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First and foremost: if you expect to have a complete solution of how the SC2's ratings work, you will be very much disappointed.
My goal with this thread is to report what I know for sure, which I feel some people will learn a bit on the system, and what are my hypotheses on its functioning, as well as answer some questions or critics about that system and get some feedback from you guys to try and dig it further.
ON THE NUMBER OF POINTS EARNED/LOST
What is known for sure
The number of points you earn/lose after each game follows this formula :
edit #3 : rewritten the formula to better formalize it (but it did not change whatsoever, big thanks to edahl for this)
p = c + x + b
where p : the total number of points (in absolute value)
c : a constant equal to 12
x : the relative expected skill level (or rating) between opponents
b : the points you get from your bonus pool (which includes the rested pool)
=> x is a value in in {-12,...,12}, positive numbers are when your opponent is favored
- if the game says you are even, x = 0
- if it says your opponent is slightly favored, then x is in {-3,...,3}
- if it says your opponent is favored, then x is in {-12,...,-4; 4,...12}
(of course, if you are the slightly/favored player, then x is negative)
This is true when you win, it is actually the opposite when you lose (that's why I wrote the absolute of x), this means you lose more than 12 points after a defeat where you were the favored player.
=> b is different from 0 under 2 conditions :
{your bonus pool is >0
{you are victorious
If these 2 conditions are met, then b = 12 + x (again, if your opponent was favored, x > 0)
edit #2 Note : there is a known issue with the indication of who was favored in the detailed breakdown of points after each game.
What is uncertain & my own hypotheses
=> The exact calculation of x is unknown, but I highly doubt it is calculated based on the current rating differential. Rather, it probably considers the expected rating, that is what the system considers to be your "true rating". That value is of course accompanied with a certain interval for which there is a probability that your rating is contained. If this is the case, then the "30 games" mark makes absolute sense with probabilistic distributions as it is a value where you can expect the rating of a player to be in the proper margin with 95% confidence (which is standard level).
Alright, enough technical blabbering, in short : I'm fairly sure blizzard's formula follows something close to the glicko rating system, adapted for the multiple divisions system.
Example calculation
Grrr plays Bisu, Grrr wins. Bisu was slightly favored, exact value being 2.
Grrr will then get p = 12 + 2 + (12+2) = 28 pts for this win. Had Grrr lost, he would have lost : y = 12 - 2 = 10 pts
Conclusions
The value of x is exactly the reason why top players were often getting 0-2pts from wins and losing 20+ when they lost early on, their opponents were rated much lower.
In the end, no, the number of players in a division does not matter and the rating of players within a league CAN be compared. (see bonus pool and rested points)
The maximum number of points you can earn is 48, with the bonus pool, the minimum you can lose is 0 - but these extremes are highly unlikely as bnet will probably not match players that could have such great disparity anymore.
ON BONUS POOL AND RESTED POINTS
What is known for sure
- The bonus pool is the sum of all "bonus points" you can get, which are added to the rating points you earn after a victory.
edit #2 & #3 - The rested points are earned over a period of time at a constant rate (without any "activation period"), the exact value being 1pt per 4 hours period. These are used FIRST OUT of you bonus pool, that means if you have 100 rested points in a total of 300 bonus pool and you increase your rating by 200 total (100 "normal" points and 100 "bonus"), you will have depleted only your rested points and the rest of your bonus pool is still untouched.
edit #3 - "Missed rested points" (the points you could not get as you made an account after the beginning of the count) are added directly to your total. In short, if you create an account 10 days after the beginning of the season, you will get 60 rested points just to allow you to catch up.
- You earn bonus points after your 10 placement games, the exact factors and reasons for this are unknown, but it's easy to imagine these act as an incentive to keep playing in order to reach your "anticipated potential" quicker.
- You also earn bonus points after you get reranked, or using a more general principle : "whenever you enter a league."
edit #3 - You get 1 point to your bonus pool for each player in your division, that applies also if you join an unfilled division and players are added over time.
edit #2 - There is apparently a bug regarding the rested points : if you hit 0 rested points (that is, if you used them all), it will stay at 0 for good. Instead, your rested points will go directly into the bonus pool and will get displayed only after a defeat (although you can still earn them in case of a victory).
edit #3 : as per the Blizzard ladder FAQ, the display of rested points is a bug entirely, only bonus pool should appear (cf. http://forums.battle.net/thread.html?topicId=23766799717&sid=3000)
What is uncertain & my own hypotheses
edit #3 Nothing is uncertain at the moment.. except that which we have no clue whatsoever!
Conclusions
edit #2 : Because the number of bonus points you get has the number of players in the division as a factor, players inside a big division are able to get more rating points in the same number of games compared to players in other divisions.
ALTHOUGH, even if this is correct, that applies to the bonus pool only which is emptied after merely a few dozen wins. The higher the number of wins a player has, the more accurate his rating is and THAT allows us to compare players between divisions. Or more formally: the higher the amount of wins 2 players of 2 different divisions have, the more accurate the rating comparison between these 2 players is.
ON THE FAVORED STATUS AND RERANKING
What is known for sure
- Reranking (edit: being moved from a league to another), if required, is done after the 30th game, no matter how you performed in the last few games. There are other occurrences where players will get reranked.
edit #3 According to a quick survey of the "favored" status and opponent pitted against me (cf. post #52 for the details), we can draw the following conclusions :
- There is NO correlation between the actual rating of two opponents and the "favored" status
- There is NO correlation between the rank of two opponents and the "favored" status
What is uncertain & my own hypotheses
edit #3 - We don't know the actual mechanics of reranking, it was hypothesized that there would be fixed checkpoints, but according to reports, it did occur at around 200 games (for link0) as well as (in my case) at the 112th game. According to Blizzard's ladder FAQ, "[t]he time and frequency of these reviews is kept hidden", which probably suggests there are no "hard-set checkpoints". (source of the FAQ : http://forums.battle.net/thread.html?topicId=23766799717&sid=3000)
Conclusions
edit #3 - The fact that there is no correlation between rank and favoritism is coherent with the system, otherwise players ranked 1 would be constantly at a disadvantage versus almost any player, no matter which league they are in, compared to players ranked lower. Same thing applies for players in a newly created division, they would not be able to earn points as fast since their rank is much higher than everyone else's (on average).
To me, this point supports the hypothesis that the rating of players in different divisions can be compared as their ranking inside their own division has no influence on the points they earn. The only deviation that occurs here regards the differential of bonus points awarded to players of different division size, although the impact of this deviation is diminishing as the number of games played increases (and is pretty much nil after a few hundred games).
This is a work in progress and a couple things need verification. I would also like if you guys have any additional info on the division system : why is there such a great disparity in the number of players between division...
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The numbers are pretty close to what i have seen within the game, being an abnormally high rated copper player I play quite a few games where the numbers are heavilly skewed and i have seen +34 point games and -0 pt losses.
However many people have claimed league changes have happened well over the 30th game. In some cases they claim to have been moved to plat after 100+ games. It makes sense for me though, as ive been stuck in copper and the first 30 of my games i suffered heavy losses but made up for later as im at almost 2100 rating now.
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not bad. i don't see anything incorrect from my own judgments about the system.
after the 30th game though, there seems to be some mysterious period of time(2 weeks i'm guessing) that corresponds with a season and therefore is the time when the system re-ranks you according to your consistent level of play.
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If by reranking you mean changing divisions, it can happen well after 30 games - I got bumped up from Gold to Platinum after almost 200 games - and I wasn't even particularly highly rated within my gold division (~15th). However, that was part of forming a new Platinum division (12), so it's possible that rules are a bit different when they need to form a new division.
What's been puzzling me lately is how they decide who's "favored" and by how much, and/or whether ratings can be compared across divisions of the same tier. That is: a couple days ago, while rated ~1500 (platinum), I played a player from another Platinum division who was rated somewhat lower (~1450, as I recall), yet he showed as slightly favored. Which implies either that:
a) Being "favored" includes factors other than simply your rating - it might, for instance, include your performance in various matchups (or whatever), or
b) Ratings aren't directly comparable between different divisions, even if both are (for instance) Platinum.
Anyone have any ideas about which might be the case?
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[B]On March 14 2010 19:54 Steve496 wrote:
What's been puzzling me lately is how they decide who's "favored" and by how much, and/or whether ratings can be compared across divisions of the same tier. That is: a couple days ago, while rated ~1500 (platinum), I played a player from another Platinum division who was rated somewhat lower (~1450, as I recall), yet he showed as slightly favored. Which implies either that:
a) Being "favored" includes factors other than simply your rating - it might, for instance, include your performance in various matchups (or whatever), or
b) Ratings aren't directly comparable between different divisions, even if both are (for instance) Platinum.
Anyone have any ideas about which might be the case?
Im pretty sure they put into account your record vs a certain race, and how well you do on the map you are playing on. If someone in the same league has a higher ranking/rating than you but suffers the majority of their losses against the race you play and you do particularly well against theirs, you should be favored. I also think map records play a role as well since its actually a statistic in your profile.
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I think it takes into account your match up win % and some sort of averaged comparison of your scores. Like the system knows if 1500 in one division is greater/lower than 1500 in another.
Its kind of a weird system but I haven't had much trouble with playing people far below me like I did in the first week so its ok. I like the bonus pool system for encouraging people to play.
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Their was a huge wave of players getting moved to leagues like a week or 2 after beta started. It appears that blizzard reranks everyone into leagues periodically. Why not just put them into different leagues when they deserve or why even have multiple divisions doesn't make much sense.
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To rank up I think you just have to win vs people in a particular league more than you lose while ALSO winning vs people in your league.
ie, beat like 4/5 platinum people and beat 9/10 gold people and you will rank up. The problem is if you lose a few in a row the system waits longer and longer before it is positive of what your level is.
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However many people have claimed league changes have happened well over the 30th game. In some cases they claim to have been moved to plat after 100+ games. It makes sense for me though, as ive been stuck in copper and the first 30 of my games i suffered heavy losses but made up for later as im at almost 2100 rating now.
TBH, I don't know why I wrote "I believe not" on this point (I'll blame it on fatigue, being in a LAN atm and having slept once until sunday morning, as well as my 2v2 partner who was waiting for me to get playing games!) There is most probably other times where players will get reranked, but I feel these are fixed, no matter how good you have performed in the past 20-50-etc. games
after the 30th game though, there seems to be some mysterious period of time(2 weeks i'm guessing) that corresponds with a season and therefore is the time when the system re-ranks you according to your consistent level of play.
so we had a completed season already, with no shuffling of the divisions (for the players who stayed in the same league) and no tournament as is indicated in the ladder? (and some info released by blizzard)
On March 14 2010 19:54 Steve496 wrote:
If by reranking you mean changing divisions, it can happen well after 30 games - I got bumped up from Gold to Platinum after almost 200 games - and I wasn't even particularly highly rated within my gold division (~15th). However, that was part of forming a new Platinum division (12), so it's possible that rules are a bit different when they need to form a new division.
Yeah, that's one of the big question mark I have, but so far I don't think divisions are created manually, 3 main reasons for that :
- It would be too simple to set up a few rules for division creation compared to paying someone do the job manually.
- Divisions get created every so often, platinum 1v1 has about 17 or 18 at the moment, but other leagues and other match types (2v2, 2v2 random) have WAY more than that.
- There have been many screenshots of divisions with less than 5-10 players in them, and they get filled over the next couple of hours.
What's been puzzling me lately is how they decide who's "favored" and by how much, and/or whether ratings can be compared across divisions of the same tier. That is: a couple days ago, while rated ~1500 (platinum), I played a player from another Platinum division who was rated somewhat lower (~1450, as I recall), yet he showed as slightly favored. Which implies either that:
a) Being "favored" includes factors other than simply your rating - it might, for instance, include your performance in various matchups (or whatever), or
b) Ratings aren't directly comparable between different divisions, even if both are (for instance) Platinum.
Anyone have any ideas about which might be the case?
As I wrote in the 2nd part of my OP, I think the actual rating is not even a factor of who's favored over who => Blizzard says their system is the most advanced, therefore I don't see how they could use a rating system based on the actual rating, such as ELO. They most probably want to set up a system where people are advancing depending on the skill level of their opponent (didn't they repeated over and over they wanted to match people of the same skill level for bnet 2.0?), that means they have to use the expected rating instead of the actual, but yeah...there can be other factors as well.
Additionally, regarding your b) option, since you can play players from any division, if my formula is correct, that automatically means you can compare ratings between divisions. To support this, there are quite a few players that are WAY above the rest of their division, if the rating was relative to the players in the same division (such as in an ELO rating system), then it would mean those players are totally dominating everyone in their division, which is hardly the case if we look at the win ratio of those players and those right below them (because top1-2 players don't play exclusively other top1-2 players).
On March 14 2010 20:12 CagedMind wrote:
Their was a huge wave of players getting moved to leagues like a week or 2 after beta started. It appears that blizzard reranks everyone into leagues periodically. Why not just put them into different leagues when they deserve or why even have multiple divisions doesn't make much sense.
you're correct about the wave of players being switched leagues, but I think this is due strictly to the beta being a beta : they test a few things and they then made a one-time (or so) major adjustment to the rankings of many players, I doubt that move was hard coded in bnet 2.0
On March 14 2010 20:51 red.venom wrote:
To rank up I think you just have to win vs people in a particular league more than you lose while ALSO winning vs people in your league.
ie, beat like 4/5 platinum people and beat 9/10 gold people and you will rank up. The problem is if you lose a few in a row the system waits longer and longer before it is positive of what your level is.
the question that interests me the most is when rather than how, it's very obvious that you have to be performing fairly better than the average people in your own league to move up
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we want to know how to pass from a division to another ! not this stuff!
thanks anyway 
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On March 14 2010 21:48 LuDwig- wrote:
we want to know how to pass from a division to another ! not this stuff!
but then again, the reasons you will be moved from a league to another is related to how the system works, which is obviously related to this "stuff" - if you understand a part of it, you are more likely to understand/figure out the rest
I had hopes this would be a starting point and with the information people on TL would bring in, we could get further and further - until we could answer such questions as yours.
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On March 14 2010 21:48 LuDwig- wrote:we want to know how to pass from a division to another ! not this stuff! thanks anyway
play 30games, have good winrating and u will rise a league
myself went to platin today, i had 20-8 stats in gold and was ranked 28, today i lost two ladder games and went up to platin with 20-10 stats (points: 14xx ----> 10xx)
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ive been first in my gold div for over a week with ~280ish games and nutting.
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Was anyone promoted twice yet? If so - after how many games?!
PS: I got promoted after exactly 30 games,too.
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Do you have a source for this info?
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On March 15 2010 01:48 Sfydjklm wrote:
ive been first in my gold div for over a week with ~280ish games and nutting.
have you ever been moved from a league to another?
if not could you please report if you get moved during the beta please? if that has to happen after x games, it might be 400 as the WC3's ladder system was done to show an accurate ranking (level, actually) at about that number of games played
On March 15 2010 01:59 glassmazarin wrote:
Do you have a source for this info?
not that I could retrieve in a minute, it's mostly based on 3 things :
- players' reporting of their experience
- my own observations
- theoretical knowledge of rating systems
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What's the difference between bonus points and rested points?
I thought they were the same thing o_O
Also none of mine have been showing up since 2 patches ago 
I still get the benefit after games tho, just can't see how many I have
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On March 15 2010 03:20 Tamerlane wrote:Show nested quote +On March 15 2010 01:48 Sfydjklm wrote:
ive been first in my gold div for over a week with ~280ish games and nutting. have you ever been moved from a league to another? if not could you please report if you get moved during the beta please? if that has to happen after x games, it might be 400 as the WC3's ladder system was done to show an accurate ranking (level, actually) at about that number of games played
nope was gold from the get go, never been to any other.
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All i can say about reranking is that I could be on a 3match lose-streak and then win the next game against a silver player (being bronze myself) and immediatly get promoted..
So...I would guess you simply have to beat a player of a higher division X number of times to advance, regardless of your current position/stats in the league you're in.
Speculation ofc..
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EPT
