigma form a bell curve per player. It is possible to combine the bell curves into a 3D probability distribution. This is done by combining the data to form a shape like this:
It may help to think of it as combining the two 2D curves perpendicularly and forming this 3D shape. This shape is centered on a point in the (x,y) plane, where x represents player 1’s skill, and y represents the skill of player 2. Intuitively, the best matches will be between ratings where x=y. Thus, Blizzard attempts to keep it as close as possible. Looking at this same shape top-down (try to visualize it as a topographical map):
Run a line along x=y, and you will split the shape into 2 pieces. If you sum the volume under the shape on each side of this split, and compare their relative size you will get the probability of a player victory. If the curve is contained wholly within one side of the graph then clearly that player is overwhelmingly favored by the system (Note: this is NOT the same thing as the “Favored” display on the loading screen!). Also note that this does not need to be circular when looking at a top-down section. If players have different confidence values it will look like an ellipse.
Note that this figure is taken from a TrueSkill presentation, and is copyright Microsoft. TrueSkill incorporates the possibility of a draw. More intuitively, it can be thought of as the “matchmaking sweet spot”, and something similar is likely used by SC2’s ladder to provide the system some wiggle room in matchmaking.
After a match finishes, the system needs to update the MMR and sigma for both players. Displayed rating will be discussed later in this post. Whenever a match finishes the winner’s MMR increases and the loser’s decreases. More interesting is what happens to the sigmas. If the match finished as expected with the MMR favored player winning (and remember, the loading screen “favored” display is NOT this) then both players' sigmas will decrease. That is, the system gains confidence in the ratings it has assigned to the players. If the match finishes in an upset and both players' sigmas are small, then the sigmas for both players will increase as the system thinks it may have an incorrect rating assigned to both. The change in sigma scales based upon the difference in MMR and the difference in sigmas. That is, losing to someone close to your own rank will not change your sigma too much (though it will over the course of several games).
If a lower-MMR player wins then what happens depends a lot more on their precise equations they are using. If a player's sigma is large in an upset (whether he's the winner or loser) it can decrease. That is because, given the right MMR and sigma values, it's possible in theory for the system to learn about that player's skill and rate him more accurately. If a player's sigma is small, however, it can become larger after an upset if that upset was truly unexpected.
To summarize: combining the MMR and uncertainty factor of a player creates a curve. Take two of these curves and form a 3D shape. This shape shows the probability of victory when split along x=y. Matchmaking tries to have x=y, but will expand the search if no match is found quickly.
Promotion
As initially theorized, promotion requires your MMR to be above a certain league threshold. However, because MMR changes greatly after each match and the opponent variation is so wide, often spanning multiple leagues, the system requires a particular degree of confidence before it allows promotion. Our initial theory assumed that sigma just needed to be small enough to allow promotion, but it's been confirmed that sigma never gets this small. Instead, it does this by a moving average. Here's an example:
MMR is erratic. A moving average seeks to smooth out the rapidly changing data points over time by evaluating your progress over X number of games. As we previously estimated, the system doesn't use your full match history because if it did, you would eventually get stuck in a league. Once your moving average crosses a particular league threshold, that's when you'll get promoted.
Players like CauthonLuck and Ret who had obscene win ratios had their MMR data points skyrocket. However, the moving average lags behind. In the cases of those players, it will take much longer for the moving average to reach that required threshold. This is why players like IdrA who were affected by this problem have decided to intentionally throw games in order to get promoted, because it allows the moving average to catch up more quickly.
Possibly related is players that aren't getting promoted or demoted properly despite a high likelihood that their moving average would have crossed the confidence threshold. Blizzard has said that this is indeed a bug and will be fixed by moving the affected players to new divisions.
Displayed Rating
Ok, how does all of this tie into displayed rating and the whole “favored” deal? If you remember back to WoW, ratings changed based on a direct comparison of your displayed rating to the other team’s MMR. So if your current rating was 500 and you were playing people with MMRs of 2000, your rating would jump significantly after every win because of the wide disparity. Now, we’ve identified that on the loading screen quite often players are seeing the other person as favored and the opponent (who is nominally “favored”) also sees his opponent as favored! How can this be? The theory put forth here is the system is again comparing your displayed rating to your opponent’s hidden MMR.
The reason for this is so that the system brings you toward your MMR more quickly. kzn explains:
On August 08 2010 14:30 kzn wrote: How it works was like this: Say you've got a MMR of 2500, and you start a new team. It starts at 0 rating, but the matchmaking system will match you with other players of MMR 2500. If you lose a game, your team rating would not change at all. If you won, it would increase by 47 (a hard cap that was in place at least when I played). This was not explained as arising due to an interaction between the team rating and the opponent's MMR, however - it was explained as the system trying to get your team's rating as close as possible to your team's MMR rapidly.
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens? - His MMR will increase - My MMR will decrease - Both of our sigmas will decrease - His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500 - My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally to 2450 vs 2600.
Conclusions
SC2 uses a Bayesian inference system for its skill determination which forms an MMR and a confidence value for each player. These form a Gaussian distribution useful in determining win probability. Promotions/demotions occur when a player exceeds/drops below a threshold with sufficient confidence. Displayed rating changes according to a combination of the rating itself combined with the hidden MMR and league thresholds.
More clarifications from Vanick:
On August 08 2010 11:33 vanick wrote: To be clear, the player's skill is never pinpointed. The sigma is never 0. All players vary in their performance from game to game and over time as their skill increases (or decreases!).
I left a point out in my writeup that I probably should have included. TrueSkill, and likely SC2's ladder, have a factor based off the time since your last game that increases the player's uncertainty level (sigma) by an amount related to that. Even if you're playing games back to back this factor will have a minimum value that will still increase sigma. This allows the system to adapt to a player whose skill increases over time.
Questions
Some of these have answers. Some are open questions. You can add on; I will answer them as best I can.
Q: So how do bonus points affect the display rating changes? If the displayed rating change is based upon the comparison of the opponent's MMR with the player's displayed rating + the player's league cutoff, then wouldn't bonus points inflate the displayed rating and cause problems? A: I'm not sure how they account for this. One possibility is they keep track of bonus points that make up your displayed rating, and ignore them when performing the calculation in the back-end.
Excal: It seems more likely that the bonus pool is only used to increase the displayed rating for division ranking purposes and ignored in back-end calculation because the bonus pool increases at the same rate for all players. This introduces a constant that is easily discarded when assessing actual skill within the system. Furthermore, if bonus points were considered in the process of point calculation, it would present an unfair advantage for players who have not yet used up their bonus pool (because their rating is therefore inflated giving them more to lose).
Q: Would it take longer to get promoted if you've played lots of games? Assuming someone played a large amount of games (say 100 with a 50% win/loss ratio). If he were to start winning 70% of his games, would it be harder for him to get promoted than someone with similar percentages but fewer games played? A: It would take longer, yes. The moving average trails behind sharp increases in skill.
Antiquated or Incorrect Information for Archival Purposes + Show Spoiler +
[u]Promotion[u]
At this point we have established how matchmaking works, and how the skill belief system is updated (through MMR and sigma). How does promotion work? Our current theory is that it uses a checkpoint system, in which after a certain number of games the player’s MMR is checked and if it is above or below a certain threshold it will promote/demote that player. That may or may not exist still, based upon evidence people have provided in the release version of SC2. In any case, this section will attempt to describe the thresholds further.
In prior descriptions, it has been said that in order to be promoted, your MMR must be above the threshold for that league. That is still true. What we propose here is that your MMR must be above that threshold with 99% confidence. What does this mean? To determine this with 99% confidence, your MMR – (3 standard deviations (sigma)) must be above the threshold. For example:
Your MMR: 2500 Your sigma: 100 Diamond Threshold: 2300
Since (2500 – 3*100) = 2200, this value is less than the threshold even though your MMR is higher. In order to be promoted you would need to increase your MMR, decrease your sigma, or both. This notably creates the situation where you can be highly ranked in Platinum, but still be better than players in Diamond. In addition, if you are a borderline player who is promoted to Diamond, you would need to lose a lot of MMR to be demoted again. That is, if your MMR is 2450 and your sigma is 50 and you are in Diamond, you would need to drop to an MMR of 2150 (assuming sigma remains constant) before demotion would occur.
This above description is more theoretical than the matchmaking description, for which we have more direct evidence. However, this does go a certain length to describing some of the behavior seen with promotion/demotion, and given such a system the checkpoint review system as originally conceived may be incorrect.
Edited as the system has changed since this post Q: So what’s the deal with people stuck in Platinum who can’t get promoted to Diamond despite clearly belonging there? A: Short answer? It’s a bug. Longer answer: a lot of people have suggested that the system requires you to lose in order to build its confidence factor. This is almost certainly incorrect. The system in theory learns enough about you from your wins to promote you. Intuitively, if your record is 60-5 against diamond players, you ought to be in Diamond. The TrueSkill system can determine this, and I would be dollars to donuts that Blizzard’s system can too, as designed anyways. Implementation may have introduced bugs that certain players hit under certain conditions. We don’t have enough evidence to flat out state that the system requires you to lose. It may be a workaround to the bug, however.
One possible explanation is that the moving average lags so far behind that more games are required in order to cross the promotion threshold. It's also possible that the bug prevents the moving average from changing.
EDIT 10/25/2010: Made crucial updates to several sections in light of new information acquired from Blizzcon 2010.
EDIT 8/11/2010: Made an important clarification to the Matchmaking section.
EDIT 8/10/2010: Added a third question related to promotion opportunity.
EDIT 8/9/2010: Added extra information to the first question about the circumstances under which sigma may increase or decrease. Also removed a misleading sentence regarding ideal matches.
EDIT 8/7//2010: Modified the second question to make it less vague, and removed incorrect information from the Displayed Ratings section.
_________ Thanks to myself for proofreading, editing, and analytical input (hehhh self-credit).
Just to be clear since I am afraid I was inconsistent in my naming: the "confidence" value is referring to the uncertainty factor (sigma). It is often easier to think of it in terms of confidence, even though what is stored and used for the distribution is the uncertainty. High confidence merely refers to low uncertainty while low confidence would refer to high uncertainty.
Q: So what’s the deal with people stuck in Platinum who can’t get promoted to Diamond despite clearly belonging there? A: Short answer? It’s a bug. Longer answer: a lot of people have suggested that the system requires you to lose in order to build its confidence factor. This is almost certainly incorrect. The system in theory learns enough about you from your wins to promote you. Intuitively, if your record is 60-5 against diamond players, you ought to be in Diamond. The TrueSkill system can determine this, and I would be dollars to donuts that Blizzard’s system can too, as designed anyways. Implementation may have introduced bugs that certain players hit under certain conditions. We don’t have enough evidence to flat out state that the system requires you to lose. It may be a workaround to the bug, however.
_________ Thanks to myself for proofreading, editing, and analytical input (hehhh self-credit).
This happened in Halo 3 as well ( it uses a modified Trueskill system fit for 4v4 matches so not entirely the same.), you'd have to look up which Bungie weekly update it is discussed in. In general though it was a case of a few friends playing together and getting stuck due to the certainty factor i believe, they ended up in level 26 or so (ouf of 50) where they proceeded to go 46-0 in games or something retarded like that without ranking up.
Edit: very well done btw, i was reading a lot about trueskill when halo 3 came around and the ranking system was a hot topic. It really hit some points home for me, especially the 3d distribution is very enlightening.
On August 08 2010 10:07 jamesr12 wrote: Very nice right up, well done. Math major?
Computer science.
And, gerundium, it's interesting to hear that about Halo 3. From my understanding even though the system receives less information from people (or groups of people) never losing it does get enough information to in theory promote them. TrueSkill has its own functionality that is supposed to allow it to rank individuals who play in random teams (as does SC2, see 2v2 random etc.). Perhaps there was a bug there?
More interesting is what happens to the sigmas. If the match finished as expected with the MMR favored player winning (and remember, the loading screen “favored” display is NOT this) then both players' sigmas will decrease. That is, the system gains confidence in the ratings it has assigned to the players. If the match finishes in an upset then the sigmas for both players will increase as the system thinks it may have an incorrect rating assigned to both. The change in sigma scales based upon the difference in MMR. That is, losing to someone close to your own rank will not change your sigma too much (though it will over the course of several games).
I think there is a huge problem with this system. The system is basically setting every player as an average joe and have it continually play games and use its MMR&Sigma to determine its skill level.
However, it has already been said that in order for this to work, it requires the player to play a course a game. The system can assign a player as a GOLD level and then when it looses to a silver, the uncertainty increases. This will have to continue to happen until a consistency is reached. The problem lies in the fact that player GETS BETTER and over the course of the games necessary to pinpoint the players skill level. By the time the system can safely assume a players skill level, the player skill level has already changed.
Meaning the first 3 games used to pinpoint a players skill level is now negligible because that player is not longer the same player as he was 3 games ago.
Now all this is assuming the player is a fast learner. However the rate @ which players learn is completely random, so i wonder how they can utilize math to incorporate this into their system (which imo is impossible).
For this example I used 3 games but I am sure for the system to reach any sort of consistency it may take at least 20 games or so (which is possibly why most people get into diamond league in 20 games or so). And I don't know about you guys but my 21st game and my 3rd game of Sc2 are in fact different. After each game a person gets better, be it big or small. The difference is enough to change the W/L expected (considering the system puts you at some sort of equal setting)
To be clear, the player's skill is never pinpointed. The sigma is never 0. All players vary in their performance from game to game and over time as their skill increases (or decreases!).
I left a point out in my writeup that I probably should have included. TrueSkill, and likely SC2's ladder, have a factor based off the time since your last game that increases the player's uncertainty level (sigma) by an amount related to that. Even if you're playing games back to back this factor will have a minimum value that will still increase sigma. This allows the system to adapt to a player whose skill increases over time.
I left a point out in my writeup that I probably should have included. TrueSkill, and likely SC2's ladder, have a factor based off the time since your last game that increases the player's uncertainty level (sigma) by an amount related to that.
yes but thats also very icky because we have no idea how accurate that is and how that differentiates from person to person. I am assuming it is a constant which would assume all players learn @ the same rate which they don't. Sure you can get a general consensus that in 1 week time a player should be X better and therefor we would adjust our system in accordance with X by mutliplying certain varaibles by Y or w/e but it still won't be accurate or anything near accurate.
Even if you're playing games back to back this factor will have a minimum value that will still increase sigma. This allows the system to adapt to a player whose skill increases over time.
Again I dont quite understand how this can be accurate though, this minimum value? Can you explain a lil more.
I left a point out in my writeup that I probably should have included. TrueSkill, and likely SC2's ladder, have a factor based off the time since your last game that increases the player's uncertainty level (sigma) by an amount related to that.
yes but thats also very icky because we have no idea how accurate that is and how that differentiates from person to person. I am assuming it is a constant which would assume all players learn @ the same rate which they don't. Sure you can get a general consensus that in 1 week time a player should be X better and therefor we would adjust our system in accordance with X by mutliplying certain varaibles by Y or w/e but it still won't be accurate or anything near accurate.
Even if you're playing games back to back this factor will have a minimum value that will still increase sigma. This allows the system to adapt to a player whose skill increases over time.
Again I dont quite understand how this can be accurate though, this minimum value? Can you explain a lil more.
The way it determines your skill level (MMR) is to move your MMR up and down until it finds a point where you win and lose 50% of your games.
On August 08 2010 12:08 catamorphist wrote: How did you infer all this? Do you have a lot of mined data sitting around about wins and losses?
Good question. I think obviously is the answer but Im curious too.
No mined data. We don't have that for SC2. It is based on what we know about WoW Arena, what we know about SC2 ladder, and how Bayesian inference ranking systems work. This isn't necessarily how it works, though obviously I believe this is close to the truth. I'm sure there are incorrect parts not only of this post, but of the original ladder analysis. This is a theory that tries to describe the behavior we're observing, since the actual ladder mechanics occur within a black box.
virgo: paralleluniverse is right. Your MMR is an approximation of your true skill, and it moves according to your performance by winning/losing. How much it moves depends on many factors, as detailed in the original post.
On August 08 2010 08:59 Excalibur_Z wrote: Q: So how do bonus points affect all this? Wouldn’t that mess up the rating gains over time? A: Yes, they would. I am not sure how they correct for this. It’s possible that they inflate MMR over time by an equal amount so things still work. It’s possible they correct for the bonus pool instead. I don’t know.
I don't think the displayed rating value has any bearing on match making at all. If it did then the bonus pool would make no sense. I'm a freshly placed platinum player and I was winning 42 points on a win (due to my bonus pool) and losing 2 or 4 for losses. Assuming I was going 50/50 for my first few games (I wasn't but that isn't the point), it is an impossibility for my MMR to constantly be sky rocketing after each win and not changing after each loss; otherwise the system would not be an accurate reflection of my performance. No, I believe that the displayed points are purely fluff which is inflated by the bonus pool to make everyone feel as if they are constantly progressing when playing multiplayer. It is used to reflect rank on the ladder, again purely for the sense of progression, but does not and cannot reflect skill.
Further consider that the displayed rating cannot be compared across divisions as stated by Blizzard; therefore it makes no sense to use displayed rating to influence the "opponent is favored" display because your opponents can come from divisions other than your own.
Okay so heres what Im stuck on 1.) You play a game 2.) The system assigns you a random MMR with a 50% uncertainty factor 3.) You play more games 4.) The system moves your uncertainty factor up or down depending on how correct the system was in guessing your MMR (if you win vs the ones you should win, the ufactor goes down and if you loose vs the one you should win, the ufactor goes up)
If that is rigth so far, I am asking on the fact that between 2-4, you are required to play more games. "4.)" is based upon the games from "3.)" and the analyzation from "2.)". If you have improved since "2.)" then how would that be accurate?
Vanick tells me there is this
Even if you're playing games back to back this factor will have a minimum value that will still increase sigma. This allows the system to adapt to a player whose skill increases over time
This factor will have a minimum value that wil still increase sigma? I dont quite understand that? What is this minimum value and how do they come about it?
hopefully you can help me with this as you know so much about the ladder (maybe its a glitch?), but i went 5-0 in placements then im 3-3 in platinum. my question is, even though ive been placed in a league i havent been giving a rank and judging by my score (wins - losses in points) i should be somewhere in the middle of the pack? my score screen shows me as undefined, or after a matched ranked something like 327. any ideas??
On August 08 2010 08:59 Excalibur_Z wrote: Q: So how do bonus points affect all this? Wouldn’t that mess up the rating gains over time? A: Yes, they would. I am not sure how they correct for this. It’s possible that they inflate MMR over time by an equal amount so things still work. It’s possible they correct for the bonus pool instead. I don’t know.
I don't think the displayed rating value has any bearing on match making at all. If it did then the bonus pool would make no sense. I'm a freshly placed platinum player and I was winning 42 points on a win (due to my bonus pool) and losing 2 or 4 for losses. Assuming I was going 50/50 for my first few games (I wasn't but that isn't the point), it is an impossibility for my MMR to constantly be sky rocketing after each win and not changing after each loss; otherwise the system would not be an accurate reflection of my performance. No, I believe that the displayed points are purely fluff which is inflated by the bonus pool to make everyone feel as if they are constantly progressing when playing multiplayer. It is used to reflect rank on the ladder, again purely for the sense of progression, but does not and cannot reflect skill.
Further consider that the displayed rating cannot be compared across divisions as stated by Blizzard; therefore it makes no sense to use displayed rating to influence the "opponent is favored" display because your opponents can come from divisions other than your own.
Excal thought this Q/A was worded confusingly and I said "nooo that's impossible" but it is true
I agree with you that displayed rating value has no bearing. The question here arises from my theory on how display rating change is calculated, since it seems that the change in displayed rating comes from the comparison of that rating to the opponent's MMR. I was merely illustrating an unanswered question regarding that. Change in MMR is always purely a result of the players' MMRs and sigmas. I've asked Excal to help clarify this segment.
virgo: Please read through the TrueSkill primer and other pages on the site if you're having trouble understanding the post. A lot of the concepts are better explained on the Microsoft Research site.
On August 08 2010 12:46 virgozero wrote: Okay so heres what Im stuck on 1.) You play a game 2.) The system assigns you a random MMR with a 50% uncertainty factor 3.) You play more games 4.) The system moves your uncertainty factor up or down depending on how correct the system was in guessing your MMR (if you win vs the ones you should win, the ufactor goes down and if you loose vs the one you should win, the ufactor goes up)
If that is rigth so far, I am asking on the fact that between 2-4, you are required to play more games. "4.)" is based upon the games from "3.)" and the analyzation from "2.)". If you have improved since "2.)" then how would that be accurate?
Even if you're playing games back to back this factor will have a minimum value that will still increase sigma. This allows the system to adapt to a player whose skill increases over time
This factor will have a minimum value that wil still increase sigma? I dont quite understand that? What is this minimum value and how do they come about it?
You don't start with a random MMR, you start with an average MMR, i.e. a new player is assume to be better than 50% of players, and worse than 50% of players.
This MMR and sigma moves up and down depending on your performance in games.
You seem to think that the system guesses a random MMR and tests whether its guess is correct. That's not how it works.
The link above to a thread on the WoW forums explains this better.
Thanks for the summary of this type of matchmaking.
It would be really nice if we had a way to see our MMR & σ, rather than just a league and "rating" which don't mean much.
I'm interested in how the bonus pool plays into this. Do you think eventually the available pool points will do down as a player's rating value approaches their MMR? Or will it stay entirely separate from the MMR rating? I don't know how this worked in WoW Arena, or if they will use the system the same way.
On August 08 2010 12:46 virgozero wrote: Okay so heres what Im stuck on 1.) You play a game 2.) The system assigns you a random MMR with a 50% uncertainty factor 3.) You play more games 4.) The system moves your uncertainty factor up or down depending on how correct the system was in guessing your MMR (if you win vs the ones you should win, the ufactor goes down and if you loose vs the one you should win, the ufactor goes up)
If that is rigth so far, I am asking on the fact that between 2-4, you are required to play more games. "4.)" is based upon the games from "3.)" and the analyzation from "2.)". If you have improved since "2.)" then how would that be accurate?
Vanick tells me there is this
Even if you're playing games back to back this factor will have a minimum value that will still increase sigma. This allows the system to adapt to a player whose skill increases over time
This factor will have a minimum value that wil still increase sigma? I dont quite understand that? What is this minimum value and how do they come about it?
You don't start with a random MMR, you start with an average MMR, i.e. a new player is assume to be better than 50% of players, and worse than 50% of players.
This MMR and sigma moves up and down depending on your performance in games.
You seem to think that the system guesses a random MMR and tests whether its guess is correct. That's not how it works.
The link above to a thread on the WoW forums explains this better.
Alright thanks for that clarification. But the problem I am proposing remains there, the system will keep on adjusting your mmr and sigma but it will never reach a point that is accurate or anywhere near accurate of you.
Is anyone understanding what I am saying or am I stuck in my own world lol.
On August 08 2010 13:09 potatoedoughnut wrote: Thanks for the summary of this type of matchmaking.
It would be really nice if we had a way to see our MMR & σ, rather than just a league and "rating" which don't mean much.
I'm interested in how the bonus pool plays into this. Do you think eventually the available pool points will do down as a player's rating value approaches their MMR? Or will it stay entirely separate from the MMR rating? I don't know how this worked in WoW Arena, or if they will use the system the same way.
I personally think the bonus pool will inflate everyone's points equally and indefinitely, at least until the ladder resets.
On August 08 2010 12:46 virgozero wrote: Okay so heres what Im stuck on 1.) You play a game 2.) The system assigns you a random MMR with a 50% uncertainty factor 3.) You play more games 4.) The system moves your uncertainty factor up or down depending on how correct the system was in guessing your MMR (if you win vs the ones you should win, the ufactor goes down and if you loose vs the one you should win, the ufactor goes up)
If that is rigth so far, I am asking on the fact that between 2-4, you are required to play more games. "4.)" is based upon the games from "3.)" and the analyzation from "2.)". If you have improved since "2.)" then how would that be accurate?
Vanick tells me there is this
Even if you're playing games back to back this factor will have a minimum value that will still increase sigma. This allows the system to adapt to a player whose skill increases over time
This factor will have a minimum value that wil still increase sigma? I dont quite understand that? What is this minimum value and how do they come about it?
You don't start with a random MMR, you start with an average MMR, i.e. a new player is assume to be better than 50% of players, and worse than 50% of players.
This MMR and sigma moves up and down depending on your performance in games.
You seem to think that the system guesses a random MMR and tests whether its guess is correct. That's not how it works.
The link above to a thread on the WoW forums explains this better.
Alright thanks for that clarification. But the problem I am proposing remains there, the system will keep on adjusting your mmr and sigma but it will never reach a point that is accurate or anywhere near accurate of you.
Is anyone understanding what I am saying or am I stuck in my own world lol.
The MMR will get more accurate as sigma, which is the uncertainty, decreases.
As sigma decreases your MMR is adjusted less after each game, because the system is more certain of your skill.
The WoW forum link above has an explicit numerical example of this.
I love how even the feedback is so above me Im looking at cherubs. Thats a quality OP right there. Fix that stuff for the cherubs OP! or not...I wouldn't know lol
On August 08 2010 08:59 Excalibur_Z wrote: Q: So how do bonus points affect all this? Wouldn’t that mess up the rating gains over time? A: Yes, they would. I am not sure how they correct for this. It’s possible that they inflate MMR over time by an equal amount so things still work. It’s possible they correct for the bonus pool instead. I don’t know.
I don't think the displayed rating value has any bearing on match making at all. If it did then the bonus pool would make no sense. I'm a freshly placed platinum player and I was winning 42 points on a win (due to my bonus pool) and losing 2 or 4 for losses. Assuming I was going 50/50 for my first few games (I wasn't but that isn't the point), it is an impossibility for my MMR to constantly be sky rocketing after each win and not changing after each loss; otherwise the system would not be an accurate reflection of my performance. No, I believe that the displayed points are purely fluff which is inflated by the bonus pool to make everyone feel as if they are constantly progressing when playing multiplayer. It is used to reflect rank on the ladder, again purely for the sense of progression, but does not and cannot reflect skill.
Further consider that the displayed rating cannot be compared across divisions as stated by Blizzard; therefore it makes no sense to use displayed rating to influence the "opponent is favored" display because your opponents can come from divisions other than your own.
I edited the second question to make it easier to understand:
Q: So how do bonus points affect the display rating changes? If the displayed rating change is based upon the comparison of the opponent's MMR with the player's displayed rating + the player's league cutoff, then wouldn't bonus points inflate the displayed rating and cause problems? A: I'm not sure how they account for this. One possibility is they keep track of bonus points that make up your displayed rating, and ignore them when performing the calculation in the back-end.
Excal: It seems more likely that the bonus pool is only used to increase the displayed rating for division ranking purposes and ignored in back-end calculation because the bonus pool increases at the same rate for all players. This introduces a constant that is easily discarded when assessing actual skill within the system. Furthermore, if bonus points were considered in the process of point calculation, it would present an unfair advantage for players who have not yet used up their bonus pool (because their rating is therefore inflated giving them more to lose).
On August 08 2010 08:59 Excalibur_Z wrote: Note that this figure is taken from a TrueSkill presentation, and is copyright Microsoft. TrueSkill incorporates the possibility of a draw. More intuitively, it can be thought of as the “matchmaking sweet spot”, and something similar is likely used by SC2’s ladder to provide the system some wiggle room in matchmaking. When the system says “Expanding Search…” it is probably expanding this green stripe.
The bolded part doesn't really make sense, with reference to the graph - the green area is a function of the two MMR/sigma values, and cannot be "expanded" by the system without modifying those values (which it is not, obviously, doing).
However, in functional terms the description is correct. What the system is trying to do, initially, is to find a player whose MMR/sigma meshes with yours to make the likelihood of each player winning rather equal. In terms of the graph shown above what I quoted, the system is trying to pick a player with whom you will form a graph that is roughly (for instance) 45% red, 10% green, and 45% blue (although given how draws are impossible, more like 50/50 red/blue).
Obviously, this is impossible if certain players are not in the matchmaking queue. So, presumably, the system has some kind of threshold in which a game is "acceptable" as long as the balance is (again, an arbitrary pick) 40/60 (or 60/40).
In the interests of speed, however, the system will expand this threshold so that people can at least find a game in a reasonable timeframe - so, as the system expands a search, the likelihood of a wildly unbalanced game increases.
Totally awesome post, excal. Really well explained. I do have one question though; do you know precisely how the MMR change is calculated after each match? In case I'm not being clear enough, what numbers does the system use to determine the increase or decrease of a player's MMR after each game? I scanned that WOW forum thread and couldn't see an obvious answer and I'm too rusty at maths(not to mention lazy) to figure it out for myself. Perhaps knowing exactly how this number changes over time might shed some light on the eternal platinum bug.
On August 08 2010 14:12 brad drac wrote: Totally awesome post, excal. Really well explained. I do have one question though; do you know precisely how the MMR change is calculated after each match? In case I'm not being clear enough, what numbers does the system use to determine the increase or decrease of a player's MMR after each game? I scanned that WOW forum thread and couldn't see an obvious answer and I'm too rusty at maths(not to mention lazy) to figure it out for myself. Perhaps knowing exactly how this number changes over time might shed some light on the eternal platinum bug.
That would be impossible to know because MMR is hidden so we can't use regression to find a formula, nor will Blizzard tell us the formula.
It's probably like the formulas used for xbox true skill with modification for league and bonus pool.
On August 08 2010 14:12 brad drac wrote: Totally awesome post, excal. Really well explained. I do have one question though; do you know precisely how the MMR change is calculated after each match? In case I'm not being clear enough, what numbers does the system use to determine the increase or decrease of a player's MMR after each game? I scanned that WOW forum thread and couldn't see an obvious answer and I'm too rusty at maths(not to mention lazy) to figure it out for myself. Perhaps knowing exactly how this number changes over time might shed some light on the eternal platinum bug.
I'm fairly certain the formula for MMR change has never been determined or released. The old arena system used a zero-sum system which made it quite easy to determine the pre-match ratings from the rating change post-match, but for some reason that now escapes me Blizzard decided to keep the formula for the new system hidden.
One possible reason for the eternal platinum thing is that TrueSkill-esque systems (at least in some implementations) will severely overweight early performances. For instance, if you played your first 50 games against players who had lower MMRs than you, (at least by my understanding) your MMR would never actually change - only your sigma value would change. This sigma value change would make it much harder for the system to later increase your MMR rapidly in response to wins against players rated higher than you.
I know in Global Agenda they used a TrueSkill based system to determine "combat ratings" for players, and for the most part people had a tremendously difficult time getting the highest rating on their first character because they'd "ruined" their hidden rating when they were learning the game.
kzn - you're right, that is inaccurate. It can be useful to think of how the system is expanding the search space by visualizing it with the green stripe starting at x=y (plus the draw probability) and slowly widening outwards which would allow for worse and worse matches. I must have got some wires crossed while writing.
edit: TrueSkill has some drawbacks for sure. Coping with rapid skill change in a player is a major one. I do think Blizzard has incorporated refinements to their system.
Also, since I'm something of a WoW Arena expert, I'll try to add to this section.
Displayed Rating
Ok, how does all of this tie into displayed rating and the whole “favored” deal? If you remember back to WoW, ratings changed based on a direct comparison of your displayed rating to the other team’s MMR. So if your current rating was 500 and you were playing people with MMRs of 2000, your rating would jump significantly after every win because of the wide disparity. Now, we’ve identified that on the loading screen quite often players are seeing the other person as favored and the opponent (who is nominally “favored”) also sees his opponent as favored! How can this be? The theory put forth here is the system is again comparing your displayed rating to your opponent’s hidden MMR.
This is not, I believe, strictly correct as a description of how WoW's system worked. As it was explained when MMR was first introduced, there was actually no interaction between your team's rating and the opposing team's MMR.
How it works was like this: Say you've got a MMR of 2500, and you start a new team. It starts at 0 rating, but the matchmaking system will match you with other players of MMR 2500. If you lose a game, your team rating would not change at all. If you won, it would increase by 47 (a hard cap that was in place at least when I played). This was not explained as arising due to an interaction between the team rating and the opponent's MMR, however - it was explained as the system trying to get your team's rating as close as possible to your team's MMR rapidly. This is perhaps accomplished by a system such as that in the quote, but I'm not sure thats actually whats going on.
However, in SC2 we do not see the same sort of drastic jumps every time we beat a “favored” opponent. If we’re playing diamond-level players then their MMR must be way higher than our displayed rating, right? Or more to the point, if you were to lose and compare your small displayed rating to your opponent’s MMR, you would lose almost no points and clearly that is not how SC2 behaves.
In my experience, limited as it is, that is actually how SC2 has behaved. WoW's system was characterized by hard caps on the change that could be made to your displayed rating from any one match (-47 to +47), and this has matched my experience in SC2 (although its closer to the high 20s, I think). The matchmaking system also makes it extremely unlikely that you will be placed in a match that could possibly result in a significant rating loss (the only way you could manage it in WoW was to swap out a player with a high MMR for one with an extremely low one, thereby bringing your team's average MMR much lower than the displayed rating. In such a case, you would see minor gains for wins and extreme losses for defeats).
[edit] The eternal platinum phenomenon actually reminds me of how the arena rating system behaved when you were at the very top end of the displayed rating scales. I played with some of the first players to ever legitimately hit a displayed rating of 3000, and their runup to that rating was dominated by hugely punishing losses, such that they had to maintain a win ratio in excess of 80% to actually make it to 3000 (which was a hard cap at the time).
kzn: Bliz probably just have the formula patented(retardedly).
I see your point with the bug. The more games you play, the lower your sigma gets, the more likely you are to be matched with someone with an extremely similar MMR and thus your MMR presumably changes by a much smaller amount each match. Some numbers on that MMR change calculation sure would be nice. Aren't there any math buffs here who would be able to roughly extrapolate from the numbers in this thread?
On August 08 2010 14:32 brad drac wrote: kzn: Bliz probably just have the formula patented(retardedly).
I see your point with the bug. The more games you play, the lower your sigma gets, the more likely you are to be matched with someone with an extremely similar MMR and thus your MMR presumably changes by a much smaller amount each match. Some numbers on that MMR change calculation sure would be nice. Aren't there any math buffs here who would be able to roughly extrapolate from the numbers in this thread?
There are no numbers to extrapolate from. MMR is hidden.
The link he gives has MMR numbers for WoW (and indeed personal MMR is not hidden in WoW). I don't think the extrapolation is possible, however, as the link gives us no numbers for sigma and I believe I am correct in thinking that there is an infinite number of sigma/function combinations that could satisfy the given MMR numbers.
[edit] Not to mention there's no guarantee that the MMR operates on the same scale in SC2 as it does in WoW. The displayed ratings certainly don't seem to.
Ok, how does all of this tie into displayed rating and the whole “favored” deal? If you remember back to WoW, ratings changed based on a direct comparison of your displayed rating to the other team’s MMR. So if your current rating was 500 and you were playing people with MMRs of 2000, your rating would jump significantly after every win because of the wide disparity. Now, we’ve identified that on the loading screen quite often players are seeing the other person as favored and the opponent (who is nominally “favored”) also sees his opponent as favored! How can this be? The theory put forth here is the system is again comparing your displayed rating to your opponent’s hidden MMR.
This is not, I believe, strictly correct as a description of how WoW's system worked. As it was explained when MMR was first introduced, there was actually no interaction between your team's rating and the opposing team's MMR.
How it works was like this: Say you've got a MMR of 2500, and you start a new team. It starts at 0 rating, but the matchmaking system will match you with other players of MMR 2500. If you lose a game, your team rating would not change at all. If you won, it would increase by 47 (a hard cap that was in place at least when I played). This was not explained as arising due to an interaction between the team rating and the opponent's MMR, however - it was explained as the system trying to get your team's rating as close as possible to your team's MMR rapidly. This is perhaps accomplished by a system such as that in the quote, but I'm not sure thats actually whats going on.
However, in SC2 we do not see the same sort of drastic jumps every time we beat a “favored” opponent. If we’re playing diamond-level players then their MMR must be way higher than our displayed rating, right? Or more to the point, if you were to lose and compare your small displayed rating to your opponent’s MMR, you would lose almost no points and clearly that is not how SC2 behaves.
In my experience, limited as it is, that is actually how SC2 has behaved. WoW's system was characterized by hard caps on the change that could be made to your displayed rating from any one match (-47 to +47), and this has matched my experience in SC2 (although its closer to the high 20s, I think). The matchmaking system also makes it extremely unlikely that you will be placed in a match that could possibly result in a significant rating loss (the only way you could manage it in WoW was to swap out a player with a high MMR for one with an extremely low one, thereby bringing your team's average MMR much lower than the displayed rating. In such a case, you would see minor gains for wins and extreme losses for defeats).
[edit] The eternal platinum phenomenon actually reminds me of how the arena rating system behaved when you were at the very top end of the displayed rating scales. I played with some of the first players to ever legitimately hit a displayed rating of 3000, and their runup to that rating was dominated by hugely punishing losses, such that they had to maintain a win ratio in excess of 80% to actually make it to 3000 (which was a hard cap at the time).
kzn you're exactly right. I think the passage you quoted is something that I missed in my initial proofread, because the way the system operates does mirror the WoW system. I'll make the appropriate edits.
kzn, regarding the interaction of the team's rating and opponent's MMR I was under the impression that was how it worked. In any case, what I mean by the drastic rating changes in SC2 is that it is indeed only +22ish points not counting bonus pool on beating a "favored" team. However, when you were at very low WoW arena ratings playing people 2k+ you would lose 0 points on a loss. In SC2 you will lose display rating on a loss even if the other team was favored. Does that make sense?
On August 08 2010 14:47 vanick wrote: kzn, regarding the interaction of the team's rating and opponent's MMR I was under the impression that was how it worked. In any case, what I mean by the drastic rating changes in SC2 is that it is indeed only +22ish points not counting bonus pool on beating a "favored" team. However, when you were at very low WoW arena ratings playing people 2k+ you would lose 0 points on a loss. In SC2 you will lose display rating on a loss even if the other team was favored. Does that make sense?
I'm not professing to understand how SC2 is determining when to display "favored" notices - if matches are indeed starting with both players being told they're favored, I can't think of anything from the WoW system that would explain that (not least because there was no such indicator in WoW). If it really is doing it, I think the best explanation is that its just fucked, and we shouldn't be reading anything into it.
I haven't played many games past placement in SC2 yet, so my experience is quite severely limited, but I certainly see indications that it is the same as WoW's system in how it determines displayed rating changes.
One of the major differences between SC2 and WoW's arena system is that we're only shortly out of release, and WoW's MMR system actually never had a "release" time on the live realms (Tournament realms, however, are a different story. More on this later). Because of this, every single player was basically assigned a default MMR.
Now, to digress to Tournament Realms. These essentially create a "release" situation in WoW's arena system, because the realm is entirely populated by new players with no history whatsoever. Thus, all players start at a default MMR (which I believe was 0, although this is getting into 2 years ago, so I'm not entirely sure). Thus, obviously, in the very first game that was played on a Tournament Realm, you had two players (teams, really, but its irrelevant) with an MMR of 0 and a displayed rating of 0. The team which won gained identical amounts on both scales, and the team which lost lost nothing (because it was at 0). This resulted in a player's MMR being identical to his team's rating for as long as that player played 100% of the games.
In these early stages, losses and wins were pretty much equal in value. The system acted approximately like the old zero-sum system, except that, since it started at 0, some inflation was guaranteed from the outset. However, as teams started to diverge and the matchmaking started to get less equal, the system started to operate more as was familiar from live realms.
Coming back to SC2, I suspect a lot of the "odd" behavior we're seeing is odd only because we are comparing a release-environment behavior with the behavior of a system that has been running for 2+ years now (I think).
[edit] Also, the league system in SC2 has no analog in WoW. The threshold values being added to displayed rating makes some sense, but strictly that would suggest that negative displayed ratings would be possible in all leagues above Bronze.
One thing I do wonder about with regards to the league system is whether or not players experience jumps or falls in the quality of their opposition after a promotion or demotion, respectively. If the quality of opposition is continuous, we could conclude that MMR is operating completely separately from the league system and displayed ratings - but if it experienced discontinuities, that would suggest that MMR itself was interacting with the league system (which I doubt, but might explain some of the weirdness).
No, I think you are. Call me simple but your the only one doing this. Nice massive paragraph info to basically say "Im right until Im not and if Im not I dont have enough info"
There's basically no way to explain how the favored notices are given out, unless we guess that it has to do with displayed rating and we're correct - which is doubtful, just based on what that kind of notice is supposed to do.
If you have a point, you're welcome to make it, but if you're just going to bitch do it in a thread thats less worth reading.
Being favored is almost certainly based on comparing your displayed rating to your opponents MMR.
Yes, this is meaningless and deceptive, and doesn't actually tell us who is really favored to win.
Yes, it *should* compare your MMR to your opponents MMR.
And no, there is no discontinuity in skill level, as you move up leagues. Matchmaking is great and is purely based on MMR, and is separate from the disastrous ranking system.
On August 08 2010 15:12 paralleluniverse wrote: Being favored is almost certainly based on comparing your displayed rating to your opponents MMR.
Yes, this is meaningless and deceptive, and doesn't actually tell us who is really favored to win.
Yes, it *should* compare your MMR to your opponents MMR.
And no, there is no discontinuity in skill level, as you move up leagues. Matchmaking is great and is purely based on MMR, and is separate from the disastrous ranking system.
Do we have evidence for this? Isn't it possible that a player is displayed favoured if his MMR is greater than your own minus a factor based on sigma? Or something along those lines. I don't really see how you could directly compare displayed rating to MMR considering displayed ratings are division independent, not to mention league independent, while MMR is an absolute measure of a player's success in the system.
kzn, about starting MMR, I'm almost completely positive that everyone starts at 1500. If you remember, when the system was first introduced, everyone's rating (and also their MMR) started at 1500. After the first few seasons, they changed it so that new teams and players start at 0 rating but they still start at 1500 MMR. The reason for the change was that under the old system, it was common for people to create new teams whenever the old one fell below 1500, thereby cluttering up the 1500 range which was supposed to be the average value on the scale (from 0-3000). Under the new system, teams still rapidly gained rating even if they had never played a single game in their history because their MMR was so far from their new rating of 0. The average was still 1500 under the new system, but the key difference was that you had to work -- and more importantly, win -- to get there. The decision to start everyone at 0 rather than a default value was also done in the early stages of the SC2 beta, where everyone went from starting at 1000 to starting at 0, presumably for similar reasons (though complicated by the fact that you can't reset your stats).
On August 08 2010 15:12 paralleluniverse wrote: Being favored is almost certainly based on comparing your displayed rating to your opponents MMR.
Yes, this is meaningless and deceptive, and doesn't actually tell us who is really favored to win.
Yes, it *should* compare your MMR to your opponents MMR.
And no, there is no discontinuity in skill level, as you move up leagues. Matchmaking is great and is purely based on MMR, and is separate from the disastrous ranking system.
Do we have evidence for this? Isn't it possible that a player is displayed favoured if his MMR is greater than your own minus a factor based on sigma? Or something along those lines. I don't really see how you could directly compare displayed rating to MMR considering displayed ratings are division independent, not to mention league independent, while MMR is an absolute measure of a player's success in the system.
We don't have direct evidence for that, but it would make sense if each league had a threshold (and we could think of this as essentially a "rating boost" for the purposes of point calculation). The original post attempts to cover this in more detail, but just to throw out some arbitrary numbers as an example, if we said it was something like:
The theory we're tinkering with now is that if you're 300 in Diamond, your "global rating" is 2800. To go even further out on a limb, these points don't include anything gained from the bonus pool. This is our attempt to prove some kind of bridge or relationship between league point values, which are so far impossible to quantify.
For the record, though, displayed ratings are not division independent -- they're comparable across all divisions in a league because everyone in that league is playing against (mostly) the same player pool. I'm going to be careful about taking this too far because there's little evidence to support it, but it's an idea to throw out there that makes rating values translatable across leagues.
Entirely possible. Its been a long time since I played WoW, and even longer since the TR I played. That TR might have been before the 1500->0 change happened. I just remember that the rating system started acting very much like the old zero-sum system when everyone's MMR's matched the displayed rating.
On August 08 2010 15:12 paralleluniverse wrote: Being favored is almost certainly based on comparing your displayed rating to your opponents MMR.
Yes, this is meaningless and deceptive, and doesn't actually tell us who is really favored to win.
Yes, it *should* compare your MMR to your opponents MMR.
And no, there is no discontinuity in skill level, as you move up leagues. Matchmaking is great and is purely based on MMR, and is separate from the disastrous ranking system.
Do we have evidence for this? Isn't it possible that a player is displayed favoured if his MMR is greater than your own minus a factor based on sigma? Or something along those lines. I don't really see how you could directly compare displayed rating to MMR considering displayed ratings are division independent, not to mention league independent, while MMR is an absolute measure of a player's success in the system.
The evidence is that your opponent is always favored until you play lots of games, and from then on, teams are nearly always even.
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens? - His MMR will increase - My MMR will decrease - Both of our sigmas will decrease - His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500 - My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally
This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.
On August 08 2010 15:47 Excalibur_Z wrote: [snip] For the record, though, displayed ratings are not division independent -- they're comparable across all divisions in a league because everyone in that league is playing against (mostly) the same player pool. I'm going to be careful about taking this too far because there's little evidence to support it, but it's an idea to throw out there that makes rating values translatable across leagues.
I hope you're right about this, but I'm less sure than I was previously. When I was promoted to diamond(a newly made division) the system said I had about 220 bonus pool, but that turned out to be just a glitch and when I logged in the next time all but a dozen or so were gone. If players put in a new division don't receive a bonus pool equivalent to players who've been in same league divisions for much longer, it'll mean players who were slower to rank up will have to have a proportionally better record to have similar ratings. Maybe previous bonus pool points are modified directly into the rating you receive initially on promotion, I have no means of figuring that out. Is that what you're proposing?
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens? - His MMR will increase - My MMR will decrease - Both of our sigmas will decrease - His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500 - My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally
This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.
I've actually found that once I hit ~300 diamond, my points gained and points received minus bonus pool balanced out very close to even. Below that level, I was getting much larger points boosts though. This has just been my experience so far, I haven't played too many matches at this level yet(diamond is hard).
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens? - His MMR will increase - My MMR will decrease - Both of our sigmas will decrease - His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500 - My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally
This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.
I think it is entirely reasonable to assume that your displayed rating value is allowed to swing upwards very quickly when you win in if the displayed value is much less than your actual MMR. This is how it works in WoW after all. The bonus pool is a relatively simple addition to this which just works like rest xp to help players who are not able to play as often keep up (in terms of ladder ranking) with those who can.
So in the above example, instead of the player with a higher MMR gaining rating due to the addition of diamond's MMR threshold and displayed rating (which is a highly arbitrary algorithm and doesn't make much sense given that displayed ratings cannot be compared between two players), it is instead simply: if you win you will gain rating based off the difference between the two players MMR additionally modified by the difference of your displayed rating and your MMR. If displayed rating is < MMR, the rating gain will be higher than if they were equal or if displayed > MMR (which only occurs due to the bonus pool).
Such a system implies though that display ratings will quickly converge towards your MMR and then slowly exceed your MMR due to the bonus pool. I don't think enough players have a display rating high enough to test this though, would need to be 2000+ up in diamond. Once players are there we can observe their point gain/loss compared to earlier games to determine if the displayed rating gain slows once it reaches MMR.
Ok, how does all of this tie into displayed rating and the whole “favored” deal? If you remember back to WoW, ratings changed based on a direct comparison of your displayed rating to the other team’s MMR. So if your current rating was 500 and you were playing people with MMRs of 2000, your rating would jump significantly after every win because of the wide disparity. Now, we’ve identified that on the loading screen quite often players are seeing the other person as favored and the opponent (who is nominally “favored”) also sees his opponent as favored! How can this be? The theory put forth here is the system is again comparing your displayed rating to your opponent’s hidden MMR.
The reason for this is so that the system brings you toward your MMR more quickly. kzn explains:
How it works was like this: Say you've got a MMR of 2500, and you start a new team. It starts at 0 rating, but the matchmaking system will match you with other players of MMR 2500. If you lose a game, your team rating would not change at all. If you won, it would increase by 47 (a hard cap that was in place at least when I played). This was not explained as arising due to an interaction between the team rating and the opponent's MMR, however - it was explained as the system trying to get your team's rating as close as possible to your team's MMR rapidly.
I think you have misunderstood Kzn's clarification. I think he is suggesting that the system compares your displayed rating to your current MMR and not your opponents (not that this makes much of a difference mathematically since, in theory, your MMR and your opponent's should be very similar). Having a large difference between your displayed rating and your MMR will result in the system skewing rating changes to favour reducing that difference. Eventually your displayed rating becomes very close, or the same as, your MMR. At least that's how I think it works in wow.
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens? - His MMR will increase - My MMR will decrease - Both of our sigmas will decrease - His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500 - My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally
This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.
I think it is entirely reasonable to assume that your displayed rating value is allowed to swing upwards very quickly when you win in if the displayed value is much less than your actual MMR. This is how it works in WoW after all. The bonus pool is a relatively simple addition to this which just works like rest xp to help players who are not able to play as often keep up (in terms of ladder ranking) with those who can.
So in the above example, instead of the player with a higher MMR gaining rating due to the addition of diamond's MMR threshold and displayed rating (which is a highly arbitrary algorithm and doesn't make much sense given that displayed ratings cannot be compared between two players), it is instead simply: if you win you will gain rating based off the difference between the two players MMR additionally modified by the difference of your displayed rating and your MMR. If displayed rating is < MMR, the rating gain will be higher than if they were equal or if displayed > MMR (which only occurs due to the bonus pool).
Such a system implies though that display ratings will quickly converge towards your MMR and then slowly exceed your MMR due to the bonus pool. I don't think enough players have a display rating high enough to test this though, would need to be 2000+ up in diamond. Once players are there we can observe their point gain/loss compared to earlier games to determine if the displayed rating gain slows once it reaches MMR.
Like I've said a bunch of other places, the bonus pool will not continually inflate ratings, since if you exceed your MMR your ratings increase will eventually (quickly if you play frequently) be offset by winning fewer points than you would if your rating were not above your MMR.
I think a better system than "Blizzard checks MMR after every 30 games" would be "You get promoted when your sigma is below a certain threshold." This would improve the game's certainty factor, and, though it would take longer to get you where you need to be, would probably put you in exactly the right spot. Maybe even set certain sigma thresholds along the way, i.e. the system checks your MMR at sigma 100, 75, 50, 25 and adjusts your positioning accordingly.
On August 09 2010 02:10 Caponed wrote: I think a better system than "Blizzard checks MMR after every 30 games" would be "You get promoted when your sigma is below a certain threshold." This would improve the game's certainty factor, and, though it would take longer to get you where you need to be, would probably put you in exactly the right spot. Maybe even set certain sigma thresholds along the way, i.e. the system checks your MMR at sigma 100, 75, 50, 25 and adjusts your positioning accordingly.
Either way, interesting read.
Well, we don't know specifically how many games it takes before you reach a review checkpoint, other than Browder's admission in the Best Buy livechat that the initial one occurs at about 30 games. That may not necessarily be true anymore (it was just a couple of weeks before release) because right now we're seeing people get promoted after 50, 40, 20, even 15 or so games (my 3v3 team was promoted after only 15 games, in fact). It's also possible that review checkpoints have been abolished entirely and that promotion depends entirely upon sigma and the league threshold, or that both factors are considered. There's really no way for us to know, but I agree that arbitrary checkpoint periods -- especially since the periods are not consistent or trackable -- don't make as much sense.
On August 09 2010 02:15 Empyrean wrote: Random question: did you use R to generate those graphs? Because they look suspiciously similar to R's basic graphics package ;D
We didn't make them. The top-down one is from a public .ppt from MS research Cambridge and the 3D one is from Google image search. :V
Ok, how does all of this tie into displayed rating and the whole “favored” deal? If you remember back to WoW, ratings changed based on a direct comparison of your displayed rating to the other team’s MMR. So if your current rating was 500 and you were playing people with MMRs of 2000, your rating would jump significantly after every win because of the wide disparity. Now, we’ve identified that on the loading screen quite often players are seeing the other person as favored and the opponent (who is nominally “favored”) also sees his opponent as favored! How can this be? The theory put forth here is the system is again comparing your displayed rating to your opponent’s hidden MMR.
The reason for this is so that the system brings you toward your MMR more quickly. kzn explains:
On August 08 2010 14:30 kzn wrote:
How it works was like this: Say you've got a MMR of 2500, and you start a new team. It starts at 0 rating, but the matchmaking system will match you with other players of MMR 2500. If you lose a game, your team rating would not change at all. If you won, it would increase by 47 (a hard cap that was in place at least when I played). This was not explained as arising due to an interaction between the team rating and the opponent's MMR, however - it was explained as the system trying to get your team's rating as close as possible to your team's MMR rapidly.
I think you have misunderstood Kzn's clarification. I think he is suggesting that the system compares your displayed rating to your current MMR and not your opponents (not that this makes much of a difference mathematically since, in theory, your MMR and your opponent's should be very similar). Having a large difference between your displayed rating and your MMR will result in the system skewing rating changes to favour reducing that difference. Eventually your displayed rating becomes very close, or the same as, your MMR. At least that's how I think it works in wow.
Your rating is supposed to rapidly approach your MMR, that's true, but it doesn't make sense for your point gains to depend on your own MMR. There needs to be an external comparison which is why it has to compare against your opponent's MMR.
On August 09 2010 02:15 Empyrean wrote: Random question: did you use R to generate those graphs? Because they look suspiciously similar to R's basic graphics package ;D
We didn't make them. The top-down one is from a public .ppt from MS research Cambridge and the 3D one is from Google image search. :V
Ok. The contour map one definitely looks like it was generated in R :D
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens? - His MMR will increase - My MMR will decrease - Both of our sigmas will decrease - His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500 - My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally
This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.
This is the danger of using arbitrary values for illustration purposes. We do not know the actual threshold for any of the leagues. The numbers included in that quote are simply to make an example of what I was describing. The threshold values could be (and likely are) higher.
Also, MMR changes do take into account the sigma of both players. I do not know whether or not the change to displayed rating does, but it would not surprise me if it did.
"The final change made by the USCF – also made possible by the increased accessibility of computers – is the transition from a normal distribution to a logistic distribution. By observing a large number of results, the USCF determined that a logistic distribution most accurately extrapolated outcomes."
So I didn't want to start another thread, but I get the gist here that "displayed rating" (points) doesn't really matter? I was looking at a friend who is in Bronze league and has more points than I do, in Diamond. I was just wondering how all of this meshes together.
On August 09 2010 06:31 VorcePA wrote: So I didn't want to start another thread, but I get the gist here that "displayed rating" (points) doesn't really matter? I was looking at a friend who is in Bronze league and has more points than I do, in Diamond. I was just wondering how all of this meshes together.
Displayed rating matters for ranking players in the same league. It's not immediately obvious how rating translates across leagues but one theory we have is that you can add whatever the breakpoint is for your league in order to get your "global rating" (and I realize the danger of using this term). In the completely baseless hypothetical example I gave before, if it were something like 0 Bronze, 1000 Silver, 1500 Gold, 2000 Platinum, 2500 Diamond, then if you had 300 Diamond and your friend had 600 Bronze you would be the equivalent of 1800 points over him (bonus points would be excluded because they're the same for all players).
Again I'll state here that we absolutely do not know what the breakpoints are or even what the overall scale is. This was just our attempt to explain the seemingly arbitrary rating that you start with after a promotion or demotion. There's clearly some kind of rating translation, we just don't know what it is.
Therefore, a corollary here is that when determining rating increase, the hidden threshold value for your league is added to your displayed rating, then compared to your opponent’s MMR, for purposes of computing the gain/loss to your displayed rating.
Example: ExcaliburZ and I play a game. His MMR: 2600, sigma: 100, displayed rating: 300. My MMR: 2500, sigma: 50, rating: 150. Diamond’s MMR threshold: 2300. Excal wins because he rules. What happens? - His MMR will increase - My MMR will decrease - Both of our sigmas will decrease - His rating will increase. How? By comparing my MMR (2500) against his rating + diamond’s MMR threshold: 300 + 2300 = 2600, his gain is thus off 2600 vs my MMR of 2500 - My rating will decrease. In the same way: his MMR: 2600. My rating + threshold: 150 + 2300. Thus I lose points proportionally
This is not really consistent with we generally observe, which is at a rating of diamond 300 and being well above the skill that gives a likelihood of being demoted, people are gaining many more points than they are losing at equal matches. The fact that you gain more points at a low number of games indicate that the point gain formula either depends on sigma, or is still using a version of comparing displayed to opponents MMR.
This is the danger of using arbitrary values for illustration purposes. We do not know the actual threshold for any of the leagues. The numbers included in that quote are simply to make an example of what I was describing. The threshold values could be (and likely are) higher.
Also, MMR changes do take into account the sigma of both players. I do not know whether or not the change to displayed rating does, but it would not surprise me if it did.
OK I was misunderstanding anyway, I see what the example means now.
As a low ranking platinum player, I lost to all of the diamond players I faced and lost to most of the platinum players too, but the system decided to promote me to diamond for some reason. Blizz seriously needs to iron out some of these bugs haha.
Its not really hard to make a fair system, though. The question is more how good is the system, to which the answer actually depends a lot on how the system is implemented.
TrueSkill has the dubious "feature" of being absolutely awful if the implementation is done badly and amazing if its done right. The SC2 implementation so far seems to be pretty average.
On August 09 2010 06:19 carwashguy wrote: Why do you assume Blizzard is using the normal distribution? I thought most rating systems use the logistic distribution nowadays.
"The final change made by the USCF – also made possible by the increased accessibility of computers – is the transition from a normal distribution to a logistic distribution. By observing a large number of results, the USCF determined that a logistic distribution most accurately extrapolated outcomes."
From my understanding reading the TrueSkill whitepapers the chess ranking systems use a logistic distribution because it is better suited to chess. TrueSkill, and by extension all Xbox games that do matchmaking, uses a Gaussian distribution. I'm not a statistician so I can't argue the relative merits between the two. That is, my knowledge of statistics is pretty good, but the pros and cons of each distribution as applied to game ranking systems would be an interesting paper to read
I am presuming MS Research had a decent insight into the usefulness of a Gaussian distribution; ease of implementation/computation would not surprise me. I would be interested in the reasons for using a logistic distribution over a Gaussian one in videogames.
Question: I read in the section describing the graphs where probabilities for player 1 and 2 are shown. "Also note that this does not need to be circular when looking at a top-down section. If players have different confidence values it will look like an ellipse."
The 3d curve that could be thought as "combination of two of the 2d" curves. Is it a combination of 2 different players curves which it seems reading the section I quoted.
Then it seems like the system has already found another player (aka system has already found a match) if it combines the two players curves into the 3d shape? *confused*
On August 09 2010 17:17 papaz wrote: A very informative post!
Question: I read in the section describing the graphs where probabilities for player 1 and 2 are shown. "Also note that this does not need to be circular when looking at a top-down section. If players have different confidence values it will look like an ellipse."
The 3d curve that could be thought as "combination of two of the 2d" curves. Is it a combination of 2 different players curves which it seems reading the section I quoted.
Then it seems like the system has already found another player (aka system has already found a match) if it combines the two players curves into the 3d shape? *confused*
The way I understand it is the system would create these graphs with each player also searching for a game. I imagine the system chooses the closest to even graph if one within the sweet spot is not found after a certain amount of time.
Assuming this is what blizz have, it's probably reasonable to assume people with win/loss ratio that differ significantly from 50% (lets assume 90%) will have a very high sigma, the system will keep matching these guys to players with much higher MMR, and they will keep beating them, causing further inflation in the sigma until they reach a point where their MMR peaks at the top of the pack. This could partially be a reason why people with these win records are stuck in a certain league.
On August 09 2010 07:20 Calidus wrote: Ty for informative post even if i brought back bad memories of Stats, Linear Algebra and Diff Eq.
its not bad. statistics junkies like me will see that this is a fair system. didn't sirlin talk about this earlier?
I remembered 1 things from my stats class last semester: Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital. ~Aaron Levenstein
Not trying to downplay your work here, but I don't see any evidence anywhere that it actually works this way. I know you said it's just speculative, but your speculation should be based on some sort of evidence right? That led you to believe it works this way? Right now all I see is "I'm about to describe one of many possible ranking systems that SC2 may or may not use with equal probability".
"No mined data. We don't have that for SC2. It is based on what we know about WoW Arena, what we know about SC2 ladder, and how Bayesian inference ranking systems work. This isn't necessarily how it works, though obviously I believe this is close to the truth."
So yeah, it's not particularly rigorous, to say the least. What I took away from the post were basically the hypotheses about how different observed behavior might be implemented in a Glicko- or TrueSkill-style system; i.e. a threshold rating for each division that takes into account ratings deviation, and the idea that the "favored" might be bugged for people who have a different real rating from their displayed rating.
I think the post was intended primarily as an introduction for people who haven't previously been exposed to the concept of a rating being paired with a certainty that improves or deteriorates over time.
I look forward to someone collecting some data regarding wins, losses, rating changes, and promotions, and making a model.
On August 10 2010 00:07 Glacierz wrote: Assuming this is what blizz have, it's probably reasonable to assume people with win/loss ratio that differ significantly from 50% (lets assume 90%) will have a very high sigma, the system will keep matching these guys to players with much higher MMR, and they will keep beating them, causing further inflation in the sigma until they reach a point where their MMR peaks at the top of the pack. This could partially be a reason why people with these win records are stuck in a certain league.
Well, yes and no, I think. We'll use CauthonLuck as an example. His MMR is pretty clearly at the very top, matching him against the best players on the ladder. Say he maintains his 85% win ratio against those top players, causing sigma to decrease because those players are below his MMR. However, because he occasionally loses against players who have a lower MMR, sigma increases and offsets each decrease. Sigma never decreases below the threshold required for promotion.
In an upset, sigma will increase for both players, but that's not universally true. If sigma is large enough, it can decrease instead. How large that is, we don't know. I'll edit that into the OP.
"No mined data. We don't have that for SC2. It is based on what we know about WoW Arena, what we know about SC2 ladder, and how Bayesian inference ranking systems work. This isn't necessarily how it works, though obviously I believe this is close to the truth."
So yeah, it's not particularly rigorous, to say the least. What I took away from the post were basically the hypotheses about how different observed behavior might be implemented in a Glicko- or TrueSkill-style system; i.e. a threshold rating for each division that takes into account ratings deviation, and the idea that the "favored" might be bugged for people who have a different real rating from their displayed rating.
I think the post was intended primarily as an introduction for people who haven't previously been exposed to the concept of a rating being paired with a certainty that improves or deteriorates over time.
I look forward to someone collecting some data regarding wins, losses, rating changes, and promotions, and making a model.
I've been tracking my 1v1 matches since I started playing yesterday (from 0 games). Once I get enough information I'll post it here.
ExcaIibur(or anyone for that matter) can your model explain this interesting situation that i can't figure out: Player A is 39 and 27 and has 460 points in plat while Player B is 38-28 and has 420 points in plat. Player A is 5 in his division while player B is 1st in a different division. Player B get promoted to diamond before player A. Both players have had the the game for the same amount of time so their bonus pools should be about that same(if that has any effect on it, i doubt it).
On August 10 2010 04:39 Calidus wrote: ExcaIibur(or anyone for that matter) can your model explain this interesting situation that i can't figure out: Player A is 39 and 27 and has 460 points in plat while Player B is 38-28 and has 420 points in plat. Player A is 5 in his division while player B is 1st in a different division. Player B get promoted to diamond before player A. Both players have had the the game for the same amount of time so their bonus pools should be about that same(if that has any effect on it, i doubt it).
If we're assuming there's a hidden rating, that's trivial. Displayed points don't necessarily have much connection to real rating, and obviously win/loss record doesn't give a good perception of rating either, so for all you know, player B hit the threshold and player A didn't.
On August 10 2010 04:39 Calidus wrote: ExcaIibur(or anyone for that matter) can your model explain this interesting situation that i can't figure out: Player A is 39 and 27 and has 460 points in plat while Player B is 38-28 and has 420 points in plat. Player A is 5 in his division while player B is 1st in a different division. Player B get promoted to diamond before player A. Both players have had the the game for the same amount of time so their bonus pools should be about that same(if that has any effect on it, i doubt it).
Completely dependent upon their match history and opponents. Was Player A more volatile in match outcome (did he lose matches he was expected to win and vice versa)? Did he go on a long losing streak followed by a win streak? Was Player B, by contrast, more stable and predictable in performance? Their MMRs -- and equally as important, their sigmas -- may be drastically different which we expect to be a prime factor in promotion.
On August 10 2010 04:06 monad wrote: Not trying to downplay your work here, but I don't see any evidence anywhere that it actually works this way. I know you said it's just speculative, but your speculation should be based on some sort of evidence right? That led you to believe it works this way? Right now all I see is "I'm about to describe one of many possible ranking systems that SC2 may or may not use with equal probability".
This is a theory that attempts to explain the behavior seen on battle net. It attempts to provide a model with which we can understand how the ladder works. A major problem here is we don't have the data with which to verify this conjecture. Unless we are given access to more data much of this theory cannot be definitively proven. Even still a decent working theory can be quite useful, despite its speculative nature. I think I have been clear about what evidence I am basing this off of: blizzard's own statements about wow, the available materials on a bayesian system in a videogame, the observations about the sc2 ladder, and blizzards track record in polishing existing systems instead of creating new ones from while cloth. As a result I would not think that the system detailed here is one of many and is unlikely to be true. On the contrary, I think it is highly likely that sc2 uses a system very much like this one.
So, this theory may be incorrect in parts, and I would be quite interested in reading a different theory not based on bayesian inference with gaussian skill distributions if one exists.
On August 10 2010 05:53 vanick wrote:So, this theory may be incorrect in parts, and I would be quite interested in reading a different theory not based on bayesian inference with gaussian skill distributions if one exists.
What observations have you made about the ladder that would lead you to think that, for example, it can't be just a plain zero-sum Elo system? Or perhaps, as in chess, there's a big "provisional" period where the system amplifies rating changes as it tries to place you, and then your rating changes much less with each game after that; that could help explain people's wildly variable experience with getting promoted or not promoted, depending on how long the provisional period is. I mean, there are lots of different rating systems in place somewhere, and I don't really see any public data about the ladder that seems to disqualify any reasonable system.
I'm not really saying that you're likely to be wrong. I think it's reasonable to expect that they've carried over a system very similar to WoW's system, since they spent a lot of time and effort learning from their experiences with that. I wouldn't be shocked if it were different, though; you know programmers love to reinvent wheels.
On August 10 2010 05:53 vanick wrote:So, this theory may be incorrect in parts, and I would be quite interested in reading a different theory not based on bayesian inference with gaussian skill distributions if one exists.
What observations have you made about the ladder that would lead you to think that, for example, it can't be just a plain zero-sum Elo system? Or perhaps, as in chess, there's a big "provisional" period where the system amplifies rating changes as it tries to place you, and then your rating changes much less with each game after that; that could help explain people's wildly variable experience with getting promoted or not promoted, depending on how long the provisional period is. I mean, there are lots of different rating systems in place somewhere, and I don't really see any public data about the ladder that seems to disqualify any reasonable system.
I'm not really saying that you're likely to be wrong. I think it's reasonable to expect that they've carried over a system very similar to WoW's system, since they spent a lot of time and effort learning from their experiences with that. I wouldn't be shocked if it were different, though; you know programmers love to reinvent wheels.
It's definitely not zero sum/Elo because players receive and lose different point amounts.
WoW's system used to use Elo. Teams used to start at 1500 and that was their only rating. They changed to a Bayesian inference system when they realized it didn't have the problems that the Elo system did, and they explained the change over several forum posts and FAQs. Is the SC2 system an exact mirror of WoW's system? No, very clearly not, because there are parts of the SC2 system that are unique, such as promotions. However, it's similar enough fundamentally that it makes the system easier to understand.
On August 10 2010 05:53 vanick wrote:So, this theory may be incorrect in parts, and I would be quite interested in reading a different theory not based on bayesian inference with gaussian skill distributions if one exists.
I'm not really saying that you're likely to be wrong. I think it's reasonable to expect that they've carried over a system very similar to WoW's system, since they spent a lot of time and effort learning from their experiences with that. I wouldn't be shocked if it were different, though; you know programmers love to reinvent wheels.
There's also the mantra that good programmers write good code, great programmers steal great code. Not saying it's one or the other because I know a lot about reinventing the wheel
As a followup to Excal's post, some of the problems Elo suffers from is it gives players incentive to change how they play, instead of giving them a pure incentive to win. Going back to the chess example, it often creates the incentive to play to a draw, not a win. In addition, Elo has a problem with streaks, win or lose. The system proposed here, and the one used by Arena, buffers against that.
I don't know how the system is set up but I won't actually ever get a good flow of games. I will either go on 15 game winning streaks or 15 game loosing streaks and just alternate between the two. Either I get to play people who are insanely ahead of me or I get to play scrubs and there is no inbetween.
On August 10 2010 11:05 VanGarde wrote: I don't know how the system is set up but I won't actually ever get a good flow of games. I will either go on 15 game winning streaks or 15 game loosing streaks and just alternate between the two. Either I get to play people who are insanely ahead of me or I get to play scrubs and there is no inbetween.
Can you verify? Can you post your in-game match history along with the profiles of people you've played, their rating and league, and the number of points lost or gained?
So I have a question, would it become harder to be promoted if you've played lots of games? Assuming someone was in silver for instance, having played a large amount of games (say a 100 with a 50% win/loss ratio). If he were to start winning 70%(an arbitrary amount) of his games, would it be harder for him to get to gold than someone with similar percentages but only 15 games played?
On August 11 2010 08:58 Hekmat wrote: So I have a question, would it become harder to be promoted if you've played lots of games? Assuming someone was in silver for instance, having played a large amount of games (say a 100 with a 50% win/loss ratio). If he were to start winning 70%(an arbitrary amount) of his games, would it be harder for him to get to gold than someone with similar percentages but only 15 games played?
It would take longer, yes. If you've played 100 games and gone 50-50, your sigma is probably fairly small because the system feels confident that it's put you where you belong. If someone else has played 16 games and gone 8-8, that person's sigma is going to be larger. The exact scale is something that we don't know, but we do know that your MMR never truly gets "locked" in place (it's always changing to some degree after each win or loss). Depending on where you are in the ladder, you may need to play quite a few more games to increase your sigma before you can decrease it again within the threshold of a higher league, which would make you eligible for promotion.
One thing to think about which I have not seen explicitly explained.
Player A is very good against Terran and Zerg, but almost always loses to Protoss. Player B is consistently good against all three races. Players A and B play 20 games and both go 15-5. The matchmaking system sets both players against 10 players of even 'skill' (i.e. MMR) and 10 of higher skill. Player B lost to 5 opponents of higher skill, beat 5 opponents of higher skill and all 10 of even skill. His sigma has decreased enough such that he is promoted. Meanwhile Player A beats all ten highly skilled Players (which by chance are all Terran and Zerg) and loses to 5 of even skill (all Protoss), the sigma remains high as beating players of higher MMR whilst going 50/50 at even MMR makes the 'correct' MMR uncertain. Player A is not promoted. As a caveat, because of the bonus pool Player A could additionally have a higher displayed rating than Player B [For example A gets (10+10) x 5 for his even match wins - 10 x 5 for even match losses and (15+15) x 10 = 350pts. B gets (10+10) x 10 for his even match wins - 5 x 5 for even match losses and (15+15) x 5 = 325pts.]
Or both players are equally good against all 3 race distributions and the matchmaking system puts them against equal amounts of the races. However Player A is susceptible to cheese and happens to lose a few games to lower MMR players cheesing him thus keeping a high sigma. Player B is also susceptible to cheese but fortunately none of his opponents cheese him and he only loses to players of high MMR. Still they both go 15-5 and Player B gets promoted whilst A does not.
Because the matchmaking system does not take into account race, or buildorder, or anything else except wins and losses this may go someway towards explaining how people get 'stuck' in Platinum with records like 30-6.
Because the matchmaking system does not take into account race, or buildorder, or anything else except wins and losses this may go someway towards explaining how people get 'stuck' in Platinum with records like 30-6.
The obvious downside of this system is that it ONLY takes in account win/lose ratio. If you read the TrueSkill system in the Microsoft paper it says:
it merely assumes that the outcome is due to some unobserved performance that varies around the skill of a player. If one is playing a point based game and the winner beats all the other players by a factor of ten, that player’s victory will be scored no differently than if they had only won by a single point.
Normally a player isn't good with all three races and all matchups. One step in the right direction from blizz would be to give something like you can have one character per race if you feel that your skill isn't equal in different races.
Also say that my TvP win ratio is 70% and my TvZ ratio for some reason is 30% the system won't take this in account in my matchmaking and could (and possibly would?!) hold me as favourite in too many TvZ matchups despite my win/lose ratio says otherwise.
I am by no means an expert in matchmaking systems but reading/seeing how the laddering behaves I think there is a lot of room for improvement.
Made an important edit to the Matchmaking section per Vanick's post on the Battle.net forums:
In an upset sigma does not always increase. That is, if a lower-MMR player wins then what happens depends a lot more on their precise equations they are using. If a player's sigma is large in an upset (whether he's the winner or loser) it can decrease. That is because given the right MMR and sigma values it's possible in theory for the system to learn about that player's skill and rate him more accurately. If a player's sigma is small, however, it can become larger after an upset if that upset was truly unexpected.
On August 08 2010 12:41 SnakeChomp wrote: I don't think the displayed rating value has any bearing on match making at all.
Totally agree, from as low as 250 silver league I was matched against 450 diamonds. As 500 gold I was matched against "slightly favorite" 550+ diamonds, and then I was promoted straight from gold to diamond after a bunch of games against only diamonds.
all this time I was gaining at least 20 points for each win (40 with bonus) and losing 1 - 3 points for any loss..
I'd like to weigh in on a couple of things. (very long winded, sorry -_-)
First, the "favored" notices on the loading screen are almost certainly based on your display rating compared to your opponent's MMR. This is (as previously mentioned) deceptive, because it is not based on the expected probability that you will win or lose. The evidence for this is that these notices give a preview of points at stake during this game. If you see "even match", you can expect there to be ~10-14 points at stake. "slightly favored" will get you something like -6/10 on a loss or +14-18 on a win, likewise vs a "favored" opponent you can expect -2/6 or +18/22 (all ballpark numbers). If everyone watched for this for a few games, we'd have all the evidence we needed.
About the display rating being "meaningless" or "fluff" or "wrong". Think of it this way: MMR is a quick and dirty search, attempting to locate your current skill level as fast as possible. It is likely to be very inaccurate at times, but is very valuable for quickly separating out the people who are several standard deviations outside the pack. If your MMR is extremely stable, your display rating will eventually converge with it. If (and this is more likely) your MMR tends to jump around quite a bit, your display rating acts as a damping mechanism to give you a much more stable indication of your overall performance level.
The problem is that it might take a hundred or a couple hundred games for the (very damped) display rating to reach the appropriate range for your skill level, which leads a lot of people to freak out about it. Once players get to the 1300-1500 range, expect to see more separation between the top players. That being said, I would like to see bonus pool points stop being accumulated after the ~800-1000 rating mark to take away any incentive to abuse them for ladder whores.
About promotions, I'm pretty confident in the "checkpoint" theory at this point, but it's still a pretty big mystery after the first check. I can understand the logic behind this, especially because the MMR sigmas are ridiculously huge for new players (example: guy with 15 games played on the silly and ill-conceived blizzard top 200 list). It seems pretty well established that the first checkpoint is at ~8 losses, but after that it's pretty fuzzy. To offer a data point from myself, I tanked my placements and landed in silver. After a rocky start, I was promoted to gold after my 8th loss (i was 12-8). A series of wins ended in 4 games in a row vs diamond players, ending in 4 losses, and I went to plat at ~20/12. I'm now matching against ~4-500 rated diamond players and reached my 16th loss, but have yet to be promoted at ~38/16 in plat.
Hrm I wonder, Excalibur_Z would it be any use to you for finding the checkpoints if you had a mass quantity of data? I could hookup something to the workers so whenever it sees a team change leagues it saves their points/wins/losses. The only difficulty is that number isn't going to be 100% accurate since they might get promoted and immediately play games.
On August 13 2010 07:53 Shadowed wrote: Hrm I wonder, Excalibur_Z would it be any use to you for finding the checkpoints if you had a mass quantity of data? I could hookup something to the workers so whenever it sees a team change leagues it saves their points/wins/losses. The only difficulty is that number isn't going to be 100% accurate since they might get promoted and immediately play games.
I think that would give us a rough estimate as to where these checkpoints and/or league thresholds might be. It's certainly better than nothing. I'm not entirely sure how we would graph it out, or track match history (since that's very important), but throwing around some arbitrary estimated MMRs and breakpoints we might be able to come up with something.
An update, with pictures! Shadowed was kind enough to provide me with a data set of promotions as captured by his data scraper. Thanks to him for making these possible.
Shadowed's scraper runs every so often, and when it detects that a player's league has changed it will record the player's state at that update and the previous update. For example, if the last time the scraper grabbed my stats my W/L record was 10-3, and the current time it grabs it my league has changed and my record is now 17-5, it knows that somewhere in there I had a promotion/demotion. It doesn't know precisely where, just the range of 9 games. I've taken this data and made a set of graphs.
The following graphs are of the combined games played. They include ALL league changes, both promotions and demotions. I will graph them out individually when I'm not half asleep, but I do not think they will vary too much.
The easiest 3 ways to look at this are with the previous games played, the current games played (that is, games played at update time), and the average of the two. Here is a chart combining all 3 across all the data we have currently (there are some hard to see outliers past the 600 games point):
A smaller slice excluding the long tail that decreases past the end of the image:
The total dataset is roughly 23,000 promotions/demotions. Past the 100 game mark less than 1,800 promotions/demotions occured.
What inferences can we draw from this data? - Obviously there are no data points at <5 games due to placements. - There appears to be a definite checkpoint where the system reviews a player's rating at around 22-26 games. - There is a bump in the promotions at around 15 games played. I'd need to examine it more when I'm not all sleepy. - It appears that there are no static (or clustered, anyways) checkpoints after the 25ish check. - After about 100 games played the system appears to have about 95% accuracy with regard to league placement.
Great write up! It has a good mathematical foundation and solid reasoning. I think you are very close to the truth here on a lot of this. Makes me wonder: why doesn't Blizzard disclose a lot more about its rating system? Is it to protect their intellectual property, or for the players?
Got a new update to the promotions data. This time the dataset is 56.5k league changes, around twice what we had before.
I'm not going to post the full graph unless someone really wants to see it; it looks the same as the first full graph here and all the interesting stuff happens in the 5-60 games slice.
Updated Graph:
The results are pretty similar to last time. The bump at the 12-15 game mark is a little more pronounced. After hearing an interesting argument, it's possible there is no checkpoint at 30 games. It's possible that the majority of players have their MMR/sigma criteria fall within certain levels by that point as the system converges quickly.
That's cool and all, but I really cant read that. I was just wondering out of curiosity how I still cant get out of 2v2 gold even though me and teammate are 300 points above anyone else in north america.... then again, you did explain it probably, its just your explanation is too technical and confusing. Kind of like the fear of picking up calculus 3.
I have a question for these mathers, in regards to bonus pool. It may have been answered already.
If the hypothesis that bonus pool is discounted in the matchmaking calculation is true, then in order to reach #1 in your division, wouldn't the best way to go about it be to not play games for a significant period of time before you start playing games?
The question basically is, does your MMR and sigma remain constant while you are not playing games. If that were the case, then by stocking up bonus pool, you would be gaining more perceived points, without increasing the skill level of the people you play. This would allow you to quickly rise in your division without risking a streak of losses to higher skilled players.
I imagine being top in division doesn't matter much to the really hardcore people, but to more casual players it probably does. To that end, giving more casual players an advantage in bonus pool seems a neat trick.
As an edit: I have a little bit of familiarity with GLICKO since I do a lot of tabletop wargaming and we've had leagues governed by GLICKO before, and I seem to remember the uncertainty factor in GLICKO increases if you go a long period of time without playing games.
And a second question, while I think of it.
Does bonus pool accumulate from launch, or from when somebody registers an account? I bought my copy launch day, but if new accounts gain bonus pool from the time the account was registered, it may be much harder for the system to track and discount it. Just a thought.
On August 15 2010 23:33 Ketara wrote: I have a question for these mathers, in regards to bonus pool. It may have been answered already.
If the hypothesis that bonus pool is discounted in the matchmaking calculation is true, then in order to reach #1 in your division, wouldn't the best way to go about it be to not play games for a significant period of time before you start playing games?
I'm not sure why you think that is. The fewer games you have, the greater your MMR volatility. It's not like you would skate up the rankings with a massive bonus pool because whoever is in that #1 position has likely (a) fought all the top players that you would inevitably fight with a volatile MMR and (b) consumed all of his bonus pool. Remember that Bonus Pool replenishes at a constant rate for everyone regardless of their activity level (yesterday when I was playing I actually saw my bonus pool increase by one point at 9:19pm).
The question basically is, does your MMR and sigma remain constant while you are not playing games. If that were the case, then by stocking up bonus pool, you would be gaining more perceived points, without increasing the skill level of the people you play. This would allow you to quickly rise in your division without risking a streak of losses to higher skilled players.
MMR remains constant over periods of inactivity but sigma does not. The system doesn't know if you'll come back from a break refreshed and improved or out of practice and sloppy, so an increase in sigma reflects this. Again, ignoring bonus pool for a moment, if you're at an average level then you'll inevitably play against people that give you a 50-50 record. If most of the time these turn out to be even matches with even results, your rating would stagnate. The bonus pool just prevents this stagnation for active players.
I imagine being top in division doesn't matter much to the really hardcore people, but to more casual players it probably does. To that end, giving more casual players an advantage in bonus pool seems a neat trick.
It's not really an advantage though, because relatively speaking you're not advancing any faster than other players in your division. Say you go 7-0 in your first 7 games, and you're a Gold-level player. After 7-0 you may be facing low-mid Diamond players, so you lose maybe one or two games until you start playing Gold players again. From that point on you'd go 50-50, meaning you'd have a record of 57-52... 67-62... 107-102. You wouldn't be the only person in your division to achieve this, and you'd no doubt see others in your division with similar records. If you were to go inactive for an extended period of time, only the variance in potential opponents increases, so while you may get a Silver player to fight when you return, it's just as likely you'd face a Platinum player, and you'd gain or lose points accordingly.
As an edit: I have a little bit of familiarity with GLICKO since I do a lot of tabletop wargaming and we've had leagues governed by GLICKO before, and I seem to remember the uncertainty factor in GLICKO increases if you go a long period of time without playing games.
And a second question, while I think of it.
Does bonus pool accumulate from launch, or from when somebody registers an account? I bought my copy launch day, but if new accounts gain bonus pool from the time the account was registered, it may be much harder for the system to track and discount it. Just a thought.
From launch. The current bonus pool for newly-placed teams/players is around 330 I believe.
Another proposition to explain why people get stucked in a league:
Say B is in Bronze but has high MMR and can get matched with Platinum players. However, because of high sigma, B is often matched against opponents of various skill levels. Furthermore, because of lack of data (the ladder is less than 1 month old), his opponents often have high sigma, too, which lead to sporadic win and losses that never quite reduce his sigma.
Another explanation is B is playing from a different time zone. (Always "Expanding Searches")
If these are true, the matching system will improve over time.
On August 15 2010 18:20 vanick wrote: Got a new update to the promotions data. This time the dataset is 56.5k league changes, around twice what we had before.
I'm not going to post the full graph unless someone really wants to see it; it looks the same as the first full graph here and all the interesting stuff happens in the 5-60 games slice.
Updated Graph:
The results are pretty similar to last time. The bump at the 12-15 game mark is a little more pronounced. After hearing an interesting argument, it's possible there is no checkpoint at 30 games. It's possible that the majority of players have their MMR/sigma criteria fall within certain levels by that point as the system converges quickly.
I don't know what exactly you raw data looks like but I think it would be interesting to see if their are any visible difference in the different leagues when it comes to premotions/demotions. Does the Diamond graph look signicatently different than the Plat or Gold graph?
With your note about only 1800 premotions over 100 games played. I am a High plat player 65-50, but i am Streaky as hell, for example i have gone 19-8 and 3-12. I think it would be interesting to see if i(or someone else in my position) could get Diamond on a second account in under 30 games played or would i(or someone else in my position) place lower because the number of complete clueless poeple has decreased.
On August 15 2010 18:20 vanick wrote: Got a new update to the promotions data. This time the dataset is 56.5k league changes, around twice what we had before.
I'm not going to post the full graph unless someone really wants to see it; it looks the same as the first full graph here and all the interesting stuff happens in the 5-60 games slice.
Updated Graph:
The results are pretty similar to last time. The bump at the 12-15 game mark is a little more pronounced. After hearing an interesting argument, it's possible there is no checkpoint at 30 games. It's possible that the majority of players have their MMR/sigma criteria fall within certain levels by that point as the system converges quickly.
I don't know what exactly you raw data looks like but I think it would be interesting to see if their are any visible difference in the different leagues when it comes to premotions/demotions. Does the Diamond graph look signicatently different than the Plat or Gold graph?
With your note about only 1800 premotions over 100 games played. I am a High plat player 65-50, but i am Streaky as hell, for example i have gone 19-8 and 3-12. I think it would be interesting to see if i(or someone else in my position) could get Diamond on a second account in under 30 games played or would i(or someone else in my position) place lower because the number of complete clueless poeple has decreased.
While we don't have that data broken down, I have a feeling it probably wouldn't look too much different. If the matchmaking system is doing its job, then everyone will start finding fair games after about the 10th game. After a few matches against evenly-matched opponents it should be able to gauge whether you deserve to be promoted or demoted.
How does bonus pool factor in when somebody is promoted/demoted across division?
If a new player has 300 bonus pool, placement takes them to Platinum, plays through their 300 bonus pool there, and is then promoted to diamond, is their 300 used bonus pool taken account of in their new diamond rank?
It seems like it must be, because if it weren't, then a player who placed diamond would automatically be ahead of a player who placed platinum and was then promoted to diamond.
I am really trying hard to wrap my head around bonus pool, but it seems so strange. If they're not counting it for matchmaking, then it seems totally unnecessary.
Since everybody gains bonus pool at the same rate, all it will do is slowly inflate everybodies points and make it so even with perfect 50/50 win/loss ratios, everybodies points will gradually go up.
I also remember reading something on the Blizzard site at one point saying accounts have a cap on how much bonus pool they can have saved up. Why cap it if it's not being counted?
On August 21 2010 06:08 Ketara wrote: I am really trying hard to wrap my head around bonus pool, but it seems so strange. If they're not counting it for matchmaking, then it seems totally unnecessary.
The bonus Pool Filters inactive players to bottom of the rankings that are displayed. they don't do much else as far was we know.
You can sort of get an idea as to what is happening. After placement I was getting paired against Diamond players immediately. I played against some Platinum players, but they were all Platinum players who had very few games played and a high win ratio, which suggests their MMR was well within Diamond range.
lol This system is harsh, I'm ranked 1st in 2v2 Plat and Diamond in 3v3, it cut 200~ points after the Diamond promotion. In 1v1 I got Plat after the first 5 qualifying games, and the matchmaking system only seems to put me up against Diamond players, many whom are ranked in the top 5 in their divisions with 150-300 games...
It's so confusing how it works, I just don't consider that a Plat player with 5 games should be immediately be playing top Diamond players with 300 games, but I did win half of them so I guess in some bizarre sense, the matchmaking system actually equalizes players with same skill.
I guess understanding the sigma system, I have overall exactly 60 wins, 20 losses which yields a high sigma that in turn, the system is putting me against players of equal sigma?
Also there is one thing I wonder about...if you lose allot after gaining a promotion can you get demoted because your performance is declining?
On August 21 2010 10:40 ChaseR wrote: lol This system is harsh, I'm ranked 1st in 2v2 Plat and Diamond in 3v3, it cut 200~ points after the Diamond promotion. In 1v1 I got Plat after the first 5 qualifying games, and the matchmaking system only seems to put me up against Diamond players, many whom are ranked in the top 5 in their divisions with 150-300 games...
It's so confusing how it works, I just don't consider that a Plat player with 5 games should be immediately be playing top Diamond players with 300 games, but I did win half of them so I guess in some bizarre sense, the matchmaking system actually equalizes players with same skill.
I guess understanding the sigma system, I have overall exactly 60 wins, 20 losses which yields a high sigma that in turn, the system is putting me against players of equal sigma?
Also there is one thing I wonder about...if you lose allot after gaining a promotion can you get demoted because your performance is declining?
You can't automatically assume that sigma is a result of win/loss ratio. Did you go 0-20 then 60-0? Then you probably have an extremely high sigma. Did you go 15-4 then 15-4 then 15-4 then 15-4? You probably have a high sigma. Did you go 40-0 then 20-20? You probably have a very small sigma. The system recognizes recent trends, not overall ones.
And yes, you can get demoted for declining performance after a promotion. You're never "locked" into one league.
If Chaser's MMR has a high range, it would actually make sense to match him against a high diamond player with 300+ games.
A high diamond player with 300+ games would represent a good benchmark for opponent. While the high diamond player's MMR mu and MMR sigma doesn't move much with either result. Chaser's sigma will significantly decline because he's matched against a player that the system recognized as more certain.
Is my understanding correct or did I misunderstand anything. Please give me some hint.
I think that in most cases, you've got it right. It's pretty likely that a 300-game player is going to be considered stable and would therefore have a small sigma, but there's no way to be certain, because if that player happened to have a wild streak going on then his sigma would be larger. I think your understanding is correct, though.
This system is really confusing if you massgame a bunch (i.e. narrow your sigma), then suddenly "reach a new level" of play.
After ~25 games, I was put into diamond with ~375 rating. The next 55 games or so I only managed to get another 50-60 points, putting me at around 425. I'm guessing at this point, the system is fairly sure of where it has put me in the ladder, and my sigma is pretty small.
However after that I stopped massgaming and started playing against practice partners. I experienced a pretty significant jump in skill. Now I'm regularly playing people that are 600-800 rating, and I'm only getting 10-14 points per match (the system regularly tells me that I am "even" with these people). Then I'll play someone who is 500-600, and they'll void ray rush me or something, and I'll lose those points. It's incredibly frustrating. I wonder how long it will take before I can start climbing the ladder again?
I just played an 852-rating player, and I'm at 44X. The system said we were even, and I only got 14 points for the win (+ bonus pool). That seems pretty messed up.
I don't really understand why there needs to be a seperation between MMR and "points" in addition to all this.
All I'm really gathering from this is your listed points is not a good indicator of how skilled you are. Obviously a 1000 point diamond player is likely better than a 300 point diamond player, but a 900 point diamond player may well have a higher MMR and be more expected to win vs. the 1000 point player.
I can understand breaking things into 100 person divisions, as a way to give casual players a smaller box to operate in and not make them concerned over a big picture. But I can't understand why the listed points is seperate and the MMR is not shown. Is it really just so bonus pool can sift out inactive players?
I don't know if this has been said before but if you have a provisional player without enough games to establish a stable MMR, a win or loss for the opponent should affect the opponent's ranking at all since all that would do is propagate newcomer MMR volatility.
It's good to understand that points isn't equivalent to MMR and MMR is the better indication of skill on the ladder. Good work, Excallibur.
On August 23 2010 04:28 BlasiuS wrote: This system is really confusing if you massgame a bunch (i.e. narrow your sigma), then suddenly "reach a new level" of play.
After ~25 games, I was put into diamond with ~375 rating. The next 55 games or so I only managed to get another 50-60 points, putting me at around 425. I'm guessing at this point, the system is fairly sure of where it has put me in the ladder, and my sigma is pretty small.
However after that I stopped massgaming and started playing against practice partners. I experienced a pretty significant jump in skill. Now I'm regularly playing people that are 600-800 rating, and I'm only getting 10-14 points per match (the system regularly tells me that I am "even" with these people). Then I'll play someone who is 500-600, and they'll void ray rush me or something, and I'll lose those points. It's incredibly frustrating. I wonder how long it will take before I can start climbing the ladder again?
I just played an 852-rating player, and I'm at 44X. The system said we were even, and I only got 14 points for the win (+ bonus pool). That seems pretty messed up.
yeah it's exactly like that for me. imo the system should throw bonus points at you until you're at the level that you're supposed to be at.
On August 23 2010 05:25 skindzer wrote: Im 770~ diamond and just got matched against a 280 points platinum who had only played like 25 games wtf?
Is it possible that 2v2 rankings affects this?
Not after your initial placement game. If you got paired against a 280 Platinum player then there's a good chance he's got a record like 20-5. If you take a look at my match history I was paired against a couple 700ish Diamond players within my first ten or so games.
EDIT: Specifically:
9: Protoss (Diamond 95-69 654, loss, -1) <-- Record at the time was 7-1, coming off a 2-0 streak versus ~400 Diamond players 15: Sixto (Diamond 262-231 744, loss, -2) <-- Record at the time was 10-4, coming off a 2-0 streak versus ~500 Diamond players
On August 23 2010 04:28 BlasiuS wrote: This system is really confusing if you massgame a bunch (i.e. narrow your sigma), then suddenly "reach a new level" of play.
After ~25 games, I was put into diamond with ~375 rating. The next 55 games or so I only managed to get another 50-60 points, putting me at around 425. I'm guessing at this point, the system is fairly sure of where it has put me in the ladder, and my sigma is pretty small.
However after that I stopped massgaming and started playing against practice partners. I experienced a pretty significant jump in skill. Now I'm regularly playing people that are 600-800 rating, and I'm only getting 10-14 points per match (the system regularly tells me that I am "even" with these people). Then I'll play someone who is 500-600, and they'll void ray rush me or something, and I'll lose those points. It's incredibly frustrating. I wonder how long it will take before I can start climbing the ladder again?
I just played an 852-rating player, and I'm at 44X. The system said we were even, and I only got 14 points for the win (+ bonus pool). That seems pretty messed up.
yeah it's exactly like that for me. imo the system should throw bonus points at you until you're at the level that you're supposed to be at.
Well, that's sort of how it works now. On the loading screen, whenever you see "Favored", that match will be worth more points if you win and worth less points if you lose. Favored status is determined by your opponent's MMR compared to your current points, and when the deficit is large, you're basically getting free points.
If I have 1500 MMR and 300 rating and you have 1500 MMR and 1000 rating, you'll appear as Favored to me and I'll appear as Favored to you. The end result is that one of us rapidly moves toward his MMR whereas the other will lose minimal points. It's going to be like that for a while until your MMR and displayed rating converge, which is when you'll start seeing yourself as Favored and Teams Even more and more frequently. They're not "bonus points" in the sense that they're deducted from your bonus pool, but functionally they're very similar.
On August 23 2010 04:28 BlasiuS wrote: This system is really confusing if you massgame a bunch (i.e. narrow your sigma), then suddenly "reach a new level" of play.
After ~25 games, I was put into diamond with ~375 rating. The next 55 games or so I only managed to get another 50-60 points, putting me at around 425. I'm guessing at this point, the system is fairly sure of where it has put me in the ladder, and my sigma is pretty small.
However after that I stopped massgaming and started playing against practice partners. I experienced a pretty significant jump in skill. Now I'm regularly playing people that are 600-800 rating, and I'm only getting 10-14 points per match (the system regularly tells me that I am "even" with these people). Then I'll play someone who is 500-600, and they'll void ray rush me or something, and I'll lose those points. It's incredibly frustrating. I wonder how long it will take before I can start climbing the ladder again?
I just played an 852-rating player, and I'm at 44X. The system said we were even, and I only got 14 points for the win (+ bonus pool). That seems pretty messed up.
yeah it's exactly like that for me. imo the system should throw bonus points at you until you're at the level that you're supposed to be at.
Well, that's sort of how it works now. On the loading screen, whenever you see "Favored", that match will be worth more points if you win and worth less points if you lose. Favored status is determined by your opponent's MMR compared to your current points, and when the deficit is large, you're basically getting free points.
If I have 1500 MMR and 300 rating and you have 1500 MMR and 1000 rating, you'll appear as Favored to me and I'll appear as Favored to you. The end result is that one of us rapidly moves toward his MMR whereas the other will lose minimal points. It's going to be like that for a while until your MMR and displayed rating converge, which is when you'll start seeing yourself as Favored and Teams Even more and more frequently. They're not "bonus points" in the sense that they're deducted from your bonus pool, but functionally they're very similar.
Won't the Top players MMR just keep growing and growing unless their is a cap(take a look at the old and new wow PVP ranking system). Then won't we start to get large gaps/pockets of players. Then won't those players Queue start to get longer and longer for a quick match and won't they start playing the same 20-30 people over and over again?
On August 24 2010 11:05 Calidus wrote: Won't the Top players MMR just keep growing and growing unless their is a cap(take a look at the old and new wow PVP ranking system). Then won't we start to get large gaps/pockets of players. Then won't those players Queue start to get longer and longer for a quick match and won't they start playing the same 20-30 people over and over again?
In WoW, there was a hard cap (it was 3000). I'd suppose that SC2 works in a similar way. The queue for top players in WoW wasn't bad because the search area was pretty generous. In long queues it was common for teams to get matched up despite their MMRs being like 500+ apart.
Sorry to revive a several day old thread, but to note, I think a large bit of evidence will be whether the inflation slows down or not in the coming months.
On August 28 2010 16:41 ktimekiller wrote: Sorry to revive a several day old thread, but to note, I think a large bit of evidence will be whether the inflation slows down or not in the coming months.
The inflation is going to be at a set rate. That is, 12 or so (or however quickly the bonus pool accumulates) points per day in inflation probably until the day the ladder is reset at the end of the season.
Don't feel bad about bumping this thread, either. There has been constant activity in this thread every few days since it was posted at first.
Thanks for all the details Excalibur_Z! That was really informative. Do you also know how the displayed point evolves after a league promotion?
I have a friend who is stuck in gold, while playing against diamond. I told him it was normal, his winning ratio was too high for the system to be confident about his skill (sigma too large), and that when he would be promoted, he would be bumped directly into diamond.
However it looks like you lose a lot of points when you get promoted, so does it makes sense to lose on purpose to narrow your sigma sooner, and be promoted sooner without wasting all the points you get at plat?
On August 29 2010 10:30 gondolin wrote: Thanks for all the details Excalibur_Z! That was really informative. Do you also know how the displayed point evolves after a league promotion?
I have a friend who is stuck in gold, while playing against diamond. I told him it was normal, his winning ratio was too high for the system to be confident about his skill (sigma too large), and that when he would be promoted, he would be bumped directly into diamond.
However it looks like you lose a lot of points when you get promoted, so does it makes sense to lose on purpose to narrow your sigma sooner, and be promoted sooner without wasting all the points you get at plat?
We need more data on this, so I urge people to post full match histories like I did on page 8, if they haven't played any ladder matches yet in a particular bracket or team. One theory that Angstrom on the Bnet forums had was that the point deduction involves a "league multiplier", this was how he applied it to my point loss:
Disparity between points: 63 Net points from winning vs plat: 110 points lost vs plat: -8
1/2 points from plat toward diamond = -55 double points lost from losing plat = -8 There's your 63 points.
Wins from plat give 1/2 points toward diamond, and losses from plat cost 2x as much to your diamond points?
Refinement: Assumptions: You have points in every league within your bracket. You can only play players in leagues directly under you, your leagues, and leagues above you. Points shown are pre-adjusted to match your league. (i.e. 10pts from a win in -1 is actually a 20pt game, but pre-adjusted to show 20*.5)
Multipliers on adjusted (what you see when you win the game) points:
Wins in platinum league: Versus a Gold player: 1x to platinum and under, .25x to diamond Versus a Plat player: 1x to platinum and under, .5x to diamond Versus a Diamond player: 1x to diamond and under
Losses in platinum league: Versus a Gold player: 1x to platinum and under, 4x to diamond Versus a Plat player: 1x to platinum and under, 2x to diamond Versus a Diamond player: 1x to diamond and under
It would be interesting to see if that holds true for other point loss, as well as whether the point loss is more severe when you move across multiple leagues (because you'll have more games against players of lower leagues).
Great, thanks a lot! It's really fun reverse engineering the system, you did a great job!
If this is true this mean two things: 1) When you get promoted to diamond, your points get converted as if you were in diamond since the beginning. So there is no reason to try to get promoted sooner. 2) Since the point loss depend on the match history, there is no way to compare points across leagues.
But it should be possible to compare points between division, when they have started to converge, right?
On August 29 2010 12:11 gondolin wrote: Great, thanks a lot! It's really fun reverse engineering the system, you did a great job!
If this is true this mean two things: 1) When you get promoted to diamond, your points get converted as if you were in diamond since the beginning. So there is no reason to try to get promoted sooner. 2) Since the point loss depend on the match history, there is no way to compare points across leagues.
But it should be possible to compare points between division, when they have started to converge, right?
I have no reason to believe that points are not comparable across divisions. Of course, we have no proof, but some players have said that divisions carry some kind of point averaging which allows the highly-ranked players to prop up the casual players. The theory there is that if you play against someone from a division with a high point average and you are part of a low point division, you will earn more points for a win. If that is true, then points are almost completely meaningless because your points are weighted further against others in your division.
I don't believe this to be true. Everyone gets access to the same amount of bonus pool which means the rate of inflation is the same. Everyone plays against the same player pool (roughly). If you take a look at SC2Ranks, you can see that the point totals of players roughly coincide with the Blizzard Top 200 rankings which we know to not be based on points. It would just make too little sense to have divisions be that... well... divided from each other.
The only reason I would say the idea they keep track of your points across every league is wrong, is that seems far more complicated than it needs to be. Since it doesn't have to place your points exactly where you are, it just has to make sure you aren't going to be #1 in Diamond with 1,400 points cause you were promoted from 1,400 in Platinum.
I have one question: if you only play when you have bonus pool points available and stop when you run out, is this "abusing" the system (getting to a bigger point value than you would if you just massed games)?
No. You can think of the bonus pool as a constant inflation in the number of points. This is useful to prevent people from having lucky streaks and stop playing before reaching equilibrium: if they stop playing, the will be depassed by people at equilibrium using the bonus pool.
So you can't really "abuse" the system with the bonus pool, you just need to consume it so that you can use the inflation induced by it. Once you have reached the equilibrium (assuming you don't progress), you will hover at it, with a bonus pool or not. The only difference is that with the bonus pool, your equilibrium point will be moving up (because of the inflation).
On August 30 2010 06:40 Vei wrote: I have one question: if you only play when you have bonus pool points available and stop when you run out, is this "abusing" the system (getting to a bigger point value than you would if you just massed games)?
No because the bonus pool system is designed to quickly get you to where the system believes you belong. If the inflation is 100 points a week and you stop playing for two weeks, you'd probably have close to 200 points in the bank when you come back, but even if you earn all those points you'd still be on par with people who didn't take a break.
On August 30 2010 15:53 Subversion wrote: this is really cool and all, but the system just so often seems to do the weirdest things that aren't accounted for by this kind of analysis
i dont know if its just buggy as hell or if we're missing something.
for example its been pretty much proven that you will not be promoted without losing any games. but the OP flat out denies this.
meh, i dont really understand how to apply this to the actual BS we see online =/
I have no doubt that we're missing some things because obviously there are some unanswered questions out there. I had this sweet sample game list to illustrate the concept but it was going to have so many inaccuracies that it wouldn't be reliable and people would just get hung up on analyzing the made-up numbers rather than following the trend.
Anyway, Shadowed hooked us up with some numbers that showed several examples of people with perfect records getting promoted. It all has to do with who you play against. If you're winning games you're expected to win and sigma decreases enough, you'll get promoted. Losing games you're expected to lose will cause sigma to decrease as well. It's all about reaching that MMR-sigma*3 > threshold point.
You can get a rough estimate of how close you are to promotion by the range of opponents you're facing. Playing a 300 Diamond followed by an 800 Diamond? You may still be far from promotion. Playing a 500 Diamond followed by a 450 Diamond? You may be pretty close. There are some factors that confuse things like how much bonus pool your opponents have consumed (for best accuracy they'd need to have consumed most or all of it) and how many games they've played (whether or not their point value is close to their MMR), but you should be able to get some vague idea of where you stand.
Can someone explain to me why during my placement matches I got paired up against 3 Plat lost to all of them, 1 Bronze, and 1 Silv won against both. It put me in Bronze, and now I'm sitting there playing against people who's w/l are in the hundreds, and when I do get promoted to Silver, the match making starts putting me up against plat players? I'm roughly 10-20 right now. Now, it may be just me, but I don't think Match Making is working correctly, since I beta I was in Gold the entire time (After one of the wipes I was thrown into silver and then climbed my way back to gold.) And now I'm having difficulty winning games in copper >.>
On August 30 2010 06:40 Vei wrote: I have one question: if you only play when you have bonus pool points available and stop when you run out, is this "abusing" the system (getting to a bigger point value than you would if you just massed games)?
Coming back to your post: if you want to "abuse" the system, you could procede as follow. Let assume that you are able to determine your equilibrium rating A and your sigma. By definition of the equilibrium, and forgetting about bonus points for now you will hover at A + or - \lambda sigma, according to whether you have lucky or unlucky streaks. And the higher the lambda the more unlikely it is to reach it (it is quite easier to reach A +sigma than A+3sigma). So without inflation, when you reach A+3sigma, you could stop playing.
Now with the bonus pool, this won't work. But you could use a strategy like that: while my rating - unused bonus pool is larger than A+2 sigma I don't play, and when it goes below play until my rating -unused bonus pool is larger than A + used bonus pool + 3sigma. This way you can keep being +2-3 sigma above your 'true' rank.
Excalibur_Z: How can it be that I'm constantly matched with much higher (visibly) rated players (like +100 - 300 points more than me, I'm diamond 750), but it's even matched all the time so I get few points when I win and lose a lot when I lose? I thought the system tries to bring me close to my MMR as soon as possible, whereas I have the impression that it's slowing me down.
On August 31 2010 04:29 heishe wrote: Excalibur_Z: How can it be that I'm constantly matched with much higher (visibly) rated players (like +100 - 300 points more than me, I'm diamond 750), but it's even matched all the time so I get few points when I win and lose a lot when I lose? I thought the system tries to bring me close to my MMR as soon as possible, whereas I have the impression that it's slowing me down.
I have no idea, sorry. Maybe those people just came off some losses and pushed their MMR down to "even" levels with you? Maybe 300 points still qualifies as "even"? Do you have a large amount of unspent bonus pool? There are a lot of possibilities for this, unfortunately.
I'm too lazy to read all the posts and even the op but I skimmed some. I just had an even game against a gold player and I got about 20 points for the win. I'm in diamond. I've been getting about 20 points beating 700-900 diamond players. At the end of the game it said I was evenly matched with the gold player. The games with the 700-900 players it also said I was evenly matched and I had half their points at the time. I wonder if it accounts for matchups or maps or something since I go random?
On August 31 2010 13:44 guitarizt wrote: I'm too lazy to read all the posts and even the op but I skimmed some. I just had an even game against a gold player and I got about 20 points for the win. I'm in diamond. I've been getting about 20 points beating 700-900 diamond players. At the end of the game it said I was evenly matched with the gold player. The games with the 700-900 players it also said I was evenly matched and I had half their points at the time. I wonder if it accounts for matchups or maps or something since I go random?
Please don't bring the "I'm too lazy to read this thread or even the OP" into this thread. It's too easy for long posts like the OP to be ignored and this thread cluttered with posts like yours. Go back and look at the Gold player you played that it said was an even match. Chances are he's been playing Diamond-level players for a while or his win ratio is very high with few games played. His MMR is close to your displayed rating, so it was an even match. He saw you as favored on the loading screen and lost minimal points for that game.
Let's see if I Got this straight if i were the lowest possible bronze and the highest diammond logged in my acc and done, let's say ... 30 wins in a row, he would still need to lose and probably would be climbed straight to gold or plat ?
On August 30 2010 06:40 Vei wrote: I have one question: if you only play when you have bonus pool points available and stop when you run out, is this "abusing" the system (getting to a bigger point value than you would if you just massed games)?
The short answer is yes. If you are maintaining a 50% win ratio, then the extra bonus points will push you higher than if you had massed games. The chances for a net loss of points are increased through massing games because you don't have bonus points to cushion your losses, and there are factors beyond the game such as mental fatigue that can contribute to an overall decline.
Relatively speaking, though, it doesn't have much of an overall impact because everyone the bonus pool accumulates at the same rate for everyone. At a 50% win ratio, you'll basically be riding the wave of inflation just like everyone else.
Just thought I'd add in my experience. Having just started my second account and knowing that I'm a Diamond player, it took me 34 games to be promoted to Diamond.
My placement matches were TERRIBLE. I played 3 high level Diamonds and 2 people also doing their placements (wtf?). Needless to say, I went 3-2 and was placed in Silver-- I felt disgusted at my luck. But I had faith in the system to put me in the right place. Almost immediately, I was playing and beating 700+ Diamonds (as a Silver, must suck for them). Anyway, I was promoted to Gold around ~14 games, then promoted again to Platinum at 24 games, and finally to Diamond at 34; I was 20-14.
My last 5 matches before promotion went like this:
Me vs 600 Diamond - Loss Me vs 500 Platinum - Win Me vs 500 Gold (wtf?) - LOSS!? Me vs 700 Diamond - Win Me vs 700 Diamond - Win Promoted to Diamond.
The points are approximate, but accurate enough. I hope I've helped at least a little-- perhaps I can go back later and get a more detailed match history.
It's been said a couple times in this thread-- honestly, just have faith in the system. Yeah, you might be one of those unfortunate ones that get stuck in Platinum (lol Cauthon), but whatever you do, don't lose on purpose. Yeah, you might need some losses for the system to finally feel comfortable about placing you, but the losses will come eventually, don't cheat yourself and throw games.
My first account hit Diamond almost immediately... but that was near launch. I imagine it must have been significantly easier to achieve that back then?
Regardless, good luck fellas!
edit: Forgot to add that I think I got pretty damn lucky on my points! I still have some bonus pool left! I was #1 Platinum before promoted (it was a brand new division) at around 480pts. When I was placed in Diamond, I had 465pts. I'll take that.
That Gold player probably had something like a 17-3 record though. I'm sure that guy will end up in Diamond soon. Thanks for the report, it's too bad there aren't more details though =)
I have just a couple of small comments to make on the OP to clarify the TruSkill system.
I am a research associate at the University of Saskatchewan. I have corroborated in the past with one of the designers of TruSkill for my own implementation of the TruSkill algorithm for Go ratings purposes.
First, the outcome of a game always decreases both players associated sigmas - both expected outcomes and unlikely outcomes. This is contrary to what is stated in the OP. I see in other posts that you suggest this is the case, but you might want to update the OP to reflect this.
The way uncertainty is added to the system to account for skill drift (e.g. learning) is through another factor (TruSkill calls tau). The process is to simply add (in quadtrature) a constant amount (or an amount based on the amount of time between games) of uncertainty between every game.
I got promoted to platinum couple of days ago upon losing a match xD
Too bad that same leagues have so much skill discrepancy. I beat Diamond players no problem and they say I should be in Diamond then comes a Platinum or even Gold player and runs me to the ground.
On September 02 2010 03:18 LiQuidTalon wrote: That may be accurate for TruSkill; however, I have reason to believe that unexpected outcomes in SC2 do NOT decrease the certainty values.
If Blizzard increases uncertainty after a unexpected outcome, than they do so contrary to Bayesian Inference and Information theory.
Having sigma always decrease after an outcome isn't a flaw in the way TruSkill works. Consider that each game outcome is a piece of information and the sum of all player sigmas is the degree to which you are uncertain about the system as a whole. How can a new piece of information make you less certain about the system as a whole. This is irrational. New information can only make you *more* certain about the system as a whole, otherwise it wouldn't be information.
The correct way to account for skill changes is the way TruSkill works: to add in quadrature a best estimate of skill volatility between every game. The point of contention becomes how much volatility to add. Add to much, and the system remains uncertain even about stable players. Add to little and the system reacts slowly to quickly increasing/decreasing players. It is a trade-off.
I imagine Blizzard like the TruSkill implementation I am familiar with, use a global variable as it would be quite computationally intensive to try and come up with a time dependent player dependent variable. Perceived flaws in TruSkill and systems like this probably come about because players skill increases too fast for the system to account for; but the system designers have to think of the whole and not of a small percentage of players.
I guess my suggestion to the OP would be to describe the TruSkill algorithm as accurately as possible as it is probably the best starting point to understanding Blizzard's hidden algorithm, then explain how he thinks Blizzard's system might deviate from this based on collected evidence.
I also think Blizzard should publish their algorithms (at least a paper on the mathematics not necessarily the codebase) and make the underlying match making variables known --- not just the semi-useless points they have now.
I think there are definite differences between Blizzard's SC2 and WoW Arena systems and TrueSkill. We borrow some concepts from TrueSkill because the information is published, but we're not saying that Blizzard uses an implementation of TrueSkill. In WoW Arena, where the MMR is visible, the change of MMR increases during a streak. Vanick says that means that either sigma increases as we've argued here, or the skill drift factor is per-user, is updatable, and is functionally very similar. Either way, the end result in rating update is the same (in the theoretical Blizzard system) and there's no way for us to make a distinction because the information isn't readily available. Sigma increasing is not impossible in TrueSkill, and to my knowledge is not contrary to Bayesian inference.
I have read your ladder analysis and I must say it explained a lot to me. I also played WoW Arena couple years ago, 2150 rating!, so it felt all familiar. MMR is the main ingredient in your summary. But I have a problem with your assumption between MMR and the public ladder.
Let me start with these 2 statements. (1) When you promote you lose points. (2) I started in Bronze league, 100 games later I find myself in Platinum league. Also I have been playing against Platinum players while being in Gold.
My problem: In the 100 games I played I almost always played against slightly more favored people. Except when I was topping my division and promotion was near. According to you this indicates that my public rating is trying to get higher to get closer to my MMR
Now with promoting from Gold to Platinum I lost a bit more than 200 points. But this doesn’t make sense if there is such a big correlation with your MMR. I know that everybody loses points when they promote. It is not about my QQing over my points. But I like to understand why.
When I -as gold player- played against a platinum player than this player was always (slightly) favored. This means that my public rating is lower as the average platinum player his hidden MMR. In your analysis you assume that MRR and Public rating try to reach the same amount. You also assume that your MMR needs to exceed a certain number to qualify for promotion. One of these 2 assumptions is wrong and it seems to be the first. Because it doesn’t make sense that I and others lose points when gaining promotion if obviously your Public rating is lower than the required MMR for platinum.
Unless there is something I am overlooking. Your paragraph about displayed rating is incorrect. You are probably close to the truth but not on it.
PS: Does any1 know if you gain points when you demote? If it is a fixed number of points you lose when you promote or a percentage?
lol i wasnt able to comprehend this post but i realise it was alot of effort and judging from the great feedback others have given you seem to have hit the nail on the head, so well done sir.
On September 02 2010 22:48 Koshi wrote: I have read your ladder analysis and I must say it explained a lot to me. I also played WoW Arena couple years ago, 2150 rating!, so it felt all familiar. MMR is the main ingredient in your summary. But I have a problem with your assumption between MMR and the public ladder.
Let me start with these 2 statements. (1) When you promote you lose points. (2) I started in Bronze league, 100 games later I find myself in Platinum league. Also I have been playing against Platinum players while being in Gold.
My problem: In the 100 games I played I almost always played against slightly more favored people. Except when I was topping my division and promotion was near. According to you this indicates that my public rating is trying to get higher to get closer to my MMR
Now with promoting from Gold to Platinum I lost a bit more than 200 points. But this doesn’t make sense if there is such a big correlation with your MMR. I know that everybody loses points when they promote. It is not about my QQing over my points. But I like to understand why.
When I -as gold player- played against a platinum player than this player was always (slightly) favored. This means that my public rating is lower as the average platinum player his hidden MMR. In your analysis you assume that MRR and Public rating try to reach the same amount. You also assume that your MMR needs to exceed a certain number to qualify for promotion. One of these 2 assumptions is wrong and it seems to be the first. Because it doesn’t make sense that I and others lose points when gaining promotion if obviously your Public rating is lower than the required MMR for platinum.
Unless there is something I am overlooking. Your paragraph about displayed rating is incorrect. You are probably close to the truth but not on it.
PS: Does any1 know if you gain points when you demote? If it is a fixed number of points you lose when you promote or a percentage?
There needs to be some correlation between MMR and displayed rating or else the displayed rating is meaningless and things start to break down. The only disconnect we see between displayed rating and MMR that still keeps things consistent is the bonus pool, which inflates displayed rating for everyone at the same rate. For this reason, we believe any points earned through the bonus pool are ignored when determining favored status. I believe the maximum bonus pool at the time of this post is somewhere around 560.
As far as losing points when you're promoted, we're aware of that but just don't have enough data to explain it. Earlier in this thread, in one of the later pages, I posted one possible explanation offered by someone on the Bnet forums, where point gains and losses are worth more or less based on the league of your opponent. For example, points earned against Diamond players would be worth twice as much as points earned from Platinum players, but points lost to Diamond players would cost you only half as much as points lost to Platinum players. It may be possible that this is how it works when translating your Platinum points to Diamond points at the time of promotion, but until we see more full match histories like the one I made on page 8, we don't have enough concrete data to draw any firm conclusions.
I think that point loss is there to prevent abuse. Since you can't get below 0 in your rating (correct me if I am wrong), you could lose a lot to pull your MMR down, and then climb up the ladder by having "free wins" until you reach your level. Now if the theory of point loss mentioned by Excalibur_Z is correct, the point you gain at bronze are worth 1/2^4 "diamond' points. so the free wins you get don't really get you much diamond points.
On September 02 2010 04:48 CaeZaR wrote: The correct way to account for skill changes is the way TruSkill works: to add in quadrature a best estimate of skill volatility between every game. The point of contention becomes how much volatility to add. Add to much, and the system remains uncertain even about stable players. Add to little and the system reacts slowly to quickly increasing/decreasing players. It is a trade-off.
Yes, but with this system, the sigma can increase even with true skill. Consider this: you add a uncertainty to the sigma, and you win according to what is expected (like when you have a winning streak). Then your sigma will not change much, but since there was uncertainty added, it will increase. Cf:
This makes sense from an information theory point of view: the quantity you are trying to measure (skill) is not fixed, so the quantity of information you have about it may not increase (for an extreme example: consider you switch one player for the other, then you have 0 information on the new player).
On September 03 2010 05:00 gondolin wrote: I think that point loss is there to prevent abuse. Since you can't get below 0 in your rating (correct me if I am wrong), you could lose a lot to pull your MMR down, and then climb up the ladder by having "free wins" until you reach your level. Now if the theory of point loss mentioned by Excalibur_Z is correct, the point you gain at bronze are worth 1/2^4 "diamond' points. so the free wins you get don't really get you much diamond points.
That's possible, but I'm really hesitant to add that to the original post as fact until we get some more data. I asked Vanick to bomb all his 1v1 placement games and tank his MMR, so we'll see when he finally gets promoted whether Angstrom's point translation theory is correct, as well as how quickly his MMR climbs.
I encourage everyone who hasn't played in a particular bracket to start tracking their matches from the beginning, too, and to post full histories in this thread so we can work with more data and figure this thing out.
Currently I'm Gold Rank 1 at 901 points. I only recently started adding the points of my most recent opponents. And I regret not throwing in where my promotions were (as I started out in Bronze).
I'll make another post when I manage to reach diamond glhf
Currently I'm Gold Rank 1 at 901 points. I only recently started adding the points of my most recent opponents. And I regret not throwing in where my promotions were (as I started out in Bronze).
I'll make another post when I manage to reach diamond glhf
No offense, but could you paste the contents of the spreadsheet into this thread, or convert it to txt or something? I don't have Office on my home computer and I'm wary of opening strange xls's on my work computer (particularly since I have macros enabled there).
Map Result Race League / Rank Rank Rating Points Blistering Sands W T Platinum 6 Metalopolis L P Forfeit Forfeit Blistering Sands L P Forfeit Forfeit Stepps of War L P Forfeit Forfeit Metalopolis L P Forfeit Forfeit Kulas Ravine W Z Bronze 33 Desert Oasis W P Silver 7 Kulas Ravine W Z Gold 24 Kulas Ravine W Z Gold 10 Lost Temple W Z Platinum 47 Desert Oasis W P Platinum 24 Blistering Sands W P Platinum 6 Desert Oasis W P Diamond 14 Stepps of War W T Diamond 92 Xel'Naga Caverns L P Platinum 17 Scrap Station W Z Diamond 49 Delta Quadrant W P Platinum 52 Kulas Ravine W P Diamond 75 Scrap Station W Z Diamond 59 Blistering Sands W P Diamond 58 Kulas Ravine W T Diamond 46 Metalopolis W Z Diamond 30 Lost Temple W Z Platinum 79 Kulas Ravine W Z Platinum 12 Stepps of War W P Diamond 67 Metalopolis L Z Diamond 11 Lost Temple W T Diamond 50 Delta Quadrant W T Platinum 23 Blistering Sands L T Diamond 27 Scrap Station W T Match not Found (Suspect Dia) Lost Temple L P Diamond 9 Delta Quadrant L Z Diamond 12 Scrap Station W P Diamond 11 Metalopolis W Z Diamond 26 Blistering Sands W P Diamond 16 Delta Quadrant L P Diamond 9 Stepps of War L T Diamond 1 976 Metalopolis L T Diamond 12 852 Delta Quadrant W Z Diamond 21 808 Lost Temple W P Diamond 44 349 Xel'Naga Caverns L P Diamond 2 901 Metalopolis W P Diamond 1 908 Metalopolis W Z Diamond 40 895 Stepps of War L T Diamond 4 976 Metalopolis W Z Diamond 41 538
Q: Would it take longer to get promoted if you've played lots of games? Assuming someone played a large amount of games (say a 100 with a 50% win/loss ratio). If he were to start winning 70% of his games, would it be harder for him to get promoted than someone with similar percentages but fewer games played? A: It would take longer, yes. If you've played 100 games and gone 50-50, your sigma is probably fairly small because the system feels confident that it's put you where you belong. If someone else has played 16 games and gone 8-8, that person's sigma is going to be larger. The exact scale is something that we don't know, but we do know that your MMR never truly gets "locked" in place (it's always changing to some degree after each win or loss). Depending on where you are in the ladder, you may need to play quite a few more games to increase your sigma before you can decrease it again within the threshold of a higher league, which would make you eligible for promotion.
So that makes demotion kind of an everlasting curse, then? By the time you've built your skill up to where you belong back in the division you were demoted from, you have a lot more games under your belt, and the ladder's going to be a real hardass about promoting you. What effect would having most of your wins at the end of your career have on this situation?
I placed in silver and got demoted because I kept getting fucking dropped from BNet and it counts as a loss whenever that happens. So I was never really bad enough to be bronze, yet here I am, sitting here in the top 5 of my division forever with like a 15 game win streak. Are all my promotions going to be like this because of a fluke demotion fucking with my uncertainty factor or whatever?
Unfortunately, without the opponent rating information, opponent win-loss record, promotion markers, and the amount of points gained and lost per match, there's not too much we can do with this information. The ranks are determined by rating, so it's the rating that we really would need to see. The amount of points gained/lost helps determine how close you are to your MMR. The opponent win-loss record helps identify whether they may be close to their MMR (and therefore validates their rating). For example:
L Diamond 200 20-6 (-4)
That alone doesn't tell us very much, but we can get some info from it. With a 20-6 record, the chances that this guy actually belongs at 200 rating is very low. He was probably recently promoted. The -4 from the loss tells us that he was Favored, which reinforces that his MMR is high (and at the very least, higher than our current rating). Now if we added another game:
W Diamond 600 70-56 (+15)
This, combined with the previous game, tells us that the guy's 600 rating is a little more accurate than the other guy's 200 rating because he has more games played. It also tells us that his MMR is a little closer to our displayed rating because he was only slightly favored. That likely means that our MMR is closer to that area, but we don't know for sure until we see more games.
Now, if we take a look at your last 9 games, we can still get a fair amount of info from them. We don't know how concrete these players' ratings are because we can't see their records, but we can at least assume that if they're in the 900 range that they must be pretty good (inflation is about 570 or so at this point in time). The outliers here are the guy with 349 and the guy with 538, so if you're being matched against them it probably means their MMRs are around that of the 900-level players but they just haven't played enough games to get up that high.
I'd say that a promotion to Diamond is inevitable, but it may depend on the variance in opponents shrinking first. If you're holding your own against 900 Diamond players, you'll just have to even out a bit more to decrease your uncertainty value which will allow promotion.
They are probably using glicko-2. I don't see why they would make up their own system when the algorithm has already been written. It also could be checking every 5 games to see if you have improved enough, I do like the idea of promoting people based on their mean - 2 * sigma though. To prevent players who haven't played in a while from being automatically demoted though, the glicko-2 system sigma decreases really fast and maybe there is a threshold like "after 5 recent games and with a sigma < x or 10 recent games and sigma < 2*x", check promotion status. What I really hate though is the fact that you can't see your real ranking. Maybe though there is a hard cap on the total number of rested points (probably 750).
Maybe the points you gain is based on checking the difference between your real rating and your points.
So say if you have 0 points, but a real rating of 1300, and you win gaining 15 real rating, then your points will increase by 15 + sqrt((1300 - 0)/2) = 15 + 25 = 40 points (20 + 20 rested). This way once rested points are gone and your points and real rating are close.
Just played 6 more matches, now I'm ranked #1 in my division. This is bullshit.
For the record, I'm 51-47 right now.
My last 10 matches: Win, Silver, 125-120, +14 Win, Bronze, 6-6*, +12 Win, Bronze, 11-10*, +14 Loss, Bronze, 47-44, -12 Loss, Bronze, 49-42, -12 Loss, Silver, 20-22, -13 (connection dropped just as I was pushing for the kill, arrrrrgh) Win, Silver, 10-8, +14 Win, Placer, 1-1*, +22 Win, Gold, 77-81, +28 Win, Placer, 3-1*, +20
I only listed their 1v1 stats. All the people with *s are experienced team players who are gold in some team league. The rest have like 5 team games at most.
On September 04 2010 02:23 darmousseh wrote: They are probably using glicko-2. I don't see why they would make up their own system when the algorithm has already been written. It also could be checking every 5 games to see if you have improved enough, I do like the idea of promoting people based on their mean - 2 * sigma though. To prevent players who haven't played in a while from being automatically demoted though, the glicko-2 system sigma decreases really fast and maybe there is a threshold like "after 5 recent games and with a sigma < x or 10 recent games and sigma < 2*x", check promotion status. What I really hate though is the fact that you can't see your real ranking. Maybe though there is a hard cap on the total number of rested points (probably 750).
Maybe the points you gain is based on checking the difference between your real rating and your points.
So say if you have 0 points, but a real rating of 1300, and you win gaining 15 real rating, then your points will increase by 15 + sqrt((1300 - 0)/2) = 15 + 25 = 40 points (20 + 20 rested). This way once rested points are gone and your points and real rating are close.
This way it would take about 100 games or so for your real rating and points to be nearly identical.
Very possible. Glicko and TrueSkill have a lot in common, we just used TrueSkill because its documentation was readily available and it's used commonly in video games. Of course, it would be excellent if we could work out any kind of proper formula, but I think that's outside the scope of threads like this one. Also, they probably changed a bit to suit SC2's unique ladder structure.
On September 04 2010 03:07 Lavitage wrote: Just played 6 more matches, now I'm ranked #1 in my division. This is bullshit.
For the record, I'm 51-47 right now.
My last 10 matches: Win, Silver, 125-120, +14 Win, Bronze, 6-6*, +12 Win, Bronze, 11-10*, +14 Loss, Bronze, 47-44, -12 Loss, Bronze, 49-42, -12 Loss, Silver, 20-22, -13 (connection dropped just as I was pushing for the kill, arrrrrgh) Win, Silver, 10-8, +14 Win, Placer, 1-1*, +22 Win, Gold, 77-81, +28 Win, Placer, 3-1*, +20
I only listed their 1v1 stats. All the people with *s are experienced team players who are gold in some team league. The rest have like 5 team games at most.
Yeah, just from a quick glance, it looks like you'll be fighting for a promotion for some time. Sounds like a lot of your losses are coming from disconnects, so maybe you'll want to identify what the problem is there before continuing to grind up the ladder, because each of those disconnects is going to set you back to Bronze at the rate it's causing you losses.
On September 04 2010 02:13 Excalibur_Z wrote: Unfortunately, without the opponent rating information, opponent win-loss record, promotion markers, and the amount of points gained and lost per match, there's not too much we can do with this information. The ranks are determined by rating, so it's the rating that we really would need to see. The amount of points gained/lost helps determine how close you are to your MMR. The opponent win-loss record helps identify whether they may be close to their MMR (and therefore validates their rating). For example:
L Diamond 200 20-6 (-4)
That alone doesn't tell us very much, but we can get some info from it. With a 20-6 record, the chances that this guy actually belongs at 200 rating is very low. He was probably recently promoted. The -4 from the loss tells us that he was Favored, which reinforces that his MMR is high (and at the very least, higher than our current rating). Now if we added another game:
W Diamond 600 70-56 (+15)
This, combined with the previous game, tells us that the guy's 600 rating is a little more accurate than the other guy's 200 rating because he has more games played. It also tells us that his MMR is a little closer to our displayed rating because he was only slightly favored. That likely means that our MMR is closer to that area, but we don't know for sure until we see more games.
Now, if we take a look at your last 9 games, we can still get a fair amount of info from them. We don't know how concrete these players' ratings are because we can't see their records, but we can at least assume that if they're in the 900 range that they must be pretty good (inflation is about 570 or so at this point in time). The outliers here are the guy with 349 and the guy with 538, so if you're being matched against them it probably means their MMRs are around that of the 900-level players but they just haven't played enough games to get up that high.
I'd say that a promotion to Diamond is inevitable, but it may depend on the variance in opponents shrinking first. If you're holding your own against 900 Diamond players, you'll just have to even out a bit more to decrease your uncertainty value which will allow promotion.
Would there be a reason why I haven't played an even game in a super long time? Every game I play is against a favored opponent and I was favored on their screen as well.
On September 04 2010 03:07 Lavitage wrote: Just played 6 more matches, now I'm ranked #1 in my division. This is bullshit.
For the record, I'm 51-47 right now.
My last 10 matches: Win, Silver, 125-120, +14 Win, Bronze, 6-6*, +12 Win, Bronze, 11-10*, +14 Loss, Bronze, 47-44, -12 Loss, Bronze, 49-42, -12 Loss, Silver, 20-22, -13 (connection dropped just as I was pushing for the kill, arrrrrgh) Win, Silver, 10-8, +14 Win, Placer, 1-1*, +22 Win, Gold, 77-81, +28 Win, Placer, 3-1*, +20
I only listed their 1v1 stats. All the people with *s are experienced team players who are gold in some team league. The rest have like 5 team games at most.
Yeah, just from a quick glance, it looks like you'll be fighting for a promotion for some time. Sounds like a lot of your losses are coming from disconnects, so maybe you'll want to identify what the problem is there before continuing to grind up the ladder, because each of those disconnects is going to set you back to Bronze at the rate it's causing you losses.
I know the cause. It's because the people I live with start using the internet (they're all wired to the router, I'm not.) I'll start playing when I have the internet all to myself, have a good rhythm going, then suddenly someone jumps on to do something and bam, gg.
There's nothing I can do about it except make enough money to find a new place to live. I can't even run a wire under the house, since the crawlspace is filled with sharp rusty gutters and black widows and god knows what else.
I have about 10 losses and 5 draws due to being dropped (a draw happens when you disconnect after you've found a player, but before the match can actually start.)
Awesome analysis, with some points I never considered before. The whole sigma thing and its interactions is interesting.
Especially the interaction of sigma with promotion, and the possible problem/bug is also fun to think about. Running a simulation might uncover this behaviour (it'd be easy to write). I'm sure Blizzard will come up with a fix, anyway. A simple secondary override formula would do it.
And to simplify things for you witches and wizards out there-- Blizzard uses a sorting hat.
If you're good, it takes a while to "grind" your ladder rating up to your MMR. Same for your opponents. When you see "favored" just think to yourself "oh good i'm moving up" don't read it as the ladder trying to screw you over or something like that.
Basically, you shouldn't want to see "even match" because that means you're plateauing
On September 04 2010 02:13 Excalibur_Z wrote: Unfortunately, without the opponent rating information, opponent win-loss record, promotion markers, and the amount of points gained and lost per match, there's not too much we can do with this information. The ranks are determined by rating, so it's the rating that we really would need to see. The amount of points gained/lost helps determine how close you are to your MMR. The opponent win-loss record helps identify whether they may be close to their MMR (and therefore validates their rating). For example:
L Diamond 200 20-6 (-4)
That alone doesn't tell us very much, but we can get some info from it. With a 20-6 record, the chances that this guy actually belongs at 200 rating is very low. He was probably recently promoted. The -4 from the loss tells us that he was Favored, which reinforces that his MMR is high (and at the very least, higher than our current rating). Now if we added another game:
W Diamond 600 70-56 (+15)
This, combined with the previous game, tells us that the guy's 600 rating is a little more accurate than the other guy's 200 rating because he has more games played. It also tells us that his MMR is a little closer to our displayed rating because he was only slightly favored. That likely means that our MMR is closer to that area, but we don't know for sure until we see more games.
Now, if we take a look at your last 9 games, we can still get a fair amount of info from them. We don't know how concrete these players' ratings are because we can't see their records, but we can at least assume that if they're in the 900 range that they must be pretty good (inflation is about 570 or so at this point in time). The outliers here are the guy with 349 and the guy with 538, so if you're being matched against them it probably means their MMRs are around that of the 900-level players but they just haven't played enough games to get up that high.
I'd say that a promotion to Diamond is inevitable, but it may depend on the variance in opponents shrinking first. If you're holding your own against 900 Diamond players, you'll just have to even out a bit more to decrease your uncertainty value which will allow promotion.
Would there be a reason why I haven't played an even game in a super long time? Every game I play is against a favored opponent and I was favored on their screen as well.
On September 04 2010 05:41 pezyuan wrote: Would there be a reason why I haven't played an even game in a super long time? Every game I play is against a favored opponent and I was favored on their screen as well.
"Teams Even" will show up in two situations:
- Early on, when you have a large sigma and few games played, there is a small chance that you will be matched against players whose MMR is close to your displayed rating.
- Once your displayed rating has come close to your MMR, the size of your sigma will determine the chances of encountering even matches. The smaller the sigma (and typically how long you remain at a certain level over more games played), the more likely you'll see an even match.
I want to add a point about bonus pool and "rating inflation".
MMR is completely disconnected from ladder rating, and therefore unaffected by bonus pool. Bonus pool therefore has no cumulative inflationary impact on ladder ratings.
On the flip side, ladder rating is attached to MMR, and will by design converge on your MMR in a damped/stable way. The bonus pool will affect the system by making your ladder rating trend above your MMR (after you manage to reach it). This is not the reason the top players ratings continue to climb.
Think of it this way... if you only play when you have bonus pool, you can expect your ladder rating to float above your MMR by some constant average. As your ladder rating gets too high above your MMR, you will start losing more points for losses than you gain for wins, and no amount of bonus pool will result in you continuing to move up in rating. Likewise, your inflated rating will have no impact on anyone elses point gains, because those are based on your (lower) MMR.
I'm not sure how much (average) inflation you would expect from this. Maybe 150 points, maybe 50... but it does not keep going up over time.
The "inflation" in the ladder is the natural process of (and whole point of) the system. As information is added, the rating distribution becomes smoother, and players that are several standard deviations out in skill will spread out more smoothly in rating (so that in the end Huk and White_ra will get further out in front of Trump, even if he continues to out pace them dramatically in games played)
I don't get this system at all. I was 702 rating in Diamond this morning and I've started doing 1v1 again and this was the result
<Result> vs <rating of opponent> = score change
1) Win vs 1050 = +10 (+10 bonus) 2) Loss vs 1082 = -7 3) Win vs 1022 = +9 (+9 bonus) 4) Loss vs 922 = -16 5) Win vs 1017 = +16 (+16 bonus) 6) Win vs 910 = +12 (+12 bonus) 7) Loss vs 1143 = -16 8) Loss vs 869 = -14 9) Loss vs 1141 = -10 10) Win vs 980 = +10 (+10 bonus) 11) Loss vs 904 = -11 12) Win vs 949 = +11 (+11 bonus)
Some of those just don't make sense at all. Why did I lose 16 rating against an 1143 guy in game 6, and 14 against an 869 guy in game 8? Why so little gain beating the guy in games 1 and 3?
On September 04 2010 07:35 Bibdy wrote: Some of those just don't make sense at all. Why did I lose 16 rating against an 1143 guy in game 6, and 14 against an 869 guy in game 8? Why so little gain beating the guy in games 1 and 3?
Did you read the OP and not understand it, or just read your match history and assume that it is in conflict with the logic and you should post about it?
On September 04 2010 07:35 Bibdy wrote: Some of those just don't make sense at all. Why did I lose 16 rating against an 1143 guy in game 6, and 14 against an 869 guy in game 8? Why so little gain beating the guy in games 1 and 3?
Did you read the OP and not understand it, or just read your match history and assume that it is in conflict with the logic and you should post about it?
I have and the displayed rating makes no sense either. All of my opponents have been well beyond 100 to even 400 games played, so you'd think they would be close to their own MMR by now, but apparently it likes to give me enormous boosts when I beat people with low-rating and doesn't know what to do when I beat someone with a high rating.
Either that, or there's a hell of a lot of people sitting at a high displayed rating, even though their MMR is really low...so why is their MMR so low? You'd think it would be the other way around.
On September 04 2010 07:35 Bibdy wrote: Some of those just don't make sense at all. Why did I lose 16 rating against an 1143 guy in game 6, and 14 against an 869 guy in game 8? Why so little gain beating the guy in games 1 and 3?
Did you read the OP and not understand it, or just read your match history and assume that it is in conflict with the logic and you should post about it?
I have and the displayed rating makes no sense either. All of my opponents have been well beyond 100 to even 400 games played, so you'd think they would be close to their own MMR by now, but apparently it likes to give me enormous boosts when I beat people with low-rating and doesn't know what to do when I beat someone with a high rating.
Either that, or there's a hell of a lot of people sitting at a high displayed rating, even though their MMR is really low...so why is their MMR so low? You'd think it would be the other way around.
Display rating is designed to be relatively stable. MMR is not. If MMR was a stable reflection of skill, what would be the point of the display rating?
You need not "expect" anything about your opponent's MMR, except that you be matched with whoever else is queuing and has one that is close-ish to yours.
On September 04 2010 06:59 taffy wrote: I want to add a point about bonus pool and "rating inflation".
MMR is completely disconnected from ladder rating, and therefore unaffected by bonus pool. Bonus pool therefore has no cumulative inflationary impact on ladder ratings.
On the flip side, ladder rating is attached to MMR, and will by design converge on your MMR in a damped/stable way. The bonus pool will affect the system by making your ladder rating trend above your MMR (after you manage to reach it). This is not the reason the top players ratings continue to climb.
Think of it this way... if you only play when you have bonus pool, you can expect your ladder rating to float above your MMR by some constant average. As your ladder rating gets too high above your MMR, you will start losing more points for losses than you gain for wins, and no amount of bonus pool will result in you continuing to move up in rating. Likewise, your inflated rating will have no impact on anyone elses point gains, because those are based on your (lower) MMR.
I'm not sure how much (average) inflation you would expect from this. Maybe 150 points, maybe 50... but it does not keep going up over time.
The "inflation" in the ladder is the natural process of (and whole point of) the system. As information is added, the rating distribution becomes smoother, and players that are several standard deviations out in skill will spread out more smoothly in rating (so that in the end Huk and White_ra will get further out in front of Trump, even if he continues to out pace them dramatically in games played)
That's possible, but I don't know that I believe in that. In the system you describe, you'd gain bonus points but then inevitably gravitate back toward your MMR. However, say I have 500 unspent bonus pool whereas you've spent all yours and you're 500 points higher than me in the ladder. If we played each other, you would lose more points than me which means your spent bonus pool becomes a liability and effectively works against you. This means that it would be better strategically to just stock up bonus pool as high as possible then mass spend it toward the end of the season.
It seems to contradict the intention of the bonus pool, which is to promote a minimum level of activity. If it does operate in the way you described, then that would be poor design because the incentive to play is lowered the more bonus points you spend. Even worse, once you get to zero bonus pool, the incentive is to not play.
The system as we described it completely ignores bonus pool (both spent and unspent) in all calculations, which conveniently sidesteps that potential pitfall. Not to say that we're absolutely sure that's how it works, but it does prevent gaming the system if it is set up that way.
On September 04 2010 06:59 taffy wrote: I want to add a point about bonus pool and "rating inflation".
MMR is completely disconnected from ladder rating, and therefore unaffected by bonus pool. Bonus pool therefore has no cumulative inflationary impact on ladder ratings.
On the flip side, ladder rating is attached to MMR, and will by design converge on your MMR in a damped/stable way. The bonus pool will affect the system by making your ladder rating trend above your MMR (after you manage to reach it). This is not the reason the top players ratings continue to climb.
Think of it this way... if you only play when you have bonus pool, you can expect your ladder rating to float above your MMR by some constant average. As your ladder rating gets too high above your MMR, you will start losing more points for losses than you gain for wins, and no amount of bonus pool will result in you continuing to move up in rating. Likewise, your inflated rating will have no impact on anyone elses point gains, because those are based on your (lower) MMR.
I'm not sure how much (average) inflation you would expect from this. Maybe 150 points, maybe 50... but it does not keep going up over time.
The "inflation" in the ladder is the natural process of (and whole point of) the system. As information is added, the rating distribution becomes smoother, and players that are several standard deviations out in skill will spread out more smoothly in rating (so that in the end Huk and White_ra will get further out in front of Trump, even if he continues to out pace them dramatically in games played)
That's possible, but I don't know that I believe in that. In the system you describe, you'd gain bonus points but then inevitably gravitate back toward your MMR. However, say I have 500 unspent bonus pool whereas you've spent all yours and you're 500 points higher than me in the ladder. If we played each other, you would lose more points than me which means your spent bonus pool becomes a liability and effectively works against you.
First, happy birthday
My bonus pool isn't really working against me, I just happen to have an inflated rating. As I play games without bonus pool, my rating will trend back towards my MMR. This is in line with the intended purpose of the ladder rating.
On September 04 2010 08:47 Excalibur_Z wrote: This means that it would be better strategically to just stock up bonus pool as high as possible then mass spend it toward the end of the season.
Assuming a WoW style gladiator race, absolutely. Though probably not so much "as high as possible". I suppose you would want to peak your rating, then sit on it and accumulate bonus pool, then at the end, play until you reach your peak rating + the bonus inflation constant (whatever it is) or until you ran out.
On September 04 2010 08:47 Excalibur_Z wrote: It seems to contradict the intention of the bonus pool, which is to promote a minimum level of activity. If it does operate in the way you described, then that would be poor design because the incentive to play is lowered the more bonus points you spend. Even worse, once you get to zero bonus pool, the incentive is to not play.
The system as we described it completely ignores bonus pool (both spent and unspent) in all calculations, which conveniently sidesteps that potential pitfall. Not to say that we're absolutely sure that's how it works, but it does prevent gaming the system if it is set up that way.
You may be falling into the trap of trying to rationalize what you see in numbers with what you think the intentions are. I'm not sure what makes you think bonus pool exists to promote a minimum level of play. I'm also not sure what makes you think that it would work perfectly towards its intended purpose
I wasn't really using any assumptions in my post, so there's not really anything there to "believe" in. Barring a straight up logical flaw, I'm just describing what the bonus pool does to ladder rating (given the MMR system theory is true, which has pretty overwhelming evidence for it). You might be intuiting that there is another hidden bonus pool that also gives you an MMR bonus, but I don't see any evidence for that, and imo it would be a pretty horrible feature in the algo.
I personally assumed the reason for the bonus pool was to de-emphasize the "grind" aspect of laddering. As ratings spread out, players who play a ton of games will tend to stay on the cutting edge of the current spread, and therefore have a huge rank advantage on similarly skilled players who play less games. The bonus pool effectively cuts into this advantage.
I was hoping that they would stop distributing bonus pool to players once they reached a certain rating, like 1000, so that it would not distort the ratings near the top of the ladder and be a temptation for "abuse" to ladder-whore types. (seems this was not realized)
I wasn't saying that MMR inflates or is granted a bonus in any way, just that bonus pool is ignored when matching players and determining Favored status on the loading screen. Like I said, you could be right, it would just be a different design philosophy. As far as the intent of the bonus pool, it's fruitless to debate that because it is what it is, but my view was simply that it fills a similar role to War3's XP decay.
By the method in your post if you happen to go on a streak and use up all of your bonus pool you have an incentive to not play until you have a substantial bonus pool built back up and/or you have been overtaken in rank by a certain number of people. Anything that creates an incentive to not play is bad design.
Further, in our theory, if two people are of equal skill and one plays more than the other the player who plays less only needs to play enough to consume his bonus pool to stay on par with his equally skilled counterpart, provided their points are in sync with their MMRs. Going by how Arena works this means 50-100 games played total. Not a whole lot for a top-end player.
Having bonus points included in the calculations against the MMR makes it so losses become more and more expensive. Therefore if a player plays regularly it would simply cancel out the bonus points. The argument that it helps even out the top end of the ladder does not really hold water because Blizzard is publishing a top200 list that does not match up with the points rankings. If this is the case then bonus points are a totally useless feature since they do not actually help out with the top 200 player rankings.
Finally, we never suggested that MMR has a hidden bonus pool that affects it. If we did then please point it out, since that's wrong. I agree that would be poor design.
On September 04 2010 11:16 vanick wrote: By the method in your post if you happen to go on a streak and use up all of your bonus pool you have an incentive to not play until you have a substantial bonus pool built back up and/or you have been overtaken in rank by a certain number of people. Anything that creates an incentive to not play is bad design.
Again... you're both reading into the intentions of the player and assuming the system is efficient in accounting for them. I agree that Huk has a lot of incentive to use his bonus pool, retake rank 1, then stop laddering. And I doubt this is far from reality (speculation).
For me on the other hand... playing 20 more games might very plausibly result in a skill bump worth 100 rating, so there are other incentives besides preserving my bonus-inflated rating. Not to mention I might still be 100 or 200 points below my skill level even after using up my bonus pool, due to the rapidly expanding rating range.
Further, in our theory, if two people are of equal skill and one plays more than the other the player who plays less only needs to play enough to consume his bonus pool to stay on par with his equally skilled counterpart, provided their points are in sync with their MMRs. Going by how Arena works this means 50-100 games played total. Not a whole lot for a top-end player.
I'm not sure what this is in reference to. I may have missed an update to the OP about bonus pool?
Having bonus points included in the calculations against the MMR makes it so losses become more and more expensive. Therefore if a player plays regularly it would simply cancel out the bonus points. The argument that it helps even out the top end of the ladder does not really hold water because Blizzard is publishing a top200 list that does not match up with the points rankings. If this is the case then bonus points are a totally useless feature since they do not actually help out with the top 200 player rankings.
Well this sort of sums up the whole reason for my post. I am saying exactly what you assume cannot be true (and hoping to point out that it is fairly obvious)... that yes, if you just keep playing, the bonus points basically will just fade away. To counter any argument that bonus rating is somehow discounted from rating adjustments I'm tempted to simply reference occam's razor...
I didn't really say this: "it helps even out the top end of the ladder" but similar. It helps players who play less retain their "rightful" ranks while the ratings are expanding.
As for Blizzard publishing their "top 200" list... this is another thing altogether. In my opinion, publishing these is misleading and pretty ill-advised.
Not only is it completely inaccurate by design (they're almost surely using MMR to make the list) but it very reasonably calls into question the validity of the actual ladder to anyone who doesn't know better (ie most people) which is a pretty dumb thing for blizz to do from a communication standpoint. I can see why they published it at first... it was sort of a sneak peak of what the ladder might look like after it collects a lot more information and becomes more efficient, but it was a bad idea the first time and it's an even worse idea going forward.
The whole point of the ladder rating is to be a stable measure of skill. The whole point of the matchmaking rating is to quickly move people who are mis-rated, and to avoid punishing players who have the misfortune of playing against mis-rated opponents. MMR just so happens to be better as a skill measurement when there is very low data in the system.
Finally, we never suggested that MMR has a hidden bonus pool that affects it. If we did then please point it out, since that's wrong. I agree that would be poor design.
I was just trying to infer some possible idea in which my description didn't paint the whole picture. It was pretty arbitrary and I wasn't trying to put words in anyone's mouth. In the end I still don't understand what part of my post you take issue with.
On September 04 2010 10:59 Excalibur_Z wrote: I wasn't saying that MMR inflates or is granted a bonus in any way, just that bonus pool is ignored when matching players and determining Favored status on the loading screen.
Can you explain what led to this idea? I'm not sure I understand it, and it just seems complex and unintuitive, and therefore unlikely. I'm trying not to come off like i'm doing 'intellectual posturing' or something like that, but I can't help but think you had an idea of what the bonus pool was for and then forced a theory that matched it.
I'm basically just stating what the bonus pool does based on observations and pointing out the misconception about inflation, just like your initial post pointing out (very clearly so) that matchmaking and rating adjustments imply a hidden MMR system.
On September 04 2010 10:59 Excalibur_Z wrote: I wasn't saying that MMR inflates or is granted a bonus in any way, just that bonus pool is ignored when matching players and determining Favored status on the loading screen.
Can you explain what led to this idea? I'm not sure I understand it, and it just seems complex and unintuitive, and therefore unlikely. I'm trying not to come off like i'm doing 'intellectual posturing' or something like that, but I can't help but think you had an idea of what the bonus pool was for and then forced a theory that matched it.
I don't see why you see that idea complex. How complex can it be to just ignore the bonus pool for the rating computation? It's just a global variable!
There are two theories: - bonus pool is used for rating computation. - bonus pool is not used for rating computation.
You support the first theory by saying it is simpler than the other one (you even invoke Occam razor). But I disagree with you: 1) it is not really simpler (it makes the role of the bonus pool harder to grasp than just *ignore it*. 2) There are very good arguments against it: it would lead to abuse. You have never really answered to this argument, taking into account bonus pool is very easily abusable, and I am sure Blizzard wants to prevent abuse (this is the main reason they give for not publishing the system). And this is *very important*, for some Blizzard tourneys in Warcraft 3, the invited player were chosen according to their ranks in the ladder, and they were loads of abuse and controversy with this system.
Anyway the theory is easy to test, we have to see how the average points of people having used their whole bonus pool converge over time.
On September 04 2010 10:59 Excalibur_Z wrote: I wasn't saying that MMR inflates or is granted a bonus in any way, just that bonus pool is ignored when matching players and determining Favored status on the loading screen.
Can you explain what led to this idea? I'm not sure I understand it, and it just seems complex and unintuitive, and therefore unlikely. I'm trying not to come off like i'm doing 'intellectual posturing' or something like that, but I can't help but think you had an idea of what the bonus pool was for and then forced a theory that matched it.
I don't see why you see that idea complex. How complex can it be to just ignore the bonus pool for the rating computation? It's just a global variable!
There are two theories: - bonus pool is used for rating computation. - bonus pool is not used for rating computation.
You support the first theory by saying it is simpler than the other one (you even invoke Occam razor). But I disagree with you: 1) it is not really simpler (it makes the role of the bonus pool harder to grasp than just *ignore it*. 2) There are very good arguments against it: it would lead to abuse. You have never really answered to this argument, taking into account bonus pool is very easily abusable, and I am sure Blizzard wants to prevent abuse (this is the main reason they give for not publishing the system). And this is *very important*, for some Blizzard tourneys in Warcraft 3, the invited player were chosen according to their ranks in the ladder, and they were loads of abuse and controversy with this system.
Anyway the theory is easy to test, we have to see how the average points of people having used their whole bonus pool converge over time.
Ok I really didn't think there were several of you organized around this theory. I still don't see any evidence or reason behind having some constant growing number that is subtracted from everyone's score. As far as I know, if you create an account today you will not have the 600 or whatever accumulative bonus pool, so then there would be a personal bonus pool number and a constant number used to inflate everyones rating?
Anyway I can look at this tomorrow but it still sounds really shaky to me. I still haven't heard any problem with my explanation other than it sounds irresponsible, but I don't see how that makes it less logical or less likely. (it's blizzard, and it's new).
Also remember that it's not THAT exploitable. Like I said, it will only make your rating trend above your MMR (while you have it). This is a big deal at the cutoff rating for invite tourneys, but not a big deal for everyone else.
I feel so outnumbered that I'll definitely review and see if I'm just being crazy (but it's late
On September 04 2010 16:17 taffy wrote: Ok I really didn't think there were several of you organized around this theory. I still don't see any evidence or reason behind having some constant growing number that is subtracted from everyone's score. As far as I know, if you create an account today you will not have the 600 or whatever accumulative bonus pool, so then there would be a personal bonus pool number and a constant number used to inflate everyones rating?
We are not organized around this theory, I don't know Excalibur_Z or Vannick at all. Personally I just find their theory of growing bonus pool more logical and elegant. I was just trying to explain why I find it this way, this is not your case, and you may very well be right: if indeed newer players don't have the whole cumulative bonus pool, then this is not the way blizzard implemented it.
As you say:
Anyway I can look at this tomorrow but it still sounds really shaky to me. I still haven't heard any problem with my explanation other than it sounds irresponsible, but I don't see how that makes it less logical or less likely. (it's blizzard, and it's new).
Also remember that it's not THAT exploitable. Like I said, it will only make your rating trend above your MMR (while you have it). This is a big deal at the cutoff rating for invite tourneys, but not a big deal for everyone else.
Maybe Blizzard did implement it the way you describe. The reasons I think/hope they did not are: - preventing abuse *is* important for them, they know it *will* happen, we can hope they try to minimize the way it can happen. - In Warcraft III, they force activity on an account via an XP decay. It would be strange if they did not follow the same principle with sc2; and this is exactly what we think the bonus pool is for. With your theory, if people use their bonus pool to get above their MMR, they should stop playing. You answer that by saying they should continue playing to improve (and don't care about their ratings). That's true and is the long term point of view, but I think that people would prefer the ability to brag about their inflated points
Hmm so I think I understand, so basically if you placed poorly at the beginning but then continued to improve over a fair number of games, it is going to take you much much longer to be promoted then someone who just started but is at a lower skill level?
I'm asking this because, stupidly, I jumped right into ladder games, and for my first about 30-50 games I was really just learning how to play zerg at all. Now I'm stuck in bronze at about 130 games played.
On September 04 2010 16:17 taffy wrote: As far as I know, if you create an account today you will not have the 600 or whatever accumulative bonus pool
That's actually exactly how it happens. The bonus pool increases globally from Launch Day so that newer players don't fall behind. I'm logged into the game right now. I have a 3v3 team that joined a division on 8/2/2010 and hasn't played any games beyond placement matches. Its bonus pool is 593 right now. I have a 4v4 team that joined a division on 8/15/2010, no games beyond placement used, and its bonus pool is 593. I have another 4v4 team that placed just last night and we quit after placements. Its bonus pool: 593.
Because the bonus pool total is the same for everyone, it becomes an easy global variable that can be elegantly removed from any equations regarding matchmaking or point earnings. However, because you can't see the bonus pools of others, this introduces some confusion because there's no way to determine how much bonus pool a player has consumed and how much they still have banked.
On September 04 2010 18:15 Tomo009 wrote: Hmm so I think I understand, so basically if you placed poorly at the beginning but then continued to improve over a fair number of games, it is going to take you much much longer to be promoted then someone who just started but is at a lower skill level?
I'm asking this because, stupidly, I jumped right into ladder games, and for my first about 30-50 games I was really just learning how to play zerg at all. Now I'm stuck in bronze at about 130 games played.
"Much much longer" is relative, but it would take longer. The same is true for demotions. There was a guy on the Bnet forums yesterday who was looking to tank his rating so he could get bumped down to Bronze from Platinum and start over as Zerg. He was pretty solidly in Platinum, finding Even Matches routinely with about 190 or so games played. He originally started off by instantly leaving every game until he dropped out of 26 games, at which point he started being matched against Bronze players and he had to start going 50-50 against those players to drop his sigma quickly. Looks like he got demoted to Silver today with a little over 230 games played.
From firm Platinum to Silver in about 35 games. His sigma was quite large after that 26th loss in a row I'll bet, but it looks like it decreased to within league boundaries within 9 games, which isn't too bad.
I just got promoted to Diamond directly from gold. So here's the data that I had. I added some more field in light of what I thought you might need.
Map / Win or Loss / Number of Points / Race / League / Rank / Points / WL Record / Win Loss Last 10 Games (Left is most recent game)
Delta Quadrant W +44 T Platinum 23 Blistering Sands L -1 T Diamond 27 Scrap Station W T Match not Found (Suspect Dia) Lost Temple L -1 P Diamond 9 Delta Quadrant L -2 Z Diamond 12 Scrap Station W +46 P Diamond 11 Metalopolis W +44 Z Diamond 26 Blistering Sands W +44 P Diamond 16 Delta Quadrant L -1 P Diamond 9 Stepps of War L -1 T Diamond 1 976 Metalopolis L -2 T Diamond 12 852 Delta Quadrant W +42 Z Diamond 21 808 Lost Temple W +46 P Diamond 44 349 Xel'Naga Caverns L -3 P Diamond 2 901 Metalopolis W +44 P Diamond 1 908 Metalopolis W +44 Z Diamond 40 895 Stepps of War L -2 T Diamond 4 976 Metalopolis W +44 Z Diamond 41 538 Metalopolis L -3 Z Diamond 3 988 141-117 WWLLWWWWLL Xel'Naga Caverns L -4 Z Diamond 9 930 58-32 WWLWLWLWWW Stepps of War L -3 P Platinum 68 132 8-0 WWWWWWW Kulas Ravine L -3 T Diamond 3 964 199-164 WLLLWWWWW Delta Quadrant L -4 P Diamond 2 843 114-89 WLWWWLWWWW Metalopolis W +42 T Diamond 13 841 85-62 LWWLWLLLWW
That's great stuff pez. So you lost to a 988 stable Diamond, a 930 stable Diamond, an unstable undefeated Platinum (which probably puts his MMR around 950 Diamond), an 843 stable Diamond, and beat an 841 stable Diamond. The system appears to have received numerous validations that you do belong above the 800 Diamond level while determining that you lost fairly regularly against Diamond players that are above 950.
On September 04 2010 16:17 taffy wrote: As far as I know, if you create an account today you will not have the 600 or whatever accumulative bonus pool
That's actually exactly how it happens. The bonus pool increases globally from Launch Day so that newer players don't fall behind. I'm logged into the game right now. I have a 3v3 team that joined a division on 8/2/2010 and hasn't played any games beyond placement matches. Its bonus pool is 593 right now. I have a 4v4 team that joined a division on 8/15/2010, no games beyond placement used, and its bonus pool is 593. I have another 4v4 team that placed just last night and we quit after placements. Its bonus pool: 593.
Wow I completely missed that, which makes your theory a lot more plausible. Now it's me having to consider that I'm ignoring a possibility because I disagree so strongly with the design philosophy.
Anyway, good work. Hope you're wrong about this one though
Just a FYI. Also confirmed your theory of points transferred. I went from 901 points (in gold) to 591 (in diamond) 19 losses total which means each loss was on average 16 points.
On September 04 2010 05:46 Lavitage wrote: I know the cause. It's because the people I live with start using the internet (they're all wired to the router, I'm not.) I'll start playing when I have the internet all to myself, have a good rhythm going, then suddenly someone jumps on to do something and bam, gg.
There's nothing I can do about it except make enough money to find a new place to live. I can't even run a wire under the house, since the crawlspace is filled with sharp rusty gutters and black widows and god knows what else.
I would look into a powerline adapter if you can't run a wire and the wireless is causing you issues.
On September 11 2010 03:03 Jin wrote: Bumping this thread because I found this explanation of statistical machine learning to be really good, a really good layman explanation:
That is an excellent explanation of the TrueSkill system, and I recommend it for anyone who wants to learn the basics of TrueSkill. Anyone who chooses to read it should remember that there are some key differences between TrueSkill and Blizzard's SC2 Ladder, most notably with how sigma is treated and how players are divided into leagues. While there are a great number of similarities, the differences are what we should keep in mind.
As someone with a math degree, I really enjoyed this writeup and all the follow up info provided. Sounds perfectly plausible, and actually somewhat standard (with tweaks).
Would love to see more data from people like what Pez has shown here, that's great data.
Great thread, very educational. There are a couple of things I've seen recently though that I'm still at a loss about and am unable to understand... if anyone could enlighten me I'd appreciate it.
I believe the reason that promotions seem random and can be delayed are due to the nature of the division system. There are a limited number of spots in each division and if each spot is filled then it is not possible to promote someone until a spot opens up. A spot can open up either due to someone else being demoted or a new division being created.
As the trigger for promotion is playing a game, if you never happen to play a game when a spot is open, then no promotion will occur, even if you are long overdue for one.
On September 11 2010 13:51 Dwar wrote: I believe the reason that promotions seem random and can be delayed are due to the nature of the division system. There are a limited number of spots in each division and if each spot is filled then it is not possible to promote someone until a spot opens up. A spot can open up either due to someone else being demoted or a new division being created.
As the trigger for promotion is playing a game, if you never happen to play a game when a spot is open, then no promotion will occur, even if you are long overdue for one.
I don't think I buy into that theory. Divisions have to start somewhere, and there are plenty of examples of people being promoted or demoted into a division where they're the sole member (at least, for a few minutes or so, then it starts populating).
Here's my record so far, following pezyuan's format: 5-0 Beginning: Won five placement matches, placed into the bottom of a Platinum division (do I need any more information about this?) 5-1 Delta Quadrant L P Diamond 891 6-1 Blistering Sands W +44 T Diamond 899 6-2 Desert Oasis L -2 Z Diamond 1039 7-2 Blistering Sands W +40 Z Gold 507 7-3 Metalopolis L -2 T Diamond 934 7-4 Metalopolis L -4 P Diamond 764 8-4 Steppes of War W +40 P Diamond 842 8-5 Delta Quadrant L -3 T Diamond 865 8-6 Lost Temple L -6 P Diamond 616 9-6 Scrap Station W +34 T Diamond 315 10-6 Steppes of War W +40 P Diamond 481 11-6 Desert Oasis W +36 P Platinum 942 12-6 Delta Quadrant W +36 T Diamond 753 12-7 Lost Temple L -4 Z Diamond 635 13-7 Kulas Ravine W +38 P Diamond 716 13-8 Steppes of War L -5 P Diamond 892 13-9 Metalopolis L -4 Diamond 694 13-10 Delta Quadrant L -7 P Diamond 558 14-10 Steppes of War W +38 P Diamond 829 15-10 Xel'Naga Caverns W +34 P Diamond 767 16-10 Xel'Naga Caverns W +34 Z Diamond 653 17-10 Steppes of War W +36 T Diamond 752 17-11 Lost Temple L -4 T Diamond 852 18-11 Xel'Naga Caverns W +38 Z Diamond 890 - Promoted to Diamond
On September 19 2010 06:21 littlechava wrote: Here's my record so far, following pezyuan's format: 5-0 Beginning: Won five placement matches, placed into the bottom of a Platinum division (do I need any more information about this?) 5-1 Delta Quadrant L P Diamond 891 6-1 Blistering Sands W +44 T Diamond 899 6-2 Desert Oasis L -2 Z Diamond 1039 7-2 Blistering Sands W +40 Z Gold 507 7-3 Metalopolis L -2 T Diamond 934 7-4 Metalopolis L -4 P Diamond 764 8-4 Steppes of War W +40 P Diamond 842 8-5 Delta Quadrant L -3 T Diamond 865 8-6 Lost Temple L -6 P Diamond 616 9-6 Scrap Station W +34 T Diamond 315 10-6 Steppes of War W +40 P Diamond 481 11-6 Desert Oasis W +36 P Platinum 942 12-6 Delta Quadrant W +36 T Diamond 753 12-7 Lost Temple L -4 Z Diamond 635 13-7 Kulas Ravine W +38 P Diamond 716 13-8 Steppes of War L -5 P Diamond 892 13-9 Metalopolis L -4 Diamond 694 13-10 Delta Quadrant L -7 P Diamond 558 14-10 Steppes of War W +38 P Diamond 829 15-10 Xel'Naga Caverns W +34 P Diamond 767 16-10 Xel'Naga Caverns W +34 Z Diamond 653 17-10 Steppes of War W +36 T Diamond 752 17-11 Lost Temple L -4 T Diamond 852 18-11 Xel'Naga Caverns W +38 Z Diamond 890 - Promoted to Diamond
Opponent W-L records would be nice. For example, that Gold guy at 500 is probably like 19-2. We can't really do very much with the displayed ratings of the rest of these players without seeing their W-L or how much bonus pool they've used, so we have to make assumptions.
That win against the 899 player was huge, and put you up against a 1k player right after that. It probably figures that you're not that high. The 500 Gold player after that likely had an MMR that was around the 800-900 Diamond region, because the win against him put you against a 900 Diamond. As you play more games, you're anchoring around the 700-800 region, and depending on bonus pool consumed, that's either right in the middle of Diamond or a little better or worse. The last couple of games against the 850 and 890 must have sealed it and kept you over the threshold with a smaller sigma.
On September 19 2010 06:21 littlechava wrote: Here's my record so far, following pezyuan's format: 5-0 Beginning: Won five placement matches, placed into the bottom of a Platinum division (do I need any more information about this?) 5-1 Delta Quadrant L P Diamond 891 6-1 Blistering Sands W +44 T Diamond 899 6-2 Desert Oasis L -2 Z Diamond 1039 7-2 Blistering Sands W +40 Z Gold 507 7-3 Metalopolis L -2 T Diamond 934 7-4 Metalopolis L -4 P Diamond 764 8-4 Steppes of War W +40 P Diamond 842 8-5 Delta Quadrant L -3 T Diamond 865 8-6 Lost Temple L -6 P Diamond 616 9-6 Scrap Station W +34 T Diamond 315 10-6 Steppes of War W +40 P Diamond 481 11-6 Desert Oasis W +36 P Platinum 942 12-6 Delta Quadrant W +36 T Diamond 753 12-7 Lost Temple L -4 Z Diamond 635 13-7 Kulas Ravine W +38 P Diamond 716 13-8 Steppes of War L -5 P Diamond 892 13-9 Metalopolis L -4 Diamond 694 13-10 Delta Quadrant L -7 P Diamond 558 14-10 Steppes of War W +38 P Diamond 829 15-10 Xel'Naga Caverns W +34 P Diamond 767 16-10 Xel'Naga Caverns W +34 Z Diamond 653 17-10 Steppes of War W +36 T Diamond 752 17-11 Lost Temple L -4 T Diamond 852 18-11 Xel'Naga Caverns W +38 Z Diamond 890 - Promoted to Diamond
Opponent W-L records would be nice. For example, that Gold guy at 500 is probably like 19-2. We can't really do very much with the displayed ratings of the rest of these players without seeing their W-L or how much bonus pool they've used, so we have to make assumptions.
That win against the 899 player was huge, and put you up against a 1k player right after that. It probably figures that you're not that high. The 500 Gold player after that likely had an MMR that was around the 800-900 Diamond region, because the win against him put you against a 900 Diamond. As you play more games, you're anchoring around the 700-800 region, and depending on bonus pool consumed, that's either right in the middle of Diamond or a little better or worse. The last couple of games against the 850 and 890 must have sealed it and kept you over the threshold with a smaller sigma.
Good stuff chava, thanks.
blah sorry about that, some of the games are pretty old though so it's kinda hard to record their wins before our match. for the last three (game to the right being the game right before we played): 17-10 Steppes of War W +36 T Diamond 752 overall: 84-70 LLLLLLLWLW 17-11 Lost Temple L -4 T Diamond 852 overall: 81-45 WWLWLWWLWW 18-11 Xel'Naga Caverns W +38 Z Diamond 890 overall: 251-243 WLLLLWLWWW edit: that gold guy was 21-10 before our game, going 9-1 in his last ten matches.
ok i saw this in a friend of mines league, he had just been promoted to diamond, and we had been playing the around the same level of guys and had the same w/l at 40-30 he gets into diamond so i check the people in his league and at the bottom is a guy called "LastDays" (cc: 574) i checked out his match history and i saw he had lost 30 games in a row and then won 10 and had been put into diamond... i was FLIPPED, you all can check it out too if you want, but i've check back on him and he's back into silver, but i mean he found a way to trick the system into letting him into diamond
as of writing to see how far back those games were, it is listed at 2 days ago
Edit: not to mention the guys he played in those 10 games were all bronze, cept for that last guy who got promoted to silver shortly after, but at the time of playing all 10 were bronze.
Well written and convincing analysis. Can you speculate whether using a non-linear scale for sigma would alleviate the problems of 'run-away' sigma preventing the promotion of players being 'stuck' in lower leagues despite extraordinary win/loss ratios?
On September 19 2010 11:01 francoskiyo wrote: ok i saw this in a friend of mines league, he had just been promoted to diamond, and we had been playing the around the same level of guys and had the same w/l at 40-30 he gets into diamond so i check the people in his league and at the bottom is a guy called "LastDays" (cc: 574) i checked out his match history and i saw he had lost 30 games in a row and then won 10 and had been put into diamond... i was FLIPPED, you all can check it out too if you want, but i've check back on him and he's back into silver, but i mean he found a way to trick the system into letting him into diamond
as of writing to see how far back those games were, it is listed at 2 days ago
Edit: not to mention the guys he played in those 10 games were all bronze, cept for that last guy who got promoted to silver shortly after, but at the time of playing all 10 were bronze.
I'm trying to follow what you're saying, but I'm not seeing any evidence of any exploit here. What happened is that the guy got into Diamond probably around his 20th game, as many do. Once he got into Diamond, he completely tanked his rating and lost a bunch of games in a row. That alone will not demote you, because if you read the analysis, stability is required before you get relocated. After his rating had been sufficiently thrown, he won a few games against Bronze players to stabilize it. However, he won too many, and ended up stabilizing in Silver. That was when he got demoted. It sounds like you just don't understand how the system works, please read the analysis again and reply back if you still don't follow.
Great Read. I will update my recent matches when i get promoted(assuming that I do lol)
One comment that I thought I would add is that this system seems to approach the problem of matchmaking from a perspective where player's true skill doesnt change much over time(i.e. the player doesnt improve or learn much on a short time scale.) I think this is actually a pretty big flaw in the system as especially for new players, their skill should improve quickly. I would like to see something that incorperated rate of change bsed logic in addition to historical trends.
I am now a 1200 gold player at rank 1 (, I get matched up with nothing but platinum and diamond, and I win alot of matches against platinum and some against diamond.
But when I get matched up with platinum players that have close to the equal amount of points they are "Evenly matched", should they be? Im still in gold and they are still platinum, so its strange that I get evenly matched with someone who is an entire league above me.
And I dont think I belong in gold anymore, even if the system seems to think so, despite the fact that I have alot of wins against plat, and some against diamond. I apologize if I could find this answer in this thread, or the part 1, but I havent read all of it.
Also my experience with the ladder system tells me that I have to get to rank 1 and then I get promoted, that is the way I did it from bronze -> silver -> gold. (I know this isnt "the way you have to do it", but its the way I've had to do it, probably just working as intended seeing as I didnt have much RTS experience before SC2, so I basically belonged in those leagues.
Should I be able to get this many points in a gold league? I think that this should tell the system that it is time to promote me, and the fact that i also play in some plat/diamond teams (not that this is a particularly good pointer to solo league skill level, but I'm starting to worry that my ladder-games are somehow bugged and that I wont be able to be promoted in a million years :>
I didn't see it mentioned in this thread, so I thought I should bring it up: The "Bonus Pool" number on the Battlenet ladder page seems to be total spent bonus points for that team. I happen to have a complete record of my match history, and if I add all my spent bonus points they add upp to 571, which is exactly what it says on my web page: http://eu.battle.net/sc2/en/profile/293343/1/Mendelfist/ladder/3134 I may play some games tonight so it may have changed when you read this. :-) This also means that the total available bonus pool is easy to find. I currently have 318 remaining bonus points, and 571+318=889.
I saw requests for match histories so for those interested here is mine: http://www.lysator.liu.se/~john/history.html It also contains data for the beta. The horizontal lines mark ladder resets. Current ladder (post beta) starts at 2010-07-27. Unfortunately I didn't start writing down spent and remaining bonus pool until recently.
I noted another thing: I have changed league once, but the "spent bonus pool" is still correct. This means that it is not reset or adjusted when you are promoted or demoted.
I hope all of this isn't old news. My match history at least maybe is of some use for those trying to analyze the ladder system.
On September 28 2010 01:46 Mendelfist wrote: I didn't see it mentioned in this thread, so I thought I should bring it up: The "Bonus Pool" number on the Battlenet ladder page seems to be total spent bonus points for that team. I happen to have a complete record of my match history, and if I add all my spent bonus points they add upp to 571, which is exactly what it says on my web page: http://eu.battle.net/sc2/en/profile/293343/1/Mendelfist/ladder/3134 I may play some games tonight so it may have changed when you read this. :-) This also means that the total available bonus pool is easy to find. I currently have 318 remaining bonus points, and 571+318=889.
I saw requests for match histories so for those interested here is mine: http://www.lysator.liu.se/~john/history.html It also contains data for the beta. The horizontal lines mark ladder resets. Current ladder (post beta) starts at 2010-07-27. Unfortunately I didn't start writing down spent and remaining bonus pool until recently.
I noted another thing: I have changed league once, but the "spent bonus pool" is still correct. This means that it is not reset or adjusted when you are promoted or demoted.
I hope all of this isn't old news. My match history at least maybe is of some use for those trying to analyze the ladder system.
We discovered recently (it was from a user on these forums, but I forget your username, sorry) that the pool on the website corresponded to consumed bonus pool, and that has been extremely useful.
Your match history looks to be very thorough, thanks a lot for that. I'll take a look and see if I can identify any trends.
Would it be possible to find the league thresholds using "adjusted ratings", ie points minus consumed bonus pool? Examine the adjusted point distribution for a large number of leagues. Suppose we found that the adjusted points for bronze leagues drop off sharply above 300. The adjusted points for silver usually start at 0 and end at 200 etc. (This is just speculation.) Would this type of analysis be feasible? If it is, there would be a way to compare ratings across leagues.
On September 28 2010 14:28 Mendelfist wrote: Would it be possible to find the league thresholds using "adjusted ratings", ie points minus consumed bonus pool? Examine the adjusted point distribution for a large number of leagues. Suppose we found that the adjusted points for bronze leagues drop off sharply above 300. The adjusted points for silver usually start at 0 and end at 200 etc. (This is just speculation.) Would this type of analysis be feasible? If it is, there would be a way to compare ratings across leagues.
We still think it's MMR-sigma*3 and nothing having to do with actual displayed rating. We can prove this by looking up points across all divisions on SC2Ranks, where some Bronze players have far more points than we would expect the threshold to be. There's a Bronze player with 2400 points, for example, one with 1900, some with 1800. The only way we could determine the league thresholds would be to have full match histories of one player as well as every player he encountered on the way to his promotion and every player they have encountered as well.
This is more me trying to understand the system than me trying to come up with useful ideas, so please bear with me.
Am I correct in that my displayed rating minus my consumed bonus pool will converge to my MMR, disregarding league thresholds/offsets, and assuming that my MMR is reasonably stable?
If so, couldn't I compare my "calculated MMR" (this is the MR column in my match history) with my gold opponents calculated MMR to determine the difference in points between the silver and gold leagues? The difference with the few data points I have seem to be around 200.
For those of you interested in general game outcome prediction systems check out http://kaggle.com/chess They're having a contest to write a better prediction system than Elo (not too hard). Elo's system was written hastily and was the first shot at doing something like this. They are providing a 65k games data set (8 thousand players) to try your hand with and judging the results versus predictions on a private set of ~8k results. There's even prize money and some stuff signed by a few World Chess champions. I'm not surprised Elo is being beaten but I am surprise that even Glicko-2 is sitting in 38th place. I might take a crack at implementing a TrueSkill like rater just to see where it stacks up. Suggestions for ideas outside the usual are welcomed. Terry O'
On September 29 2010 01:29 Mendelfist wrote: This is more me trying to understand the system than me trying to come up with useful ideas, so please bear with me.
Am I correct in that my displayed rating minus my consumed bonus pool will converge to my MMR, disregarding league thresholds/offsets, and assuming that my MMR is reasonably stable?
If so, couldn't I compare my "calculated MMR" (this is the MR column in my match history) with my gold opponents calculated MMR to determine the difference in points between the silver and gold leagues? The difference with the few data points I have seem to be around 200.
I'm not completely confident in the accuracy, but naturally I won't dissuade you from trying. If you happen to find any trends then that would be a huge leap forward.
I've seen some replay auto-renamers that parse replays and get player names and results etc. The next step for ladder analysis would be after finding the player names, look up their current ladder standings. Is there such a thing yet? Is there source code out there that would get 90% of the way there already?
On September 29 2010 00:48 Excalibur_Z wrote: We still think it's MMR-sigma*3 and nothing having to do with actual displayed rating. We can prove this by looking up points across all divisions on SC2Ranks, where some Bronze players have far more points than we would expect the threshold to be. There's a Bronze player with 2400 points, for example, one with 1900, some with 1800. The only way we could determine the league thresholds would be to have full match histories of one player as well as every player he encountered on the way to his promotion and every player they have encountered as well.
I examined some EU bronze divisions and for the top 15 players in each division I subtracted those players spent bonus pools. I expect that the resulting numbers are close to or at least somewhat related to the MMR for each player. Here are those numbers sorted from highest to lowest:
What's going on here? Why are the numbers for the last division so high? Why haven't they been promoted? I mean, its hardly likely that everyone in a randomly picked league have an unusually large sigma. What am I missing?
On September 29 2010 00:48 Excalibur_Z wrote: We still think it's MMR-sigma*3 and nothing having to do with actual displayed rating. We can prove this by looking up points across all divisions on SC2Ranks, where some Bronze players have far more points than we would expect the threshold to be. There's a Bronze player with 2400 points, for example, one with 1900, some with 1800. The only way we could determine the league thresholds would be to have full match histories of one player as well as every player he encountered on the way to his promotion and every player they have encountered as well.
I examined some EU bronze divisions and for the top 15 players in each division I subtracted those players spent bonus pools. I expect that the resulting numbers are close to or at least somewhat related to the MMR for each player. Here are those numbers sorted from highest to lowest:
What's going on here? Why are the numbers for the last division so high? Why haven't they been promoted? I mean, its hardly likely that everyone in a randomly picked league have an unusually large sigma. What am I missing?
I don't have an EU account so I can't look in-game, but did you take a look at their match histories? Looks like the first guy in Azimar Sierra has few games played and is losing few points and gaining many points for losses and wins, respectively. He probably bombed his initial placement matches intentionally and now he's won enough to play against Gold/Plat/Diamond players. I don't think I'd say he's stabilized yet, particularly if he's making such a huge leap in leagues.
The second guy has played more games which means he's probably close to stable, and he's winning and losing the same amount of points per outcome which means that's probably where he belongs.
As for that division having more points in general, that's a good question. I'd say that it's probably older, but I don't know what that would mean because we're speaking in terms of adjusted ratings. Are some divisions actually "better" than others inherently, beyond the caliber of players that reside there? That sure would make things confusing because we've been operating on the theory that points between divisions are comparable. Based on Bashiok's recent quote that people who are affected by the Bronze Zero bug will be moved into a new division, maybe there really is more to divisions than simply acting as a bucket to toss 100 random players. I'm having a hard time pinpointing what their role would be.
On October 02 2010 00:56 Excalibur_Z wrote: I don't have an EU account so I can't look in-game, but did you take a look at their match histories? Looks like the first guy in Azimar Sierra has few games played and is losing few points and gaining many points for losses and wins, respectively. He probably bombed his initial placement matches intentionally and now he's won enough to play against Gold/Plat/Diamond players. I don't think I'd say he's stabilized yet, particularly if he's making such a huge leap in leagues.
The second guy has played more games which means he's probably close to stable, and he's winning and losing the same amount of points per outcome which means that's probably where he belongs.
As for that division having more points in general, that's a good question. I'd say that it's probably older, but I don't know what that would mean because we're speaking in terms of adjusted ratings. Are some divisions actually "better" than others inherently, beyond the caliber of players that reside there? That sure would make things confusing because we've been operating on the theory that points between divisions are comparable. Based on Bashiok's recent quote that people who are affected by the Bronze Zero bug will be moved into a new division, maybe there really is more to divisions than simply acting as a bucket to toss 100 random players. I'm having a hard time pinpointing what their role would be.
No, I didn't look at their match histories. I certainly can understand a few outliers, for example the first few people in Azimar Sierra, but as you can see the average difference between the first two and the last division is large, and I did pick them randomly (I clicked around randomly on peoples profile pages). I also could not get any clues by looking at the age of the divisions. None of them are new.
This bothers me, because the theories you guys have come up with here make a lot of sense. I really thought you had most of it figured out. :-) My idea with all of this was to gain some insight in the promotion thresholds of the leagues, even if the sigma thing makes it much harder to do that. If the divisions are not equal however, it screws everything up.
On October 02 2010 00:56 Excalibur_Z wrote: I don't have an EU account so I can't look in-game, but did you take a look at their match histories? Looks like the first guy in Azimar Sierra has few games played and is losing few points and gaining many points for losses and wins, respectively. He probably bombed his initial placement matches intentionally and now he's won enough to play against Gold/Plat/Diamond players. I don't think I'd say he's stabilized yet, particularly if he's making such a huge leap in leagues.
The second guy has played more games which means he's probably close to stable, and he's winning and losing the same amount of points per outcome which means that's probably where he belongs.
As for that division having more points in general, that's a good question. I'd say that it's probably older, but I don't know what that would mean because we're speaking in terms of adjusted ratings. Are some divisions actually "better" than others inherently, beyond the caliber of players that reside there? That sure would make things confusing because we've been operating on the theory that points between divisions are comparable. Based on Bashiok's recent quote that people who are affected by the Bronze Zero bug will be moved into a new division, maybe there really is more to divisions than simply acting as a bucket to toss 100 random players. I'm having a hard time pinpointing what their role would be.
No, I didn't look at their match histories. I certainly can understand a few outliers, for example the first few people in Azimar Sierra, but as you can see the average difference between the first two and the last division is large, and I did pick them randomly (I clicked around randomly on peoples profile pages). I also could not get any clues by looking at the age of the divisions. None of them are new.
This bothers me, because the theories you guys have come up with here make a lot of sense. I really thought you had most of it figured out. :-) My idea with all of this was to gain some insight in the promotion thresholds of the leagues, even if the sigma thing makes it much harder to do that. If the divisions are not equal however, it screws everything up.
We don't have any inside information, we're just trying to piece together how it works just like everyone else. That's why we're constantly appealing to the community for more information. This is Vanick's take on the matter:
"Is it possible that the lower divisions have players who have not stabilized at a rough 50-50 record yet? That is, it is only likely that they are playing at the proper MMR when their record is about 50-50, and they have played >50 games. The number of games played is slightly arbitrary, but in general 50 games should be enough for them to be at their level if they're Bronze."
He agrees that there is probably more to divisions, which only serves to complicate things. I suspect we'll find out more once Blizzard rolls out their hotfix to Bronze Zero players.
On October 02 2010 01:37 verne wrote: Is there a TLDR version of this is English ? Thx
Your signature is highly apt.
TLDR version:
If you win you gain MMR rating. If you lose you lose MMR rating.
The amount you lose or gain is dependent on the MMR value of your opponent (win against higher rated opponent - gain more; loss against higher rated opponent - lose less).
The more games you play the more confident the system is that your MMR value is accurate. This confidence is likely based on a number of recent games, if your performance improves over 50 games you will be promoted even if your performance was static for 200 games prior.
You are matched against opponents who are near your MMR value if the system's confidence is high. You are matched against opponents who are above your MMR value if the system's confidence is low.
(MMR = matchmaking rating, this is hidden and doesn't depend on your displayed "points")
As you play more games, that uncertainty decreases and the system is more “confident” in the rating it has assigned to you
Why is that true? I don't like how it's assuming that everyone has a "natural" skill level and thus as you play more games the engine gets more accurate. However, people might change so why would sigma decrease?
The probably aren't transitive. But to use the Bayesian method, I think you need to have them to be transitive. What does it mean to be transitive? If A beats B with a 90% probability, B beats C with 90%, then A must beat C with over 90%. Well, obviously in SC2 some build orders work against some type but not others. So it's possible that A beats B, B beats C, but C also beats A.
In other words, if the engine says that B is better than C because he won more games, and A is better than B, then the engine must say that A is better than C. But that's not the case in SC2.
Long time lurker here, decided to register to respond to this post..
Why is that true? I don't like how it's assuming that everyone has a "natural" skill level and thus as you play more games the engine gets more accurate. However, people might change so why would sigma decrease?
Sigma never actually goes to 0. The fact that it is initially very large and decreases somewhat after a few games is that when you first start out, the system really has -no- idea how good you are.
In other words, if the engine says that B is better than C because he won more games, and A is better than B, then the engine must say that A is better than C. But that's not the case in SC2.
But the game has to be transitive on a pure skill basis if it is assumed to be perfectly balanced in every match-up. Whether or not SCII is currently balanced, certainly the match making system has to imply transitivity.
Why is that true? I don't like how it's assuming that everyone has a "natural" skill level and thus as you play more games the engine gets more accurate. However, people might change so why would sigma decrease?
Sigma never actually goes to 0. The fact that it is initially very large and decreases somewhat after a few games is that when you first start out, the system really has -no- idea how good you are.
In other words, if the engine says that B is better than C because he won more games, and A is better than B, then the engine must say that A is better than C. But that's not the case in SC2.
But the game has to be transitive on a pure skill basis if it is assumed to be perfectly balanced in every match-up. Whether or not SCII is currently balanced, certainly the match making system has to imply transitivity.
I've never talked about sigma going down to 0. I'm simply saying that perhaps it shouldn't even decrease.
But I think the transitivity is a bigger issue. Perhaps at the tournament level of gameplay, it's transitive, but for sub-Platinum players it's probably not transitive. I can give you an example right now.
Player A: Overall good macro and unit composition, but does not scout at all during the first 5 minutes
Player B: Very good at cannon cheese, but have no idea how to play the game if his cheese fails (bad macro, no idea of unit composition, bad economy)
Player C: Good macro (just as good as A), scouts, and good at dealing with cheeses
Now, suppose A plays with B. B wins because A is bad against cheese strategies (if he doesn't scout, then he'd probably discover the cheese way too late). If I were to ask you, who would have the highest chance against C, then without knowing their playing styles then you'll probably pick B. Afterall, B had won a game against A. Well obviously given their playing styles, A would have a better chance of beating C (even though he's still worse). However, the system would probably make the opposite prediction given the results of the first game.
That's an example of a non-transitivity. There are many other examples as well.
On September 29 2010 00:48 Excalibur_Z wrote: We still think it's MMR-sigma*3 and nothing having to do with actual displayed rating. We can prove this by looking up points across all divisions on SC2Ranks, where some Bronze players have far more points than we would expect the threshold to be. There's a Bronze player with 2400 points, for example, one with 1900, some with 1800. The only way we could determine the league thresholds would be to have full match histories of one player as well as every player he encountered on the way to his promotion and every player they have encountered as well.
I examined some EU bronze divisions and for the top 15 players in each division I subtracted those players spent bonus pools. I expect that the resulting numbers are close to or at least somewhat related to the MMR for each player. Here are those numbers sorted from highest to lowest:
What's going on here? Why are the numbers for the last division so high? Why haven't they been promoted? I mean, its hardly likely that everyone in a randomly picked league have an unusually large sigma. What am I missing?
I don't have an EU account so I can't look in-game, but did you take a look at their match histories? Looks like the first guy in Azimar Sierra has few games played and is losing few points and gaining many points for losses and wins, respectively. He probably bombed his initial placement matches intentionally and now he's won enough to play against Gold/Plat/Diamond players. I don't think I'd say he's stabilized yet, particularly if he's making such a huge leap in leagues.
The second guy has played more games which means he's probably close to stable, and he's winning and losing the same amount of points per outcome which means that's probably where he belongs.
As for that division having more points in general, that's a good question. I'd say that it's probably older, but I don't know what that would mean because we're speaking in terms of adjusted ratings. Are some divisions actually "better" than others inherently, beyond the caliber of players that reside there? That sure would make things confusing because we've been operating on the theory that points between divisions are comparable. Based on Bashiok's recent quote that people who are affected by the Bronze Zero bug will be moved into a new division, maybe there really is more to divisions than simply acting as a bucket to toss 100 random players. I'm having a hard time pinpointing what their role would be.
Correct about Azimar Sierras number 1. Guy two has had an 8 game winstreak but is still playing bronze/silver = his relatively stable at sigma, though seems to have improved i.e. learned a good tactic.
Games among top 15 in the divisions: Thor Zed: 2094 Tal'darim Nu: 2555 Azimar Sierra: 2407
Quite a gap between Thor Zed and Tal'darim Nu with no reasonable explaination! Isn't what is causing the inflation for Azimar Sierra though.
Those data are pretty interesting: Azimar Sierra has a good deal of overperformers pushing the numbers up and blurring that the rest of the players in top of that division have played more games than the other divisions and thus they have had more time to learn the game/get to their MMR.
On September 29 2010 00:48 Excalibur_Z wrote: We still think it's MMR-sigma*3 and nothing having to do with actual displayed rating. We can prove this by looking up points across all divisions on SC2Ranks, where some Bronze players have far more points than we would expect the threshold to be. There's a Bronze player with 2400 points, for example, one with 1900, some with 1800. The only way we could determine the league thresholds would be to have full match histories of one player as well as every player he encountered on the way to his promotion and every player they have encountered as well.
I examined some EU bronze divisions and for the top 15 players in each division I subtracted those players spent bonus pools. I expect that the resulting numbers are close to or at least somewhat related to the MMR for each player. Here are those numbers sorted from highest to lowest:
What's going on here? Why are the numbers for the last division so high? Why haven't they been promoted? I mean, its hardly likely that everyone in a randomly picked league have an unusually large sigma. What am I missing?
I don't have an EU account so I can't look in-game, but did you take a look at their match histories? Looks like the first guy in Azimar Sierra has few games played and is losing few points and gaining many points for losses and wins, respectively. He probably bombed his initial placement matches intentionally and now he's won enough to play against Gold/Plat/Diamond players. I don't think I'd say he's stabilized yet, particularly if he's making such a huge leap in leagues.
The second guy has played more games which means he's probably close to stable, and he's winning and losing the same amount of points per outcome which means that's probably where he belongs.
As for that division having more points in general, that's a good question. I'd say that it's probably older, but I don't know what that would mean because we're speaking in terms of adjusted ratings. Are some divisions actually "better" than others inherently, beyond the caliber of players that reside there? That sure would make things confusing because we've been operating on the theory that points between divisions are comparable. Based on Bashiok's recent quote that people who are affected by the Bronze Zero bug will be moved into a new division, maybe there really is more to divisions than simply acting as a bucket to toss 100 random players. I'm having a hard time pinpointing what their role would be.
Correct about Azimar Sierras number 1. Guy two has had an 8 game winstreak but is still playing bronze/silver = his relatively stable at sigma, though seems to have improved i.e. learned a good tactic.
Games among top 15 in the divisions: Thor Zed: 2094 Tal'darim Nu: 2555 Azimar Sierra: 2407
Quite a gap between Thor Zed and Tal'darim Nu with no reasonable explaination! Isn't what is causing the inflation for Azimar Sierra though.
Those data are pretty interesting: Azimar Sierra has a good deal of overperformers pushing the numbers up and blurring that the rest of the players in top of that division have played more games than the other divisions and thus they have had more time to learn the game/get to their MMR.
It's entirely possible that it's blind luck that better players got into Azimar Sierra than the other two divisions. A random collection of players isn't going to be even. It's also possible that there is some division weighting. I wouldn't conclude it as inflation by any means, but we'll need more data in order to determine whether there is any kind of weighting used in division placement.
I've played over 1000 league 1v1s, and am STILL rank 1-2 for Platinum. According to this, it will take me many, many more games before I get promoted. ...
On October 06 2010 17:08 Ironbound wrote: I've played over 1000 league 1v1s, and am STILL rank 1-2 for Platinum. According to this, it will take me many, many more games before I get promoted. ...
No, not necessarily. Look at your match history and opponent profiles.
Apologies for the long post. I grew interested in the points a few weeks back and off my own back worked out that the div displayed bonus matched the used bonus. I posted (on the eu boards) my own attempt to see if this could match the 'hidden' MMR in a post here
though my original ideas look a tad simplistic now
After battling though people thinking I was saying the bonus pool is used and relating the current state of the 'knowledge' on the topic I ref'd back to your original post and found your update on the original and this thread.
At this point I decided to track my own data through the system to see if this would help.I rapidly found that promotion/demotion drastically affected my opponents stats clouding the waters somewhat though some interesting facts could be gleaed from my own.
For example you will notice that when I hit 150 (or possibly 15,000) I started hitting Silvers. Some of the names are incorrectly spelt the results are as occurred so opponent stats will include the Win or loss that just occurred against me. I originally made some attempt to calc opponent MMR but found this fluctuated wildly (though if you deduct 735 from the Silvers the first group of 6 all make sense with regards to the points won/lost. Seems to drop out against highers though that might be in response to a Silver who drops rather than is promoted. Left hand side relates to me so in order Points are the DIV displayed points, bonus is the utilised bonus pool. MMR is my original attempt at looking at a simple MMR which is Points minus utilised bonus pool. Band is my current league. Result is a win loss column. VS is where I then attempted to track some small data of what they played and in some cases what they did. Score change is the impact on my score. I used Bonus for all these so if you see +14 it actually means my score went up by +28 and my bonus by +14. These are then applied to the left hand side on the following line. Then a misspelt name column. This is followed by their win losses (including presumably the one that has just occurred) the next Div indicates my opponents Division which is then followed by their rank in that division. The final three list my opponents displayed points, utilised bonus pool and Band.
If the html will cope my data is in light gray and my opponents is light blue with the game and other data in white.
Rather than confuse further I have removed my attempts to work out an MMR for the opponents.. The red text in my results is a check point. The following day after playing a group of games I screenshotted my div rank and this allowed me to double check my maths as I went along
What I was interested in was what happened when promoted and it appears as if my MMR as of the last game (218) had 735 added to it to make by strange co-incidence 953 (which happened to be my utilised bonus pool) then a further 73 was added to pump the score to 1026 with a visible utilised bonus pool of 73. I don’t quite know what to make of it but hopefully the data will prove useful. It might be a coincidence or it might not. If not then it might indicate that utilised bonus becomes score with whatever adjustment required to get to the correct div/league rank then becoming the new utilised bonus pool.
Oh and the 1143 line is the last line/game as bronze after that win I was promoted to Silver. The 1171 line is what my stats would have been if I had not been promoted. The 1026 line is the visible Blizzard stats immediately after the promotion (and will remain so until tonight when I will probably be playing again..)
I think you're on the right path but just need to make some adjustments.
First, while MMR transcends leagues, ratings do not. That means you have to make an important distinction between MMR and adjusted rating (points minus consumed bonus pool) when comparing across leagues. We believe your league threshold is added to your MMR.
For example, maybe Bronze has a threshold of 1000 while Silver has one of 2000. Look at your last three entries, around the time of promotion. Your MMR went from 1000 + 218 to 2000 - 735 after promotion. That's only speculation because we don't actually know what the thresholds are, but it's an important consideration to make when looking at the ladder as a whole.
Secondly, you have some mistakes in your data (I'm sure you're aware but I'm just pointing it out). After SnakeGreen, you stopped listing opponents by rank and substituted some unknown value. What is this value, and how does it apply? The consumed bonus pool values post-promotion are also quite confusing... can you clarify how many points you have remaining in your pool so we can determine what exactly these numbers should be? I haven't seen wild swings like that anywhere else. On the surface it doesn't seem to add up, so we need to make sure we're catching any bugs in the system that might be reported.
I'd also like to make an important clarification here about classifying points minus used bonus pool as MMR. It's not quite that simple, particularly when a player hasn't played very many games. We say that MMR and rating will eventually converge, but that's only a result of sigma shrinking such that there are less wild swings in your MMR, and that only comes after many games played. This means that some players, such as SnakeGreen and Mantton, may not be accurate reference points because their MMRs lack stability.
It seems that the battle.net web pages in EU no longer show consumed bonus pool. Instead they show remaining bonus pool exacly as in the game. I think it was a bug that they now have fixed. :-(
On October 09 2010 01:42 Mendelfist wrote: It seems that the battle.net web pages in EU no longer show consumed bonus pool. Instead they show remaining bonus pool exacly as in the game. I think it was a bug that they now have fixed. :-(
At the time you posted this, I could still see consumed bonus pool on the NA server. They rolled out a fix and now I can't =( Boo!
Oops, I will get the correct rank figure and say which is the dodgy column s when I get back to the office on Monday. In my full sheet there are lots of extra columns where I try to 'adjust' the figures with divisional weighting. Since most of that is exploratory I removed those though it looks like I must have got some columns transposed when entering..
Of the other figures I can attach a screenshot of the post promotion and the most recent pre promotion if that would help (again on Monday though). Whenever a line has red text I have a screenshot of the league board sitting in one note at work.
The figures are 1171 league points , consumed bonus pool 953 making 218 then post promotion 1026 league points with 73 consumed bonus making 953.
As you have noted the EU servers are also showing remaining bonus as opposed to consumed bonus. Since then I have played 5 games winning 4 losing 1 but will be tracking those figures separately to the above.
If you need any of those screen shots or more explanation of the figures please say.
HI, I'm passing here just to drop a testimonial Excalibur's theory is very consistent yesterday I changed my adsl connection to a new isp, about 30% of my games were battle net drop, so I was on a point with 1500 points, about #100 in my region and didnt get promoted due random battle net drops, apparently they punish drops more than surrenders .... But since I can play without having to worry, it took only about 8 hours and only 14 games (I dont mean it took 8 hours to play 14 games, I gave some breaks =P ) to get me promoted, since I was having bad bad bad battle net drops Started with very weak bronzes and in the last rounds pretty much soon to be promoted silvers to gold and golds ... If it helps W L W W W L W W W L W L WP (win and promoted ... )
some stuff I noticed during my 8000+ matches in sc2:
The Server will try to start new matches every 15 seconds.Evertime it cant match you the max difference in skill allowed for your match will increase -> if your searchtime is below 15s(->matched at first attempt) you will never face an enemy with a mmr thats really far away from yours.
If you play against the same player a LOT without getting matched against other players and keep a constant 50% win/loss ratio you will both lose more visible points than you gain -> you eventually drop to 0 points.(might take >100 matches) At the same time your mmr seems to decrease so your points for wins decrease as well and will drop to 0 after about 300 matches in a row vs the same opponent.
This is probably one of the best OP in TL in a while. Next time a friend asks why he hasn't been promoted to diamond yet just link him this thread and watch them shut up.
Curiously had another game at the weekend that indicated the impact sigma can have against ranking. My opponent was ranked as slightly favoured and at the end of the game his stats were listed as Bronze 48 179 pts 461 bonus (remaining now as opposed to consumed) 6W 6L
Now earlier matches had flagged placement matches up as favoured. This guy was not long out of placement but in Bronze yet still flagged as slightly favoured with +14 for winning. This must have been the result of the sigma still showing high uncertainty considering the amount of games played..
Hey there, really great thread, and even though I am sure I did not understand all of the specifics completely, this actually helps a lot in understanding the matchmaking system.
If you look at the first chart, which depicts my Rank, Points and the league I am placed in, I am kind of stumped as to how precise this is. First of all: Where do these come from (except for league of course)? How can my rank be at diamond level? I thought it was only my rank within my division?
Also, am I correct in assuming that the Points (which are for me also in Platinum according to that graph) represent my MMR? I though this was hidden? Can I in any way relay on that graph to tell me "Hey, I might be promoted some time soon", or is it somewhat detached from my actual skill?
Hope someone understands what I mean, I am confused to some extent about all this.
I think you misunderstood the graphics. As I see it, each colour correspond to something, that is to say in your case you are : Gold League (blue line), around 1000 pts (green line) and in the higher ranks (red line). Hope your understand what I mean.
On October 11 2010 23:49 Ch4rlesM wrote: I think you misunderstood the graphics. As I see it, each colour correspond to something, that is to say in your case you are : Gold League (blue line), around 1000 pts (green line) and in the higher ranks (red line). Hope your understand what I mean.
Aaaah! Now I get it, see I knew I was wrong about something in that graph! :D Because I feel in no way able to match up against diamonds at the moment :D
That makes way more sense than I thought about it, thank you very much!
I have a quick question regarding promotions. I am currently a 1300 pts Platinum player. Do I have, in order to get promoted, to beat people which MMR is around 1100-1200 Diamond? Or lower Diamonds will do the trick?
Not because of its quality, but because I'm currently Platinum rank #1 with about 92-92 score (50% ratio) in 2v2 RT, and I guess my chances to get promoted are quasi null.
Next we need a thread for the RT matchmaking system. Because as it stands now, I feel like battle.net purposedly steps on my face to keep me at 50% by matching me every other game with a silver/bronze caliber player having 2 units at the 7minutes mark.
The worst part is that, more often than not, it's like the matchmaking system assumes I'm supposed to carry such players vs a diamond and a platinum player, even putting me "Slightly Favored". So when I lose, I lose a lot of points, and I can only /facepalm when I look at the score screen and then check my teammates and opponents profiles.
Why can't the MM system put players of equivalent skill together? It would make for much better games than somehow try to do an average of player skills.
If i am a Diamond player who has played over 100 games with over 60% win rate ratio. To be demoted all the way into bronze, how many games do you think i need to lose ? Sorry for blatantly asking such a question, i don't request complex mathematical questions, i just want to know the rough estimates, whether it be 1000 games or 500 games or 100 games. Any input will be highly appreciated. (I do understand that there's a lot of random factors out there as I won't get to know who i will lost to and the MMR values of these players)
Why bother? If you want to get to Bronze that much then buy the game again, set up another account and lose your placement matches. It would be a lot faster.
Did anyone notice that for every league there are usually very few players above a certain bonus pool adjusted rating? For Bronze that number seems to be 500, for Silver, Gold and Platinum that number seems to be 300. Players above that number seem to get promoted pretty much asap and end up in the higher league with ~0 adjusted points. So if I assume that leagues start at 0 and that by now displayed rating pretty much equals MMR, the point/rating to league distribution would be (adjusted points only):
Difficult to tell now that the utilised bonus pool has been 'corrected' to show bonus pool remaining and not bonus pool utilised.
I am probably mis-understanding but in my case my 'adjusted' rating was around 200 when I was promoted to Silver and was at 1016 (league adjusted after promoted but at 270 by carrying on tracking the bronze figure) when I started matching against Golds.
If you look at my screen shots on page 14 you can see the figures as they moved..
Great OP. But at some point, which you learn after university, you have to be able to digest the information to present it to people in a clear way. Essentially, can you take the information you have and explain it to someone in high school.
Again, great OP, but I suspect it's from someone green in university.
On October 15 2010 18:25 Matrim wrote: Difficult to tell now that the utilised bonus pool has been 'corrected' to show bonus pool remaining and not bonus pool utilised.
When I post this total available bonus points are exactly 1120 (for EU, I don't know if other regions are in sync with this). Those interested can keep track of it either by looking at how your own bonus pool increases and add it to this number, or by just counting hours from this moment (1 point per 2 hours).
Utilised bonus pool is then of course total available bonus pool minus remaining bonus pool.
As far as I know this works even after promotions/demotions. Correct me if I'm wrong.
Seems correct though Excaliber is the authority in this thread. It used to be a lot easier with the bonus pool on your league window showing utilised whereas now it shows remaining..
On October 15 2010 23:34 ashaman771 wrote: Great OP. But at some point, which you learn after university, you have to be able to digest the information to present it to people in a clear way. Essentially, can you take the information you have and explain it to someone in high school.
Again, great OP, but I suspect it's from someone green in university.
On October 15 2010 23:34 ashaman771 wrote: Great OP. But at some point, which you learn after university, you have to be able to digest the information to present it to people in a clear way. Essentially, can you take the information you have and explain it to someone in high school.
Again, great OP, but I suspect it's from someone green in university.
It isn't. Vanick is a college graduate with a CS degree, and we've gone through several phases of proofreading and editing before posting this. I don't have a formal college education on statistics since I went to a trade school, so over those passes we made it more accessible and easier to understand (it used to be a lot more verbose than this). Not to sound condescending, but we've had a lot of comments praising this post because of how thorough and straightforward the explanations are. To quote a poster from SomethingAwful where this thread was linked, "That poster has a fucking spectacular ability to communicate, holy shit."
On October 15 2010 18:25 Matrim wrote: Difficult to tell now that the utilised bonus pool has been 'corrected' to show bonus pool remaining and not bonus pool utilised.
When I post this total available bonus points are exactly 1120 (for EU, I don't know if other regions are in sync with this). Those interested can keep track of it either by looking at how your own bonus pool increases and add it to this number, or by just counting hours from this moment (1 point per 2 hours).
Utilised bonus pool is then of course total available bonus pool minus remaining bonus pool.
As far as I know this works even after promotions/demotions. Correct me if I'm wrong.
Yeah, that's what I've noticed too. However, there was one notable exception (so it's probably a bug). When I got promoted from Platinum to Diamond, my last game earned me +20 bonus points, but -40 was deducted from my bonus pool. I saw this in someone else's match history when being promoted to Diamond too, and it was the same phenomenon: earning 20 but deducting 40. Every other match history parse I've seen has kept the bonus pool total consistent. My guess is it's just a Diamond-promotion double-deduction bug.
Hello, I am a first time poster however I have been reading carefully all the threads relating to Analysis of the SC2 Ladder. I am a bronze player and though this might been insignificant to most of you I am still confused as to why I still remain in Bronze league. I started off 1-4 due to some disconnections and continued to a dismal record of 6-19 until I started to step my game up watch some Day9 and read some TL. Now in my past 13 or so games I have been playing Top Bronze with Top Silver have won all but 2 games and a couple hours ago I defeated a rank 44 platinum that was "even" with me. Now I know that being "even" is just the displayed ratings being compared however if anyone could answer my question as to why I remain in bronze league it would be appreciative.
Why is it possible that a friend of mine is diamond with 30 games (375 rating) and I have about 100 games 60% (1000 rating) and I'm still platin -.-. Don't get it and that math here is way to complicated imho!
On October 16 2010 11:47 iDreamStar wrote: Hello, I am a first time poster however I have been reading carefully all the threads relating to Analysis of the SC2 Ladder. I am a bronze player and though this might been insignificant to most of you I am still confused as to why I still remain in Bronze league. I started off 1-4 due to some disconnections and continued to a dismal record of 6-19 until I started to step my game up watch some Day9 and read some TL. Now in my past 13 or so games I have been playing Top Bronze with Top Silver have won all but 2 games and a couple hours ago I defeated a rank 44 platinum that was "even" with me. Now I know that being "even" is just the displayed ratings being compared however if anyone could answer my question as to why I remain in bronze league it would be appreciative.
Simple: You have now confused the system significantly, and you'll get promoted when it confidently establishes which league you belong in.
In more technical terms, your sigma is very high from causing so many upsets and your MMR is likely fluctuating significantly as you play players with such varied MMRs. You will get promoted when your MMR +/- sigma falls cleanly in a particular league range.
While reading the article on Microsoft True Skill a thought occurs to me.
Sigma should be split into two separate Sigmas a high and a low. Currently the system MUST create a symmetrical bell curve around ones MMR which represents a total probability of expected performance. If you win against a higher ranked player the MMR goes up but so dose the single Sigma which causes the lower end 'tail' of your performance expectation to stagnate. Thus a players Performance curve just keeps getting 'smeared' upward and the system won't promote because of the high confidence threshold needed.
So for example Bob a Platinum with 2000 MMR plays against Jon a Diamond player with 2300 MMR. Jon is favored but Bob wins an upset victory. The systems single sigma means the system is forced to basically say "Oh I seem to have Bobs skill level wrong, he might actually be Diamond material or he could equally likely be Gold caliber." Now obviously any inference that Bob win means he is more likely to Gold caliber should not be drawn from a win against a higher ranked opponent.
While the upper end of the performance curve should indeed go up because your win means you might really be that good, it should indicate to the system that your not going to perform poorly. An upset win would incresse only the Upper-Sigma, while an upset loss would increase only the Lower-Sigma, on the flip-side an expected win decreases Lower-Sigma and and an Expected loss decreases Upper-Sigma, all of course scaled by the degree to which one is favored. In each case the system ONLY takes the logical inference of the result of a game and not an illogical 'mirror' inference on the other side of the curve.
I find it rather silly that such an obvious and easily fixed flaw in the system exists.
On October 20 2010 07:27 Impaler wrote: While reading the article on Microsoft True Skill a thought occurs to me.
Sigma should be split into two separate Sigmas a high and a low. Currently the system MUST create a symmetrical bell curve around ones MMR which represents a total probability of expected performance. If you win against a higher ranked player the MMR goes up but so dose the single Sigma which causes the lower end 'tail' of your performance expectation to stagnate. Thus a players Performance curve just keeps getting 'smeared' upward and the system won't promote because of the high confidence threshold needed.
So for example Bob a Platinum with 2000 MMR plays against Jon a Diamond player with 2300 MMR. Jon is favored but Bob wins an upset victory. The systems single sigma means the system is forced to basically say "Oh I seem to have Bobs skill level wrong, he might actually be Diamond material or he could equally likely be Gold caliber." Now obviously any inference that Bob win means he is more likely to Gold caliber should not be drawn from a win against a higher ranked opponent.
While the upper end of the performance curve should indeed go up because your win means you might really be that good, it should indicate to the system that your not going to perform poorly. An upset win would incresse only the Upper-Sigma, while an upset loss would increase only the Lower-Sigma, on the flip-side an expected win decreases Lower-Sigma and and an Expected loss decreases Upper-Sigma, all of course scaled by the degree to which one is favored. In each case the system ONLY takes the logical inference of the result of a game and not an illogical 'mirror' inference on the other side of the curve.
I find it rather silly that such an obvious and easily fixed flaw in the system exists.
I don't think you have it right. Say Bob's curve range is 1500-2500 and he beats Jon who's at 2300 and it's an upset and sigma increases. Bob's new range doesn't become 1450-2550. It would move more toward the right because his MMR increased, so the new range would be more like 1525-2625.
Yes I realize that MMR is increasing, that why I described the bell curve as 'smearing upwards'. While I'm sure the lower end of the curve would not move down because the increased MMR outweighs the increased sigma. It seems I overstated my case with the 'He might be Gold" bit, perhaps 'He might just be on a lucky streak" would be more accurate. But my central point is the low end of the spectrum could certainly be moving up too slowly if your consistently winning upsets.
Lets take your your example and construct a scenario to demonstrate my point, Bob's initial MMR is 2000 with sigma spread of 500 on each side. After the upset victory the MMR is increased to 2075 with a sigma spread of 550 on each side for the new 1525-2625 spread. The low end tail increased only 25 points. This seems reasonable for a single upset game but if the player continues being placed against opponents 300 MMR above them (cause the system is trying to bring your win percentage down like it should). Each win will add 75 points to Bobs MMR but add 50 to the sigma spread on each side resulting in the tail end of their expected range increasing by only 25 points and the upper end by 125 points.
After three such matches Bobs MMR would be 2225 but the spread would be a whopping 1625-2875, Now Bob has just beaten a 2300, 2375 and 2450 player in that order so the upper bound is not unreasonable, Bob might really be that good and until he starts to lose matches against high ranked players that upper bound should be very fuzzy. But the low end estimate is really quite absurd after that strong a performance, Bob has demonstrated play consistently above that level, if Bob was to choke on a few games and lose to a 2000 or lower player then that low end estimate is reasonable but not after repeated strong performance.
Imagine instead two separate sigma spreads, which are initially each 500 around the 2000 mean. As Bob wins upset victories the MMR moves in the same manor but only the upper sigma increases by 50 rather then both, Now the lower bound is moving up in sync with the MMR and the upper is moving up just as it was before. Now after the same matches the MMR is 2225 the lower sigma spread is still unchanged at 500 but the upper is elongated to 650 for a total spread of 1725-2875 which is a more reasonable spread given the matches that have taken place.
Another interesting side effect of this dual-sigma approach is an ability to actually capture a players likely-hood of choking. Normal True-Skill makes the in my opinion false assumption that an individuals has an equal probability of deviating above and below their average performance. In reality is is FAR more likely for performance in any skill to fall dramatically aka 'choke' then it is to proportionally over-perform. Take a runner for example who normally runs a mile in 5 minutes, it's far more likely that one day he has a bruised hamstring and dose it in 6 then it is for them to out of the blue run a 4 minute mile. And the higher the level of ones average performance the more easy it is to choke (the smallest error will do it) and the harder it is to over-perform (so many factors would have to be elevated and you may be near the maximum humanly possible performance). With a dual-sigma approach you would expect to see a larger low end sigma on nearly all high end players because of occasional chokes, players who consistently never choke will have this reflected in a narrower low-end sigma and this could significantly improve the accuracy of predictions made under this system.
Sigma will decrease instead if it is large enough. It doesn't just keep growing with each upset.
I mean, it's entirely possible that a two sigma system exists, and you make good points for how it could address the shortcomings of the TrueSkill system. However, a bell curve is more computationally efficient and is also accurate enough for the purposes of estimating skill. It doesn't seem as likely that player curves would have two peaks.
I wasn't aware it would decrease, is the sigma simply constrained when it grows beyond a certain point or is it a natural byproduct of the system, I'd assumed if one upset increases sigma then more just keep doing the same but perhaps this is ware I'm wrong? True-Skill seems to indicate that a constant inflation of sigma is applied to all players which each game whittles down as their needs to be something preventing it from collapsing to Zero.
Also the distribution wouldn't be two peaked, it would be a skewed distribution.
The math is way over my head so the best lay description I can give is that of two sigmas one above the average and one below. In reality it seems a skewed normal distribution uses a third factor to express the skew with 0 being the plain symmetrical Gaussian. In that case upset wins increases skew and upset losses decrease skew, while an expected win or loss dose not change skew (or at least changes it less). It would indeed make the math even more complex (perhaps unnecessarily) but I'm sure people though the same thing about expanding on ELO, I'll do some more searching to see if this idea has ever been explored (it would be hard to imagine that it hasn't been explored by Vegas bookies)
On October 16 2010 02:08 Excalibur_Z wrote: Yeah, that's what I've noticed too. However, there was one notable exception (so it's probably a bug). When I got promoted from Platinum to Diamond, my last game earned me +20 bonus points, but -40 was deducted from my bonus pool. I saw this in someone else's match history when being promoted to Diamond too, and it was the same phenomenon: earning 20 but deducting 40. Every other match history parse I've seen has kept the bonus pool total consistent. My guess is it's just a Diamond-promotion double-deduction bug.
Found another bug, and this time it was not after a promotion:
My points before match: 959. Spent bonus before match: 886 Points after match (loss): 978. Spent bonus after match: 902
The score screen and my match history says I lost 13 points, but my score increased 19 points. This makes no sense at first, but the difference is 32 points, and 16 points were deducted from the bonus pool. I suspect that the system thinks that I both won and lost the match at the same time. -13 for losing and 16 + 16 for winning. Curious. And annoying if you are trying to keep track of everything and make sense of it.
I saw you ask a question at the multiplayer panel, Excalbur!
Nice they confirm that this is all pretty close. Good job! They also mentioned something very important in that your ranking/points(?) is relative to the skill of your division. Not sure on the exact wording there.That point alone makes things 10000% more complicated? If it's comparing your performance vs the 99 others in your division.
On October 15 2010 23:34 ashaman771 wrote: Great OP. But at some point, which you learn after university, you have to be able to digest the information to present it to people in a clear way. Essentially, can you take the information you have and explain it to someone in high school.
Again, great OP, but I suspect it's from someone green in university.
I'm flabbergasted by this post. Has this guy 'been to university'? Clear presentation is not something you magically learn there. And what's the point of speculating on someone's level of higher education?
If I were to speculate myself, I might think that this is a high school kid who can't understand the really not too sophisticated math in the OP...
Anyway, well done OP, and congrats on that MVP status on the blizzard forums. It is a role for the brave and patient, I imagine.
Ive read most of this thread but didn't see my particular question: Is there a reason I win/lose in large streaks? Its incredibly odd, Ill lose 7-8 in a row then win the same amount, pretty consistently, its happened in about 4 cycles now.
My elo might be inflated because of a large bonus pool, I recently switched races. After the bonus pool i often come out ahead in visible rating, even though my record is quickly approaching 50/50.
So after the Multiplayer panel yesterday, we asked the Doc some more specific questions. There are some things that we're not sure about now. We now know that divisions are not equal which adds a great deal of confusion because sites like SC2Ranks are specifically designed to ignore division weighting. It seems like they've gone out of their way to put emphasis on your own division rather than your league ranking, which sort of has a side effect of screwing up global point rankings like SC2Ranks.
The other concept that he introduced was a moving average which has a similar function as sigma. Basically, if you were to track player skill game by game, it would have a ton of sharp peaks and deep valleys. Blizzard chooses to use a moving average to slowly gauge where you belong. Once your moving average crosses a certain threshold (some kind of confidence buffer), that's when you get promoted. This means that if you bomb your initial placement matches and go down into Bronze, then rapidly improve to Diamond level, it will take a long time for your moving average to cross into Diamond level and cement that level of confidence for a promotion. We believe that the moving average only covers your last X games (maybe 100 for example) otherwise players with 4000+ games played would never get out of their league.
I'll be making more corrections to the original post later on today or tomorrow.
That the divisons are not equal has been known since early beta. Copied from another thread on TL:
by Benzenn 18 Mar 2010, 19:43 Sorry I misunderstood what the OP was referring to. I didn't mean to imply that one division is ranked better than the other, but simply explaining the basics of divisions. As far as comparison across divisions it's certainly something we've considered but there are issues, such that the rankings in one division don't directly translate to the other divisions. So you couldn't compare division 10 to division 48 and compare one player's points to another.
On October 25 2010 03:12 Excalibur_Z wrote: So after the Multiplayer panel yesterday, we asked the Doc some more specific questions. There are some things that we're not sure about now. We now know that divisions are not equal which adds a great deal of confusion because sites like SC2Ranks are specifically designed to ignore division weighting. It seems like they've gone out of their way to put emphasis on your own division rather than your league ranking, which sort of has a side effect of screwing up global point rankings like SC2Ranks.
The other concept that he introduced was a moving average which has a similar function as sigma. Basically, if you were to track player skill game by game, it would have a ton of sharp peaks and deep valleys. Blizzard chooses to use a moving average to slowly gauge where you belong. Once your moving average crosses a certain threshold (some kind of confidence buffer), that's when you get promoted. This means that if you bomb your initial placement matches and go down into Bronze, then rapidly improve to Diamond level, it will take a long time for your moving average to cross into Diamond level and cement that level of confidence for a promotion. We believe that the moving average only covers your last X games (maybe 100 for example) otherwise players with 4000+ games played would never get out of their league.
I'll be making more corrections to the original post later on today or tomorrow.
Thanks for all your work, and nice sleuth work at Blizzcon.
I had a question for you; I'm not sure if you saw the Day 1 SC panel but Greg Canessa stated that Bronze / Silver / Gold / Plat / Diamond were designed to be evenly distributed at 20% of the servers player base each, obviously this doesn't match up with data from Sc2ranks which looks more like top 7% in Diamond and bottom 50% in Bronze.
Any theories on this? A symptom of inactive players perhaps?
by Benzenn 18 Mar 2010, 19:43 Sorry I misunderstood what the OP was referring to. I didn't mean to imply that one division is ranked better than the other, but simply explaining the basics of divisions. As far as comparison across divisions it's certainly something we've considered but there are issues, such that the rankings in one division don't directly translate to the other divisions. So you couldn't compare division 10 to division 48 and compare one player's points to another.
We figured that something changed because it didn't make sense (and still doesn't make sense) to set it up that way. Now that we have official confirmation of that it throws a wrench in sites like SC2Ranks. We sort of had a sinking feeling that was how it behaved but ugh... silly that it does.
He did mention that when he pulls the Top 200 lists for the week that they're purely by points, only without the division weighting.
What would to formula be for plotting the equation to determine MMR? I am having trouble trying to plot mine. I know my formula is somewhat like
12*(187 - 182) - sigma
Though, I am wondering would this formula work for calculating MMR?
G = games played Gl (the l is notation, no effect on formula) games lost O(sigma) = Formula for sigma addition or reduction based upon your opponents sigma and matchmaking ranking r = rate at which bonus pool is gained a = amount gained per time constant in bonus pool (IF APPLIED TO YOUR MATCHMAKING POINTS) m = Your match making points (the ones visible for ladder)
So the formula would work something like this
(G - Gl)*12 = m - ra = matchmaking ranking - sigma Then to graph this y = matchmaking ranking - sigma x = O(your sigma) If we apply this to an equation (of which we must use the opposite derivative of matchmaking ranking - sigma) This should two dimensionally determine your MMR, along with anyone with either less games, lower matchmaking ranking (with possible lower sigmas).
So... does this mean that I cant compare my skill lvl to the players I Battle in the top10 in my league? I mean If I have 1500 rating and Im the 3. in my league and the guys above and bellow me are around the same rating. Can I then say that Im fairly even in skill to them? Or is it hidden in the MMR?
On October 26 2010 06:35 Pippah wrote: So... does this mean that I cant compare my skill lvl to the players I Battle in the top10 in my league? I mean If I have 1500 rating and Im the 3. in my league and the guys above and bellow me are around the same rating. Can I then say that Im fairly even in skill to them? Or is it hidden in the MMR?
It is not hidden in MMR, it is a portion of uncertainty about the player's skill that is hidden in MMR that is affected by matchmaking games. (that is sigma) This sigma and MMR are used to hopefully acurrately map the player's skill, and the MMR and sigma get more defined as more games are played
Okay maybe I asked wrong, what I meant was, If I have 1500 rating and someone else in the same league (not necesarily the one im put in, but samme metal) has 1501 are we then pretty even in skill or is that uncomparable because of the bonus pool and MMR ?
Forgive me if this is a newbie question but isn't the easiest way to 'estimate' MMR to just ladder? I placed into diamond very early in retail and wasn't able to play much due to work etc.
In the last week while climbing now that I have more time I noticed while I started playing at Rating = 500, I would only get matched up with diamond 1400-1600. I assume this is due to my mmr being around 1500? Is this not the case? Of course you're going to get outliers but if you just laddered say 15 games and took the avg displayed rating of your opponents wouldn't that be pretty close to your MMR?
On October 26 2010 10:18 crms wrote: Forgive me if this is a newbie question but isn't the easiest way to 'estimate' MMR to just ladder? I placed into diamond very early in retail and wasn't able to play much due to work etc.
In the last week while climbing now that I have more time I noticed while I started playing at Rating = 500, I would only get matched up with diamond 1400-1600. I assume this is due to my mmr being around 1500? Is this not the case? Of course you're going to get outliers but if you just laddered say 15 games and took the avg displayed rating of your opponents wouldn't that be pretty close to your MMR?
It wouldn't be 100% accurate, but it would be close. The reason is that divisions aren't equal, and you also have to account for the variance in opponents (for example if you had a 1500 rating but 150 sigma you could play against a 1650 player despite being only 1500, even though you would think based on opponent ratings that you are a 1650). MMR also is tricky to track because it changes so much after each game.
On October 26 2010 10:10 Pippah wrote: Okay maybe I asked wrong, what I meant was, If I have 1500 rating and someone else in the same league (not necesarily the one im put in, but samme metal) has 1501 are we then pretty even in skill or is that uncomparable because of the bonus pool and MMR ?
Bonus pool has no effect on actual MMR. It would make it seem like you are of even skill, but he might have had a larger bonus pool, and was able to climb through that. 1501 is in no way actually comparable to 1501, unless bonus pool was removed and both players had play the same amount of games.
What determines skill comparitevly is your MMR and your sigma. So the two ratings are probably incomparable
On October 26 2010 10:10 Pippah wrote: Okay maybe I asked wrong, what I meant was, If I have 1500 rating and someone else in the same league (not necesarily the one im put in, but samme metal) has 1501 are we then pretty even in skill or is that uncomparable because of the bonus pool and MMR ?
Bonus pool has no effect on actual MMR. It would make it seem like you are of even skill, but he might have had a larger bonus pool, and was able to climb through that. 1501 is in no way actually comparable to 1501, unless bonus pool was removed and both players had play the same amount of games.
What determines skill comparitevly is your MMR and your sigma. So the two ratings are probably incomparable
That makes me sad that I now know this, Id much rather have lived in ignorance - Why even bother with rating then if you cannot compare your skill level to anyone. Why bother putting people in divisions if there is no comparable relation with your rating and the ones you are battleing for the top spot. I feel cheated that I may fight for a top spot in my league and the ones im fighting may be way better or worse than me. meh. ;/
On October 26 2010 10:10 Pippah wrote: Okay maybe I asked wrong, what I meant was, If I have 1500 rating and someone else in the same league (not necesarily the one im put in, but samme metal) has 1501 are we then pretty even in skill or is that uncomparable because of the bonus pool and MMR ?
Bonus pool has no effect on actual MMR. It would make it seem like you are of even skill, but he might have had a larger bonus pool, and was able to climb through that. 1501 is in no way actually comparable to 1501, unless bonus pool was removed and both players had play the same amount of games.
What determines skill comparitevly is your MMR and your sigma. So the two ratings are probably incomparable
That makes me sad that I now know this, Id much rather have lived in ignorance - Why even bother with rating then if you cannot compare your skill level to anyone. Why bother putting people in divisions if there is no comparable relation with your rating and the ones you are battleing for the top spot. I feel cheated that I may fight for a top spot in my league and the ones im fighting may be way better or worse than me. meh. ;/
but, remember, you are still kicking ass against players of your "skill level" so that means you are better then them
Just for fun I made a graph to see how bonus points affect ranks within a division. This graph is from my own division. On the X axis is rank with bonus pool and on the Y axis is rank with bonus pool removed. If bonus pool had no effect the graph would be a straight line from (1,1) to (100,100). Now we can see that the order is totally messed up. For example, the guy with rank 37 (red circle) would be rank 1 if noone had bonus points, and he could be closest to promotion of everyone in my division. On the other hand the guy with rank 46 (green circle) is the worst of the lot.
This is probably no news to most people here, but I think it is illustrative anyway. Some ask "I'm number one in my division, why am I not promoted?" and this shows why. Points are useless, and it kind of makes sites as sc2ranks.com useless too. I think it's sad.
For the sake of removing the influence of bonus points as I did here you don't need to know how many bonus points you've used. You can just add everyones remaining bonus pool to their score as if they had used all of it.
If you want to know how many bonus points you have used you need to subtract your remaining bonus points from the total available bonus pool, which is the same for everyone. It is currently 1290 points in EU and increases 1 point every 2 hours.
On October 29 2010 05:20 ribboo wrote: How do you see how many bonus-points you've used?
Everybody has earned the same number of bonus points, IIRC it's 1 point for every 2 hours of time since the game was released. So if you look at how many bonus points you have and subtract that from the total number of points (12/day the game has been out) you will arrive at your answer.
On October 29 2010 05:07 Mendelfist wrote: Just for fun I made a graph to see how bonus points affect ranks within a division. This graph is from my own division. On the X axis is rank with bonus pool and on the Y axis is rank with bonus pool removed. If bonus pool had no effect the graph would be a straight line from (1,1) to (100,100). Now we can see that the order is totally messed up. For example, the guy with rank 37 (red circle) would be rank 1 if noone had bonus points, and he could be closest to promotion of everyone in my division. On the other hand the guy with rank 46 (green circle) is the worst of the lot.
This is probably no news to most people here, but I think it is illustrative anyway. Some ask "I'm number one in my division, why am I not promoted?" and this shows why. Points are useless, and it kind of makes sites as sc2ranks.com useless too. I think it's sad.
So lets say 800 bonus points have been used so far. Then you just did ranking+remaining bonus pool-800 to get bonus pool removed? I don't think thats fair, since you get favoured/even more often when you have more points. So you will lose more and win less compared to people of equal skill that have less points.
Just checked the 36 first in my league, seems the only real difference between the top placed ones and the ones placed lower, are the bonus-points. Seems like I'm not 4th, but at the shared first place as well *yay* Is it really valid to count this way though?
FYI this is a rough idea of how we perceive promotions to operate. Once your moving average (black line) levels out and stabilizes within the confines of a new league, that's where you move to:
On October 29 2010 05:42 IPS.ZeRo wrote: So lets say 800 bonus points have been used so far. Then you just did ranking+remaining bonus pool-800 to get bonus pool removed? I don't think thats fair, since you get favoured/even more often when you have more points. So you will lose more and win less compared to people of equal skill that have less points.
I don't think bonus points are included in any calculations at all other than your displayed points and rank. It would not make sense. Also my own match history disproves your theory. For example, in my last match I had 1062 points in gold and met someone with 338 points in gold. The match was considered even. If we compare our points with bonus pool removed however they were much closer: 112 and 77. http://www.lysator.liu.se/~john/history.html
On October 25 2010 15:57 Slaytesics wrote: What would to formula be for plotting the equation to determine MMR? I am having trouble trying to plot mine. I know my formula is somewhat like
12*(187 - 182) - sigma
Though, I am wondering would this formula work for calculating MMR?
G = games played Gl (the l is notation, no effect on formula) games lost O(sigma) = Formula for sigma addition or reduction based upon your opponents sigma and matchmaking ranking r = rate at which bonus pool is gained a = amount gained per time constant in bonus pool (IF APPLIED TO YOUR MATCHMAKING POINTS) m = Your match making points (the ones visible for ladder)
So the formula would work something like this
(G - Gl)*12 = m - ra = matchmaking ranking - sigma Then to graph this y = matchmaking ranking - sigma x = O(your sigma) If we apply this to an equation (of which we must use the opposite derivative of matchmaking ranking - sigma) This should two dimensionally determine your MMR, along with anyone with either less games, lower matchmaking ranking (with possible lower sigmas).
I'm wondering, how do u know you sigma? as without knowing it, you cannot know ur approx. MMR ive been stuck at top of the leage for the last 20 games and want a promotion :p i wanna know if its coz my MMR is bad, or if im close....... or what :D
Any idea if this moving average is only based on X number of games, or if it has a time component too?
An extreme case for example -- if you let a high diamond player use a 500W/500L silver account (i.e. solid silver), would the diamond player be able to get the account into diamond by massing 20-30 games in a day or two, or would he need to win a couple of games a day for a week or month?
On October 29 2010 22:03 zzaaxxsscd wrote: Any idea if this moving average is only based on X number of games, or if it has a time component too?
An extreme case for example -- if you let a high diamond player use a 500W/500L silver account (i.e. solid silver), would the diamond player be able to get the account into diamond by massing 20-30 games in a day or two, or would he need to win a couple of games a day for a week or month?
I reallllly hope it is based on a smallish number of games or i'm gonna be stuck in bronze forever.
On October 29 2010 22:03 zzaaxxsscd wrote: Any idea if this moving average is only based on X number of games, or if it has a time component too?
An extreme case for example -- if you let a high diamond player use a 500W/500L silver account (i.e. solid silver), would the diamond player be able to get the account into diamond by massing 20-30 games in a day or two, or would he need to win a couple of games a day for a week or month?
It has to be just games played, otherwise it would be biased one way or the other toward or against people who don't have the opportunity to play often.
On October 25 2010 15:57 Slaytesics wrote: What would to formula be for plotting the equation to determine MMR? I am having trouble trying to plot mine. I know my formula is somewhat like
12*(187 - 182) - sigma
Though, I am wondering would this formula work for calculating MMR?
G = games played Gl (the l is notation, no effect on formula) games lost O(sigma) = Formula for sigma addition or reduction based upon your opponents sigma and matchmaking ranking r = rate at which bonus pool is gained a = amount gained per time constant in bonus pool (IF APPLIED TO YOUR MATCHMAKING POINTS) m = Your match making points (the ones visible for ladder)
So the formula would work something like this
(G - Gl)*12 = m - ra = matchmaking ranking - sigma Then to graph this y = matchmaking ranking - sigma x = O(your sigma) If we apply this to an equation (of which we must use the opposite derivative of matchmaking ranking - sigma) This should two dimensionally determine your MMR, along with anyone with either less games, lower matchmaking ranking (with possible lower sigmas).
I'm wondering, how do u know you sigma? as without knowing it, you cannot know ur approx. MMR ive been stuck at top of the leage for the last 20 games and want a promotion :p i wanna know if its coz my MMR is bad, or if im close....... or what :D
Yeah, you don't really know what your sigma is. We did hear that sigma stays relatively large, too large to be used as a confidence factor for promotion. That was when it was confirmed that sigma did not play a direct role in promotion.
I wanted to share my latest experience (in 4v4): - I was promoted twice in the first 22 games (from bronze to gold). - I was promoted from gold to diamond without passing through platinum.
I went 0-5 in the "qualification games" (bronze league) and now i'm 20-15 (promoted to diamond just now). Just a little more information...
I started laddering some time last week. I went 5-0 in my placements ~2 months ago, against something like silver silver gold plat plat (not totally sure, not sure how accurate looking at their profiles is at this point). 5-0 into plat.
Here is a spreadsheet with my opponent's info. I have usernames and map recorded as well if you also want those. I got promoted to diamond after the last game there. I kept about 80% of my points when promoted (from 314 to 250).
My other teams are: 2 plat 2v2s (8-4, 9-5), 1 bronze 3v3 (5-2) 1 plat 3v3 (5-0), and about 10 4v4s (split between diamond plat and silver - about 150 games between them). Tell me if you want any more info!
On October 29 2010 22:03 zzaaxxsscd wrote: Any idea if this moving average is only based on X number of games, or if it has a time component too?
An extreme case for example -- if you let a high diamond player use a 500W/500L silver account (i.e. solid silver), would the diamond player be able to get the account into diamond by massing 20-30 games in a day or two, or would he need to win a couple of games a day for a week or month?
We don't know exactly how the moving average is computed. We do know your more recent games count more than your older ones. I would expect that it only looks at the last N games, where N is some reasonable number (so if you were 500/500 it wouldn't really work against you if you started playing at diamond level).
Gotta say, after going from "high" plat, to "mid" diamond, I've realized how little points really matter. People love to say they're a 800+, 1300+, 1500+ diamond player. Well, I was matched up by everything from 600-1600 diamond players before promotion and pretty much won/lost against both high and low players.
Blizzard should show MMR
Is there actually a point where points stabilize? They're obviously not very reliable at 1500~ diamond. Is it better at 1,7-1,8k? 2k? Or should you really never mention your points, cuz they don't really matter?
On November 06 2010 10:30 ribboo wrote: Gotta say, after going from "high" plat, to "mid" diamond, I've realized how little points really matter. People love to say they're a 800+, 1300+, 1500+ diamond player. Well, I was matched up by everything from 600-1600 diamond players before promotion and pretty much won/lost against both high and low players.
Blizzard should show MMR
Is there actually a point where points stabilize? They're obviously not very reliable at 1500~ diamond. Is it better at 1,7-1,8k? 2k? Or should you really never mention your points, cuz they don't really matter?
I was trying to think of situations where they would matter, but I'm really falling short here.
See a guy at 500 Diamond? Maybe he has 1000 bonus pool left over. If he's used all his bonus pool, maybe he got promoted from a lower league and lost a lot of points during the promotion. Maybe he's just that bad (however, win ratio should corroborate this).
Generally speaking, though, because the max total bonus pool increases at a steady rate, points beyond that level are harder to come by so although you may not stabilize, you would at least slow your rise in points. For example, if the bonus pool total is 1300 and you have over 1300, you know that at the very least you're keeping up. Players in the top top top end who have 2700+ points you would expect to be quite good because that's 1400+ points that they've earned beyond the bonus pool max.
I have no idea wtf is up with ladder. I get matched up by a guy with 1800 points. I have 1100. The game decides we are even? wtf? I am like .500 and he was like 30 games above 500. I have no idea how our MMRs could be equal.
So since I am in silver league and have been beating diamond players does that mean the there is too much of a gap between the leagues and I'll be stuck in silver because of this bug? A friends tells me I should start throwing games to be able to get a promotion. Whats going on?
On November 10 2010 11:59 Mitchlew wrote: So since I am in silver league and have been beating diamond players does that mean the there is too much of a gap between the leagues and I'll be stuck in silver because of this bug? A friends tells me I should start throwing games to be able to get a promotion. Whats going on?
From what i understand you should just keep playing. You will eventually hit a wall and when that happens the system will place you where it sees fit, which by the looks of it seems to be diamond.
I'm curious as to how exactly the promotion mechanics work. As mentioned in the OP, my MMR has to maintain itself in the higher league to be promoted. I believe it was also mentioned at one point or another that the system re-evaluates a player after X number of games. Additionally there was mention of a bug.
After being number one in my platinum division for nearly a month (maintaining an average of 51%+ win ratio against Diamond players) I was finally promoted to Diamond today. After I got over the initial shock of it, I looked at the other players in my division. ALL of them were also just promoted to Diamond. My ENTIRE division is 100% full of recently promoted Diamonders. This also occurred after the 1.13 patch.
I'm assuming that either the "bug" has finally been fixed, or Blizzard did a massive coupe to promote higher-level Platinum players to Diamond.
I've read through the various threads here on TL but I'm thinking I've missed something as I don't quite understand how the MMR system is working for team leagues. I've been treading through 4v4 random for a while now, trying to get from platinum into diamond. I've been #1 for a little while now and am approaching 60% winrate, but I don't get how the system rates you and rewards you when you're playing in a game with all different kinds of MMR-rated players. Its a bit frustrating because I got into diamond in 1v1 and 3v3 (dont play 2v2) pretty quickly, but seem to be stuck in platinum for 4v4.
On November 13 2010 15:27 a176 wrote: I've read through the various threads here on TL but I'm thinking I've missed something as I don't quite understand how the MMR system is working for team leagues. I've been treading through 4v4 random for a while now, trying to get from platinum into diamond. I've been #1 for a little while now and am approaching 60% winrate, but I don't get how the system rates you and rewards you when you're playing in a game with all different kinds of MMR-rated players. Its a bit frustrating because I got into diamond in 1v1 and 3v3 (dont play 2v2) pretty quickly, but seem to be stuck in platinum for 4v4.
Any insight is appreciated.
We think it just averages the MMRs of each player on the random team to get the team's MMR. It's unclear whether each player receives MMR gains or losses based on their individual MMR or averaged MMR for the team versus the opposing team's MMR (my guess would be the latter). Of course, the system is basically a black box already for arranged teams and solo play, and adding a random team layer to that is like putting that black box inside another black box.
Arranged teams, of course, work just the same as solo play: each team has a separate MMR.
On November 13 2010 15:27 a176 wrote: I've read through the various threads here on TL but I'm thinking I've missed something as I don't quite understand how the MMR system is working for team leagues. I've been treading through 4v4 random for a while now, trying to get from platinum into diamond. I've been #1 for a little while now and am approaching 60% winrate, but I don't get how the system rates you and rewards you when you're playing in a game with all different kinds of MMR-rated players. Its a bit frustrating because I got into diamond in 1v1 and 3v3 (dont play 2v2) pretty quickly, but seem to be stuck in platinum for 4v4.
Any insight is appreciated.
We think it just averages the MMRs of each player on the random team to get the team's MMR. It's unclear whether each player receives MMR gains or losses based on their individual MMR or averaged MMR for the team versus the opposing team's MMR (my guess would be the latter). Of course, the system is basically a black box already for arranged teams and solo play, and adding a random team layer to that is like putting that black box inside another black box.
Arranged teams, of course, work just the same as solo play: each team has a separate MMR.
Though so. Basically it becomes infinitely harder to increase MMR because of the way bnet [seemingly] matches you with players of all different mmrs. Great :|
From what I understand, this system is actually pretty good. It pairs you against people of higher MMR and league after you are getting above 50% win ratio. If you keep beating those players with higher MMR the system keeps pairing you with people of higher MMR (or your MMR increases no ones sure) as you keep winning until you start winning at a 50% win ratio against those players with a higher MMR. Then whatever MMR you have when you start winning at 50% it then decides which league to dump you in.
So, say a Silver player has 1000 MMR, he starts winning a bunch and starts playing against players with 1500 MMR. then eventually against players with 2000 MMR and then against 2500 MMR players he wins 50% of the time and it just happens that the Gold league's threshold is around 2400. Then the system will match him against a Silver player (Or a player above your league) and if he wins then the system is then confident and his MMR will rise to that a appropriate level. This is my theory on the promotion system anyways. (the numbers are for example purposes)
Does it make any difference if you have selected 3maps that are not to be "included as often" as the other ones.
Forgot to mention this. I play toss. If i play in the morning (EU players GMT hours) then i go for multiple wins (PvP PvZ PvZ) If i play after 9pm ->1am i go for more PvZ (more losses) and PvT PvP is about 50%-50% or 60% wins 40% loss. Most of the time will get matched Vs Z i believe
I am still in Bronze with 1,898 points. Won 380, lost 349 it says on the stats
I hadn't seen this. This is definitely almost identical to the trueskill formula. Awesome.
That's not for matchmaking though, that's the calculation to determine the racial adjusted win percentages.
Looking more at this formula it is quite retarded. The 3 variables in the probability are nowhere to be found in the formula itself, so the variables on the right side are probably derived. Instead of this being a probability function it is more likely to be a distribution function acounting for race and opponents race in the equation, however, because the system does not differentiate your ratings based on matchup, they are including all of the games played. The 3 variables in the distribution(gamma, theta and psi) are usually used to represent 3 different variables to determine the distribution. One of them is most certainly skill, the other 2 are probably race and matchup (in trueskill they use skill, team, and team performance). The denonimator is very similar to the message passing equation from trueskill, and the numerator looks like a standard bayesian probabilty seperating the influences out.
So what is probably happening is that they are determining the skill distribution of each matchup while factoring out the matchup influence (easily done using bayesian probabilty) and then comparing these distributions mean and sigma to determine the win % (which is why the equation is nice and huge).
Other than that, i hate that blizzard doesn't just say what it is. The community is not retards, we went to college, we got degrees in math and science.
The final thing is that i do not believe determining a distribution is possible. If even one of those variables listed is dependant on another variable, then using trueskill is not an accurate way to determine skill (IE if performance is highly dependant on matchup). In chess, they can get away with trueskill because the number of each matchup you play is almost 50/50 (50% of the time you play white vs black, 50% you play black vs white). From that they can detemine a players skill overall. However, because of the influence of matchup to skill in starcraft determining real skill is not possible.
First off, for clarification: Blizzard does not use TrueSkill. Blizzard uses a bayesian inference system which is naturally related to other bayesian inference systems. Your final paragraph is also ambiguous because you mention player skill but the opening sentence references the probability distribution of racial expected win %. That's okay because your conclusion is not correct in either case.
If you meant player skill (which I think you probably did not) then you're saying bayesian inference systems are not good at approximating skill which is pretty demonstrably not the case.
If you meant the racial win % then what it seems like you're saying is that since most players only play a single race that skews things because their performance is not constant against various opponents. That is, Player A usually plays Terran, and is better in TvP than in TvZ. So what you're saying then is that because different players each have this difference (and some more than others) that completely confounds the calculations Blizzard does.
This is incorrect for a couple reasons. First of all, if this pattern existed then Blizzard would have the data to model it and control for it. Second of all, if this pattern existed strongly in aggregate (if most terrans were better at TvP than at TvZ, say) then that would also show up in the win percentages, because the TvP win % would be higher than it ought to be.
If i had to guess as to the reason behind the "needing to loose to rank up" phenomenon i would say that it doesnt have anything to do with a "moving average" but that the system is getting stuck at a local minimum.
Im sure Idra played a ton of games, and likely the system got very "sure" (ie the sigma value approached 0) that he belonged in whatever league he was trying to get out of - maybe because of the ranks of the people he was up against, etc. This is a common problem in learning machines that use a momentum factor. Without time taken into account i dont think the system you are describing can be guaranteed to converge.
The easiest solution to this would be to let uncertainty build up over time, then become more accurate, and repeat this in cycles (ie simmulated annealing).Losing games would raise the uncertainty (probably more rapidly than letting it build up over time) and allow you to move out of the local minimum.
It would negatively affect your MMR but you could "move around" more easily as the system becomes more uncertain.
Basically if you play 18 hours a day and run your sigma up, loosing is probably faster than waiting for it to go back down over time.
On November 20 2010 09:26 ipwnN00bz wrote: If i had to guess as to the reason behind the "needing to loose to rank up" phenomenon i would say that it doesnt have anything to do with a "moving average" but that the system is getting stuck at a local minimum.
Im sure Idra played a ton of games, and likely the system got very "sure" (ie the sigma value approached 0) that he belonged in whatever league he was trying to get out of - maybe because of the ranks of the people he was up against, etc. This is a common problem in learning machines that use a momentum factor. Without time taken into account i dont think the system you are describing can be guaranteed to converge.
The easiest solution to this would be to let uncertainty build up over time, then become more accurate, and repeat this in cycles (ie simmulated annealing).Losing games would raise the uncertainty (probably more rapidly than letting it build up over time) and allow you to move out of the local minimum.
It would negatively affect your MMR but you could "move around" more easily as the system becomes more uncertain.
Basically if you play 18 hours a day and run your sigma up, loosing is probably faster than waiting for it to go back down over time.
Just a guess.
It's definitely a moving average, we had that confirmed at Blizzcon. Your post basically outlines something similar to our initial theory, which was that it's much closer to TrueSkill. That's actually not the case, and sigma actually never shrinks that much in SC2. We were proven wrong at Blizzcon and adjusted the OP accordingly.
On November 21 2010 20:18 sqrt wrote: Wait so...if I am Bronze in Team and Platnum in 1v1, does my team rating affect my solo performance?
I have no real knowledge of this, but it seemed like it to me particularly at one point. I'm Platinum 1v1, not really having played much, very low on points. At the same time I'm Diamond 2v2, decently high rated, as 2v2 goes.
At one point my 2v2 did very well over a couple of nights gaming, and the next time I played 1v1 I seemed to be put up against higher ranked people than I would otherwise be. I was maybe 500 Platinum at the time, and was put up against 1100-1500 diamonds (and some Plats). I met some pretty good people and had a pretty bad streak, and suddenly it felt like we were facing easier opponents in 2v2.
Of course, I can very much see the possibility that this is just something I've made up in my head, and made the events fit better and have more of a connection (if any) than they really do. Damn you, human brain...
So you could take my anecdotal and admittedly uncertain story, or get a straight answer from someone who actually knows. Let's hope for the second one.
On November 21 2010 20:18 sqrt wrote: Wait so...if I am Bronze in Team and Platnum in 1v1, does my team rating affect my solo performance?
I have no real knowledge of this, but it seemed like it to me particularly at one point. I'm Platinum 1v1, not really having played much, very low on points. At the same time I'm Diamond 2v2, decently high rated, as 2v2 goes.
At one point my 2v2 did very well over a couple of nights gaming, and the next time I played 1v1 I seemed to be put up against higher ranked people than I would otherwise be. I was maybe 500 Platinum at the time, and was put up against 1100-1500 diamonds (and some Plats). I met some pretty good people and had a pretty bad streak, and suddenly it felt like we were facing easier opponents in 2v2.
Of course, I can very much see the possibility that this is just something I've made up in my head, and made the events fit better and have more of a connection (if any) than they really do. Damn you, human brain...
So you could take my anecdotal and admittedly uncertain story, or get a straight answer from someone who actually knows. Let's hope for the second one.
Well, my 2v2 partner may be looking for another person then.
On November 21 2010 20:18 sqrt wrote: Wait so...if I am Bronze in Team and Platnum in 1v1, does my team rating affect my solo performance?
Only for the first placement match in a new team or bracket. For example, Vanick and I were in a Diamond 2v2 team but I hadn't played any 1v1. When I did start 1v1, I was put against Diamond-strength opponents from the very beginning, and that's because it was carrying over my 2v2 performance into 1v1. After the first placement match, the MMRs are completely separate.
i am still in bronze. I noticed that after getting several wins with +28, +22, +28, +22 points all of my following games where with silver and diamond players. So i hope soon to be my turn. Some stats, iam 1 or 2 on my division 391 won, 357 lost, ratio of 52.27%
I watched the video of the Blizzcon discussion (including your question)- the bit about the "moving average" was ambiguous at best- it could have just been simplifying what is essentiall a graduate level computer science topic to a more approachable concept.
To be clear, what i was suggesting is something more along the lines of the wayTDGammon estimates who will win a backgammon game (http://www.research.ibm.com/massive/tdl.html) as opposed to trueskill.
On November 23 2010 01:00 ipwnN00bz wrote: I watched the video of the Blizzcon discussion (including your question)- the bit about the "moving average" was ambiguous at best- it could have just been simplifying what is essentiall a graduate level computer science topic to a more approachable concept.
Considering the subject matter and the depth that we were discussing with him after the panel ended, I don't think this is the case.
I am getting sick of still not being promoted. Out of the last 50 games I have played in Bronze 1v1, I have won 40. My w/l ratio in total stands at 90W 60L.
I clearly no longer belong in Bronze.
I'm still stuck here I think it might have something to do with being crap in 1v1 at the beginning. I honed my skills in 4v4, went back to 1v1 and started slaughtering most opponents.
On November 27 2010 11:28 ThaZenith wrote: I can almost guarantee that your rating in team matches like 2v2, 3v3, 4v4, have an impact on your 1v1 matchmaking.
He was in his third placement match in 1v1, and was "favored" even though he has lost his first 2 matches. He was gold in 2v2 with 200+ games played.
A 0-2 player favored over a maybe 30-13 (at the time) player seems silly otherwise.
We knew that already. When you start a new team or bracket it uses data from your other brackets as a starting point.
I have a problem. Basically I'm up for promotion so they put me against a silver league player or at least someone more favoured. Basically for each loss against say slightly favoured, it takes another 5 wins at even to get back up there.
It would be better if I was to consistently play against better players and consistently lose and improve my skill, rather than play a better player, lose the win the next couple of matches because I'm better than the next batch it sets me up against.
Sooo question. I bought the game and really had no idea what was going on. I lost all my preliminary matchups and than lost nine straight games. I got some help from friends and really picked up my game play. I am now 37 - 25 in a Bronze league playing and beating Silver League players.I have now won 15 in a row. Am I looking at a promotion or am I winning too much for the sigma to catch up?
Excalibur, can you explain something real quick to me?
I started a Smurf for fun purposes, and after my placements, I was immediately placed against Diamond players. I am now at 35-5 in Platinum, easily beating 2.6k+ players. Is my non-promotion a result of my MMR shooting up too fast and my moving average lagging behind?
Is it better to only play when you have at least 20 or so bonus points? Or does it not matter?
It seems like your MMR isn't affected at all by bonus points but your ladder rating is. If you are always playing people of roughly equal mmr (regardless of their ladder points in relation to yours), isn't it better to maximize the amount of ladder points you could earn from the win? Wouldn't this make your wins more efficient in terms of how they reflect your ladder ranking?
For example, player A and player B are of equal mmr. They are both rank 50th in diamond. Player A plays 10 games a day and always keeps his bonus pool empty, while player B only plays a game if he has at least 20 points. They both maintain an exactly 50% win ratio. Since they both have the same mmr, they will both be playing similarly ranked players, and will therefore be earning and losing similar amounts for wins/losses, but player B will get free bonus points added for wins. Won't player B end up with more points because his wins are making more points? Even though player A is winning more games total, he is also losing more games total. They both end up with the same mmr, but player B has more ladder points, and is ranked higher.
I was wondering the same thing and his part 1 explained it to me, or at least I feel I understand... Excalibur correct me if im wrong.
You have 2 ratings on your account, your ladder rating(displayed) and your matchmaking rating. If both of you have a 50% win rate, assuming you both started with the same match making rate, then in long run you will end up at the same point.
This is because your display rating and matchmaking rating eventually coverage. So in your example, yes he is gaining more points so just say he's at 2000 points displayed but 1800 match making. You for i.e would be at 1600 displayed but 1800 match making as well.
How they converge is that he will gain less if he wins because his 2000 displayed is much greater than his 1800 match making while you will gain a lot more when you win to get closer to your match making. Vice versa for losing as well - you will lose less then he does against the same opponent so that your displayed rating gets as close to your match making rating.
Your matchmaking rating is not affected by bonus pool.
So in theory, in the long run, you will eventually have the same amount of points assuming you use all your bonus pool .
A little information to stir the pot, or maybe just to add a little confusion. I'm a 1000 Plat player in 1v1 with a win ratio of 59% percent. Last 15 matches have all been vs diamond and I won 12/15. Last match was against a 2000 diamond and was considered "even" Two matches before that one was against a 600 diamond and he was "slightly favored" After looking at the Platinum world wide rankings, I couldn't find a single one that was over a 59% win ratio. Will I get promoted as soon as I hit that magical 60% win mark? I guess we will see....
I have given up on getting promoted from silver at this point. I am constantly beating top gold players and some plat players, but in silver i am stuck for eternity. My sc2sig.com chart looks like this:
On December 14 2010 09:40 Ghad wrote: I have given up on getting promoted from silver at this point. I am constantly beating top gold players and some plat players, but in silver i am stuck for eternity. My sc2sig.com chart looks like this:
hopefully the ladder reset can shake things up.
I'm having the exact same problem as you. I am exclusively facing mainly top gold and a few mid plat players and I'm in silver and I have a 60% win rate. It's getting kinda lame. It feels like my MMR is way lower than what it's supposed to be.
I entered silver. Nr2 then nr14 or somenthing then nr 9, now back in bronz. just poor play. But it was much faster to get domoted then promoted
EDIT: To mention that the day i was promoted a new division must have been created as all the people on it where new promotions. May be there is a sortage of divisions and when one must wait for them before one is promoted
This makes sense. I get promoted quickly because I play fewer games but win more often, but if I played a lot in the short period of time I would be still behind the needed calculations in order to formulate a solid lead.
hey can someone answer this question for me? if you are exactly evenly matched with someone. same division modifier same mmr everything is the same lets say. if you win / lose how much points do you win / lose before bonus pool is factored in?
After a match finishes, the system needs to update the MMR and sigma for both players. Displayed rating will be discussed later in this post. Whenever a match finishes the winner’s MMR increases and the loser’s decreases. More interesting is what happens to the sigmas. If the match finished as expected with the MMR favored player winning (and remember, the loading screen “favored” display is NOT this) then both players' sigmas will decrease.
I'm not sure I completely agree with this part, in a Bayes model what also needs to be taken into account is your mmr speed. Say we consider your current mmr/match, that is, the ammount of mmr you gain per match averagely. Say you just started out, you have an mmr of 1, but you're friggin pro so you win your first 50 matches non stop. So your mmr per match is constantly increasing.
Even if you're matched to someone with a lower mmr and you beat that player, your sigma would still increase because your mmr speed again increased due to that match.
The precise phrasing lies, I believe, in mmr-accelleration. If in a Bayes-based system, if your mmr accelates due to a match result, that is, it increases more than it increased last match, then your sigma should also increase, if your accelaration decreases however then it should shrink.
In practice though, it comes down to that almost every time your mmr decellarates, it's because of a match that has an expected result. But take for instance this hypothetical situation:
Say you have a 50 player pool, you have one player who is orders of magnitude above all others, each player faces each other player 1 time, while all the other palyers have around a 50/50 win/loss ratio at the end, this one player won all his 49 matches straight. At the end, this system will have given him a huge mmr, but also a huge sigma. There simply aren't any players near his level to compare him with for the system and give him a small sigma. So even though most likely after the first couple of matches he kept winning against players whom the system expected him tow in against, he would still increase his sigma.
I believe the microsfot trueskill page also says something like this. Basically for the sigma to decrease after an expected result, both players mmr must be relatively similar. (microsoft says their absolute difference must lie within the sigma of the stronger player), while the mmai matches you continually against players who have somewhat of a similar mmr, in the hypothetical situation that there is one godlike player who is heaps and bounds above all other players, this can't happen. So even though he wins every single match, and is expected to win every single match by the system, with each win his mmr and sigma increases. Which makes sense from a mathematical perspective, as in such a situation there is no way to determine just how much better he is than everyone else, only that he is better.
On December 28 2010 05:30 JiYan wrote: hey can someone answer this question for me? if you are exactly evenly matched with someone. same division modifier same mmr everything is the same lets say. if you win / lose how much points do you win / lose before bonus pool is factored in?
Seems like it's 12 or 13. I think the 'Teams Even' range is 10-15 points. I believe slightly favored will reward an upset with 16-18, and favored with 19+. I suspect it works differently if the confidence in one or both players is low, however.
I have a friend in bronze that doesnt play alot in 1v1 ladder and got something like 66% win rate and lately havet 15 wins in 16 games 5-7 of them against favoured gold league players and he doesnt get promoted. why is that?
On January 25 2011 04:56 0AtRi0 wrote: how do we know when our moving average passes the threshhold, and we should be promoted?
You don't. It's kept hidden. Furthermore a game is only counted toward promotion (wording could be clearer there) if it's against an active player by Blizzard's definition. You just have to keep playing and winning games. Unfortunately due to the nature of the random matchmaking system, you don't really know when you're going to get promoted because of the various factors involved in deciding that promotion which are hidden from the player's view.
On November 13 2010 15:27 a176 wrote: I've read through the various threads here on TL but I'm thinking I've missed something as I don't quite understand how the MMR system is working for team leagues. I've been treading through 4v4 random for a while now, trying to get from platinum into diamond. I've been #1 for a little while now and am approaching 60% winrate, but I don't get how the system rates you and rewards you when you're playing in a game with all different kinds of MMR-rated players. Its a bit frustrating because I got into diamond in 1v1 and 3v3 (dont play 2v2) pretty quickly, but seem to be stuck in platinum for 4v4.
Any insight is appreciated.
Some data for you. After 4-5 months, I have finally been put into diamond 4v4 random at 302-274 wins. This after losing a good 5 or 6 games in a row.
since game came out i've been thinking that the only explanation to promotion early/late might be the actual game points you got per time when game is finished
this is just a wild guess and i got some critisms... but the more i think about it, the more it makes sense to me... for 1, it explains a few promotions to masters with only 40-30 records their points per time is really high for 2, it explains a few players who did not get promoted even going 50-10 to masters their points per time is really low
i do not think bnet looks into each game's statistics very closely, but to record and relate to a single game by it's points per time is very simple
let's say for excal's explanation diamond mmr 2600 sigma 100 vs platinmum mmr 2200 sigma 200 and there is an upset mmr 2200 guy wins so new stats be diamond mmr 2400 sigma 150 and platinmum mmr 2400 sigma 180
and now since the platinmum guy reached the assumed diamond threshold mmr 2300 then there would be a check on the statistics of the game, this game in particular, that got the platinum's player's mmr above the threshold you can see a player's game history statistics, and i think it may be a good indication, more/less on how well the player has been playing compare the rate of economic spending, technology spending, and army spending, average APM, etc.
so to excal, if you haven't find solutions to your question, here is my thoughts use it or discard it as you wish
I'm currently experiencing the wrath of this hidden system! I pretty much only play 3k+ Diamond players and 2500+ Masters players with decent win/loss ratios. Obviously, this doesn't determine their MMR, but I can tell you something weird is going on here. Consistently I played against 5 Masters level, 2500 players. Towards the end of this set of games, I was actually slightly favored against them!? I know I read earlier in this thread that this system doesn't determine everything, but come on! If I'm constantly playing and beating players in a league above me, why doesn't it promote that? Also, relatively I have a low number of games played so you would think it could recognize that I have a higher win %, low number of games, and playing users in a league above me and winning. Anyways, below is the link to my profile so you can see what I'm talking about.
On February 09 2011 01:00 SeakayKu wrote: since game came out i've been thinking that the only explanation to promotion early/late might be the actual game points you got per time when game is finished
this is just a wild guess and i got some critisms... but the more i think about it, the more it makes sense to me... for 1, it explains a few promotions to masters with only 40-30 records their points per time is really high for 2, it explains a few players who did not get promoted even going 50-10 to masters their points per time is really low
i do not think bnet looks into each game's statistics very closely, but to record and relate to a single game by it's points per time is very simple
let's say for excal's explanation diamond mmr 2600 sigma 100 vs platinmum mmr 2200 sigma 200 and there is an upset mmr 2200 guy wins so new stats be diamond mmr 2400 sigma 150 and platinmum mmr 2400 sigma 180
and now since the platinmum guy reached the assumed diamond threshold mmr 2300 then there would be a check on the statistics of the game, this game in particular, that got the platinum's player's mmr above the threshold you can see a player's game history statistics, and i think it may be a good indication, more/less on how well the player has been playing compare the rate of economic spending, technology spending, and army spending, average APM, etc.
so to excal, if you haven't find solutions to your question, here is my thoughts use it or discard it as you wish
Nope, any in-game data is completely discarded because it's potentially exploitable. A truly unbiased system (which is the best kind of system) only cares about wins and losses and the quality of the players participating. You can find this confirmed on the official Battle.net forums, in the Multiplayer and E-Sports forum, in a sticky posted at the top called the Leagues and Ladders FAQ.
Oh, I wanted to add. Seems that 4v4 diamond league was a new one - everyone joined on the same day. So it seems blizzard has some kind of limit on the actual number of leagues? Sorry if this is old news, I skimmed the OP but I don't think I saw anything relating to that.
Ok, I have a question about this system. I understand the basics of what excalibur wrote, but I would like a couple of information about my case.
I decided to switch race, and so start from the beginning. I free lost 63 games in a row to get from diamond to bronze, and now i'm playing seriously with my new race. I won about 30 games, and lost 4 or 5, and get usually 10 wins streaks. Only thing is I've not seen a single silver opponent for the moment.
I suppose I should continue to win to eventually raise my MMR high enough to face silver players, but I'm a bit confused about the number of wins I need. If after 30 wins / 5 loss I'm fighting top 10 bronze players, it will roughly take as many wins to get promoted to silver, and then again as many to gold, etc..., but I only lost 63 times.
So maybe by intentionally losing I messed too much with my status and the ladder system is lost to properly evaluate my level. Or maybe I need a lot of wins to stabilize my incertainty rating back to decent level, and then it will be faster to get promoted once I start to play higher league players, and I can jump swiftly from bronze to platinum for example. Or maybe my occasional losses are the reason why I need so many games to face higher players, since it hurts my mmr a lot to lose vs bronze players.
Bronze is probably a much larger league (spans a greater MMR range) than Silver, Gold, or Platinum. We believe Diamond is about as large as Bronze. Getting out of Bronze is the first hurdle, but it won't take you equally long to get through the other leagues if you maintain your level of performance.
Did you lose enough till the system would demote you without the need of a win? If so, then you're probably in the lowest tier of bronze, which is interesting, can you say the division name? :D
On March 05 2011 02:27 Excalibur_Z wrote: Bronze is probably a much larger league (spans a greater MMR range) than Silver, Gold, or Platinum. We believe Diamond is about as large as Bronze. Getting out of Bronze is the first hurdle, but it won't take you equally long to get through the other leagues if you maintain your level of performance.
maybe ive missed something but why do you believe bronze is bigger than any other league? i know its the only league where you can go down forever. but i thought the assumtions were the mmr barriers for each league would shift with the population to fit expected percentages? if thats still the running theory each league should maintain its 20% of players, or 18% for the current diamond?
On March 05 2011 02:27 Excalibur_Z wrote: Bronze is probably a much larger league (spans a greater MMR range) than Silver, Gold, or Platinum. We believe Diamond is about as large as Bronze. Getting out of Bronze is the first hurdle, but it won't take you equally long to get through the other leagues if you maintain your level of performance.
maybe ive missed something but why do you believe bronze is bigger than any other league? i know its the only league where you can go down forever. but i thought the assumtions were the mmr barriers for each league would shift with the population to fit expected percentages? if thats still the running theory each league should maintain its 20% of players, or 18% for the current diamond?
The 20/20/20/20/18/2 split is for active players (who have spent, or are spending, a high proportion of their bonus pool). Sc2ranks looks at all players (or all players it can find anything about, which is likely to be more or less the same thing) and it consistently gets a figure of about 45-60% of the players are bronze.
Note that not being 'active' doesn't necessarily mean the players aren't playing Starcraft. Here, 'active' is a technical term used by Blizzard that doesn't quite correspond with your intuition.. You'll find that 45-60% of the players who played in the last week are bronze too.
Anyways, I reckon the grandparent is wrong, not because of the relative sizes of the leagues, but because of the operation of diminishing returns. My guess is that it'll be far easier to go from bronze to silver than it will from Diamond to Masters, or Platinum to Diamond, because you have to work on far more tricky and detailed parts of your game to do the latter.
This has now happened twice, so it's no longer a coincidence. Last season I lost the first match after my promotion to gold. My points however increased. The score screen said -13, but my points increased with 19. The difference is 32, which is what I got for my promotion match. It seems that I got the points for that match again.
Now the same thing happened again. I won 28 points for my promotion match to platinum (14 + 14). Then I lost the next match. The score screen said -13, but my points increased with 15, which happens to be -13 + 28.
On April 25 2011 17:40 Mendelfist wrote: This has now happened twice, so it's no longer a coincidence. Last season I lost the first match after my promotion to gold. My points however increased. The score screen said -13, but my points increased with 19. The difference is 32, which is what I got for my promotion match. It seems that I got the points for that match again.
Now the same thing happened again. I won 28 points for my promotion match to platinum (14 + 14). Then I lost the next match. The score screen said -13, but my points increased with 15, which happens to be -13 + 28.
Has anyone else noticed this?
I think things that like have been reported, but they're mostly attributed to missing wins in match history? I also don't think many players notice it because it's hard to notice unless you're tracking your points after each game (like you do).
EPT
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