SC2 Ladder Analysis - Hidden Ratings. - Page 2
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Deleted_143
Australia256 Posts
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Acritter
Syria7637 Posts
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Catreina
United States303 Posts
I am at 1532 points in diamond, and based on the formula I am around 3200 MMR. That seems high to me - it just seems weird that I would be within 1200 MMR of Dayvie: My information Rating = (division - 1) * 500 + (points) + (bonus pool remaining) + (1500 - total bonus pool) Rating = (4-1) * 500 + 1532 + 16 + 1500 - 1331 Rating = 3*500 + 1532 + 16 + 1500 - 1331 Rating = 3217 Vs Dayvie: Rating = 3*500 + 2604 + 102 + 1500 - 1331 Rating = 4375 I know this is to give an idea, but is the MMR that close for scrubs like me compared to pros and pro-level skilled players like Dayvie? | ||
darmousseh
United States3437 Posts
On November 01 2010 10:48 Catreina wrote: I am not sure, but I think (at the time of this writing) that this might be a little flawed. I am at 1532 points in diamond, and based on the formula I am around 3200 MMR. That seems high to me - it just seems weird that I would be within 1200 MMR of Dayvie: My information Rating = (division - 1) * 500 + (points) + (bonus pool remaining) + (1500 - total bonus pool) Rating = (4-1) * 500 + 1532 + 16 + 1500 - 1331 Rating = 3*500 + 1532 + 16 + 1500 - 1331 Rating = 3217 Vs Dayvie: Rating = 3*500 + 2604 + 102 + 1500 - 1331 Rating = 4375 I know this is to give an idea, but is the MMR that close for scrubs like me compared to pros and pro-level skilled players like Dayvie? Yes, remember ratings are a way of measuring the odds of beating someone. Given those two ratings you have basically a 0% chance of beating him (on average). It's probably close to 1/10,000. | ||
darmousseh
United States3437 Posts
On November 01 2010 10:44 Acritter wrote: Okay... so I started out in Gold, and within 30 or so games entered Diamond (Plat on the way, of course) at around 500 or 600 points, I forget which. I find that somewhat shockingly fast, given that my points didn't go up fast enough to account for my extremely high rating. How does your model account for that? The ratings are not very accurate if you have played under 50 games or you have an unusual streak lately. However, remember that your points will converge to your rating over time. If you are still under 200 games played, then your points will be a little high and you will play a bunch of favored games in a row which will lower your rating to help it converge to where it should be (it will say favored, but actually it's an even game, it says favored so that it can give you less points for a win and lose more points for a loss) | ||
Sanguinarius
United States3427 Posts
And it really feels that you might have it right. The question will be - is 1500 still the average in 1 month, or does the average change? Guess only time will tell. | ||
darmousseh
United States3437 Posts
On November 01 2010 10:56 Sanguinarius wrote: I'll be honest, this is the most well thought out post about MMR I have read. And it really feels that you might have it right. The question will be - is 1500 still the average in 1 month, or does the average change? Guess only time will tell. From what i've seen, and what i've read, blizzard will probably change the groups so that there are more diamond players and less bronze so expect the top of bronze to be in silver in season 2 and expect the top of plat to be in diamond. | ||
Sanguinarius
United States3427 Posts
On November 01 2010 10:48 Catreina wrote: I am not sure, but I think (at the time of this writing) that this might be a little flawed. I am at 1532 points in diamond, and based on the formula I am around 3200 MMR. That seems high to me - it just seems weird that I would be within 1200 MMR of Dayvie: My information Rating = (division - 1) * 500 + (points) + (bonus pool remaining) + (1500 - total bonus pool) Rating = (4-1) * 500 + 1532 + 16 + 1500 - 1331 Rating = 3*500 + 1532 + 16 + 1500 - 1331 Rating = 3217 Vs Dayvie: Rating = 3*500 + 2604 + 102 + 1500 - 1331 Rating = 4375 I know this is to give an idea, but is the MMR that close for scrubs like me compared to pros and pro-level skilled players like Dayvie? That rating system actually shows that you have almost no chance of beating Dayvie (1100 pt difference is well below 1%) I think in WoW, the lowest % win chance they gave someone was 5% - because they figure even pros have some off games. EDIT: darmousseh beat me to the reply | ||
ryanAnger
United States838 Posts
On November 01 2010 11:05 Sanguinarius wrote: That rating system actually shows that you have almost no chance of beating Dayvie (1100 pt difference is well below 1%) I think in WoW, the lowest % win chance they gave someone was 5% - because they figure even pros have some off games. EDIT: darmousseh beat me to the reply How are you determining the %? I'm really confused by what the MMR actually means in terms of relative skill. | ||
Blu3
United States126 Posts
Platinum, with about 1050 points, about 300 bonus pool available so, (3-1)*500 + 1050 + 300 + (1500-????) | ||
darmousseh
United States3437 Posts
On November 01 2010 11:15 Blu3 wrote: How do we know how many bonus points have been available? Platinum, with about 1050 points, about 300 bonus pool available so, (3-1)*500 + 1050 + 300 + (1500-????) The easiest way is to find a person who has played exactly 5 games and check their bonus pool. Right now it's like 1331. | ||
vanick
United States53 Posts
On November 01 2010 08:36 darmousseh wrote: First off we know that blizzard is using an ELO type of system. It is highly likely that it is either trueskill (made by microsoft) or glicko-2. Let us assume that they are using trueskill (it doesn't make that much of a difference). The ELO system is fairly far removed from the TrueSkill and Glicko systems, the main difference being the addition of variance to the mix. I am extremely interested to see your analysis of sub-diamond leagues. Specifically, with your formula you can determine each player's MMR and thus what the post-game changes to points (and thus MMRs) should be. Another issue your formula has right now is it doesn't take into account the often large swings in MMR that occur (as we saw in WoW arenas) that are dampened by the points system. As a starter test: The player kozlodoi from the RU realm. He is a high-ranked Platinum player. I don't know his actual bonus pool remaining, but the assumption that gives most benefit to your theory is that he has 0 pool remaining. The result of this calculation: Rating = (division - 1) * 500 + (points) + (bonus pool remaining) + (1500 - total bonus pool) Rating = (3 - 1) * 500 + (1787) + (0) + (1500 - 1332) Rating = (2) * 500 + 1787 + (168) Rating = 2955 He has over 400 games played and has a 55% ratio. His MMR is likely fairly stable. Your theory would predict that he should be in Diamond by now. How do you explain his lack of promotion, given what we know about the moving average? edit: haha why did I do this work. In your formula, is the (points) term your displayed points (i.e. it includes your consumed bonus pool)? If so you can simplify it because (points) = (consumed bonus) + (earned points) Therefore: Rating = (division - 1) * 500 + (points) + (bonus pool remaining) + (1500 - total bonus pool) Sub in points... Rating = (division - 1) * 500 + ((consumed bonus) + (earned points)) + (bonus pool remaining) + (1500 - total bonus pool) And until we hit the bonus pool cap (which we haven't yet, nor do we know what that cap is): (consumed bonus) + (bonus pool remaining) = (total bonus pool) So by using a bit of the commutative property we can cancel out the bonus pool terms entirely... Rating = (division - 1) * 500 + (earned points) + 1500 Leaving 1500 as a magic number uniformly applied across everyone to make the MMRs inflated for no real reason which means that your formula really boils down to: Rating = (division - 1) * 500 + (earned points) This is not very convincing when held up against what we see on the ladder every day. | ||
darmousseh
United States3437 Posts
On November 01 2010 11:42 vanick wrote: The ELO system is fairly far removed from the TrueSkill and Glicko systems, the main difference being the addition of variance to the mix. I am extremely interested to see your analysis of sub-diamond leagues. Specifically, with your formula you can determine each player's MMR and thus what the post-game changes to points (and thus MMRs) should be. Another issue your formula has right now is it doesn't take into account the often large swings in MMR that occur (as we saw in WoW arenas) that are dampened by the points system. As a starter test: The player kozlodoi from the RU realm. He is a high-ranked Platinum player. I don't know his actual bonus pool remaining, but the assumption that gives most benefit to your theory is that he has 0 pool remaining. The result of this calculation: Rating = (division - 1) * 500 + (points) + (bonus pool remaining) + (1500 - total bonus pool) Rating = (3 - 1) * 500 + (1787) + (0) + (1500 - 1332) Rating = (2) * 500 + 1787 + (168) Rating = 2955 He has over 400 games played and has a 55% ratio. His MMR is likely fairly stable. Your theory would predict that he should be in Diamond by now. How do you explain his lack of promotion, given what we know about the moving average? edit: haha why did I do this work. In your formula, is the (points) term your displayed points (i.e. it includes your consumed bonus pool)? If so you can simplify it because (points) = (consumed bonus) + (earned points) Therefore: Rating = (division - 1) * 500 + (points) + (bonus pool remaining) + (1500 - total bonus pool) Sub in points... Rating = (division - 1) * 500 + ((consumed bonus) + (earned points)) + (bonus pool remaining) + (1500 - total bonus pool) And until we hit the bonus pool cap (which we haven't yet, nor do we know what that cap is): (consumed bonus) + (bonus pool remaining) = (total bonus pool) So by using a bit of the commutative property we can cancel out the bonus pool terms entirely... Rating = (division - 1) * 500 + (earned points) + 1500 Leaving 1500 as a magic number uniformly applied across everyone to make the MMRs inflated for no real reason which means that your formula really boils down to: Rating = (division - 1) * 500 + (earned points) This is not very convincing when held up against what we see on the ladder every day. Esentially it is Rating = (division - 1) * 500 + (earned points), however most players have not played the require number of games in order consume the entire pool and therefore i had to add it into the equation. But in essence this is correct and I believe it is true since blizzard said "Your points will converge towards your actual rating". As i said in an earlier reply it is difficult to tell what this means. It's either mean - 2 * sigma mean mean + 2 * sigma. I believe it is the 3rd one because of a phenomena i noticed which is when you change divisions you start playing a bunch of Favored games. As far as that high ranked russian player, i'm not entirely sure. I did the numbers based off of the US server only. It is possible that the russian server has larger groups or that he is an abberation and the system is just waiting for his sigma to drop below a certain point. For promotions i have several theories. 1. You get promoted immediately when your mean is over the threshold. 2. you get promoted after playing X games once you mean is over the threshold during that time. 3. You get promoted after your mean - 2 * sigma is greater than the threshold. I tend to believe it is #3 since this would prevent people who have lucky streaks from just changing divisions too frequently. Also being streaky can increase your sigma, so the mean - 2 * sigma would still be in the platinum threshold. There is one possibility. MMR can fluctuate very wildly and it is likely that your points rating (+ the division bonus) can be significantly different. The system then compares your points + division bonus to your rating in order to balance out your displayed points. My equation seems to hold more true for those that play consistantly and with a higher number of games than those with less than 50 games, however, i found it to distribute evenly among all the divisions for players that have played at least 200 games. | ||
Deathfate
Spain555 Posts
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Benjilol
Australia244 Posts
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darmousseh
United States3437 Posts
On November 01 2010 12:13 Benjilol wrote: How does your forumula factor in points lost when moving up divisions? ie: losing points from ranking from Bronze -> Diamond vs Placing in Plat and ranking up once? Good question, i couldn't figure out a standard for it, but essentially I believe it just pushes your points + bonus pool + division bonus towards your MMR. Most likely it just removes points. I am still looking into this and will let you know if i have any insights. Overall the formula is more stable for those who have played 200+games. | ||
vanick
United States53 Posts
On November 01 2010 12:05 darmousseh wrote: Esentially it is Rating = (division - 1) * 500 + (earned points), however most players have not played the require number of games in order consume the entire pool and therefore i had to add it into the equation. But in essence this is correct and I believe it is true since blizzard said "Your points will converge towards your actual rating". Adding it to the equation isn't changing anything because the bonus pool terms cancel out. So what we're left with is you are simply offsetting player points by separating leagues by 500 points. As i said in an earlier reply it is difficult to tell what this means. It's either mean - 2 * sigma mean mean + 2 * sigma. I believe it is the 3rd one because of a phenomena i noticed which is when you change divisions you start playing a bunch of Favored games. Or because when you are promoted the points it starts you at aren't your MMR, and may be below it even though the points approach what your MMR is. As far as that high ranked russian player, i'm not entirely sure. I did the numbers based off of the US server only. It is possible that the russian server has larger groups or that he is an abberation and the system is just waiting for his sigma to drop below a certain point. For promotions i have several theories. 1. You get promoted immediately when your mean is over the threshold. 2. you get promoted after playing X games once you mean is over the threshold during that time. 3. You get promoted after your mean - 2 * sigma is greater than the threshold. I tend to believe it is #3 since this would prevent people who have lucky streaks from just changing divisions too frequently. Also being streaky can increase your sigma, so the mean - 2 * sigma would still be in the platinum threshold. Blizzard stated that they use a moving average. Once your moving average is stable within a league (and within the general fluctuations of your MMR) a promotion will happen. | ||
darmousseh
United States3437 Posts
On November 01 2010 12:32 vanick wrote: Adding it to the equation isn't changing anything because the bonus pool terms cancel out. So what we're left with is you are simply offsetting player points by separating leagues by 500 points. Or because when you are promoted the points it starts you at aren't your MMR, and may be below it even though the points approach what your MMR is. Blizzard stated that they use a moving average. Once your moving average is stable within a league (and within the general fluctuations of your MMR) a promotion will happen. I agree with everything you said here. The only reason i have the bonus pool added is for people who haven't used all their bonus points. The other way is to subtract the earned bonus points from each player, however we don't have that information, the only information we have is current points and bonus pool remaining. You could determine the earned points if you do a little extra math i guess, but in the end it doesn't matter like you said. All that matters is that the apparent difference between the leagues appears to be 500 points. | ||
Polygamy
Austria1114 Posts
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Excalibur_Z
United States12204 Posts
On November 01 2010 10:40 Medzo wrote: I just want to point out that your hidden rating isnt determined by your shown rating at all. If you look at the top 200 a lot of those people are not in the top 200 on scranks (shown rating ranks). It is because their hidden ratings are higher than other people with higher point ratings. Basically what it seems like to me is you are ranked in your division by your hidden rating and the system will correct itself and give you the correct amount of shown rating points so that this is accurate. I have 2 reasons for this hypothesis. First, In my own division pylon kappa last week everyone rank 9 and above was in the blizzard hidden rating top 200 in the same order of their ranking. The 9th ranked person was 1965 points which is about rank 400 in shown rating. My second reason is just from playing at a ladder and profiling my opponents when im favored or unfavored. If you have a high hidden rating you will fight other players who you are favored over who have a higher shown rating, they are usually rank 1 or 2 in their division with about 2k points but have hidden ratings similar or lower than 1600-1800 in harder divisions. At the same time you can play another player with lower or equal shown and hidden rating in equally hard or harder (medivac alamo) divisions. This is easily noticeable when you have a very high hidden rating. While I don't necessarily think it's possible to determine MMR from displayed rating concretely, I think your reasoning is wrong here. The Top 200 is a list of players by points with division influences removed, it's not by hidden rating. That is confirmed by Blizzard. The formula posted by the OP is also incorrect because it considers points even across all divisions, which we know from Blizzard not to be the case. We also don't know whether there is a division hierarchy (where Medivac Alamo > Medic Mu > Observer Mars for example) or just different tiers of divisions (where Medivac Alamo, Medic Mu, Observer Mars are Tier 1, Augustgrad X-Ray and Scout Kilo are Tier 2, etc). For example, the first week of the Top 200 had mostly Medivac Alamo, Medic Mu, Observer Mars, and Akilae Omicron members listed. The third week added a few new divisions popping up in the list: Immortal Yankee, Infestor Pepper, Pylon Kappa. If you compared their rankings in the Top 200 with some old SC2Ranks snapshots taken within a day of the Top 200 announcement, most of the scores lined up. However, there were some outliers. Dayvie is the most prominent. He had more points than most other players but was below them on the Top 200 list, and that's because his division Scout Kilo is not weighted the same as the original "top" divisions. | ||
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