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The Ladder

First off, a huge shout-out to Team Liquid and specifically Excalibur_Z. He did the vast majority of the work on deciphering this mind-boggling system in a series of posts starting here, continued here, and finished here. I have expanded on a few points, corrected a few things (possibly in relation to Blizzard fixing issues), simplified some information, and tried to put it all into a more readable format. There is no guarantee that this information is 100% correct, but it should be quite close.


The Leagues and Divisions

There are six leagues right now. In descending order of skill, they are Master (1v1 only), Diamond, Platinum, Gold, Silver, and Bronze. It has also been said that a Grand Master’s League will eventually be formed by Blizzard which will take over the top spot. Active players are distributed evenly between the five diamond-bronze leagues with 20% of active players belonging in each. The Master league siphons off the top 2% of all players in 1v1 so that diamond only contains 18% of the active population. The determination of what constitutes “active” is unknown, but it does result in much less than 20% of the total population being in diamond presumably because the diamond players are more likely to remain active. Within each league there is a large (and expandable) number of divisions. Each division can contain up to 100 players (and are typically full) so that your division rank will always be between 1 and 100 (which seems more attractive than being 133430th in the world). The way players are distributed into leagues is through their MMR.


The Matchmaking Rating

Behind the scenes, there is a hidden rating. This hidden rating is commonly referred to as the matchmaking rating (MMR). This number is extremely important as it is Battlenet’s estimate of your skill. Battlenet will use this number to try to match you against equally skilled players and then modify your MMR based on the results. Whenever you win, your MMR will go up. Whenever you lose, your MMR will drop. The specific amounts that a single game will affect your MMR are unknown. Presumably you will gain more from beating a higher MMR opponent than from a lower MMR opponent. Your MMR is based purely on your wins/losses and ignores in-game metrics such as APM.


Placement Matches

When you first start playing a game type (1v1, 2v2, 3v3, 4v4) or with a new team, you start at a specific unknown MMR. Your other MMRs in different game types have no effect on this starting MMR. From this starting point, you are forced to play five placement matches. These placement matches help estimate your skill and will allow your MMR to jump or drop dramatically depending on your wins or losses and the MMR of your opponents. After your five placement matches, you will be put into one of the leagues below diamond based on your resulting MMR. Winning the first couple games is very important to being placed in platinum or gold as your MMR will be significantly lower if you lose your first game and then win the next four as opposed to winning your first four and losing your fifth. You cannot be placed in diamond from placement matches.


The Moving Average

The MMR itself is presumed to be quite erratic throughout your career, but there is at least one tool being used to keep you stable. The system records a moving average of your last X number of games (add up the last X MMRs after each game and divide by X). The moving average likely does not populate until those X games have been played and I believe it is required for changing leagues. Working backwards, we can then determine that the moving average takes the last 20 games into account. We come to this number by noting that players don’t get promoted into diamond until they have a little more than 20 games played.


Changing Leagues

When the moving average of your MMR crosses a certain level, you will change leagues. There are more complicated and probably more correct theories that include a confidence factor, Bayesian inference, Gaussian distribution, and… ::eyes glaze over::, but we will ignore those for our purposes. The general idea is that you will have to maintain a MMR at the higher level for approximately 20 games before you actually get promoted up to that level. That doesn’t mean you actually need to win all those games, but you shouldn’t be losing to players below that level. The easiest way to tell if you are on pace to be promoted is to see if you are consistently playing against players at that level while maintaining a win percentage at or better than 50% against those players.


Displayed Points

The displayed points are the points that you can actually see. The underlying goal of the ladder system is to have your displayed points equal your MMR with some modifiers. This goal for your displayed points (MMR plus modifiers) will be called the desired displayed points (DDP). The system forces you to earn your DDP through playing many games. Your displayed points start at 0 after finishing your placement matches and increase/decrease arithmetically whenever you win/lose a game. A game against an “equal” opponent will net between 10 and 14 points. If you are “slightly favored” you will win 7-9 points (and lose 15-17 points). If you are “favored”, you will gain 1-6 points (and lose 18-24 points). Reverse those numbers if the opponent is favored. To speed up the process of obtaining your DDP, Blizzard has implemented a bonus pool.


Bonus Pool

The bonus pool starts at 0 at the beginning of every ladder season and increases by one point every 112 minutes. Even if you start playing (or start a new team) long into the season, you will have accrued those bonus points from the very beginning of the season. Whenever you win a game, your winning points are matched by your bonus pool and taken out of the pool. So if you won a game that would naturally give you 13 points, you would instead gain 26 points and 13 would be subtracted from your bonus pool. The bonus pool is unaffected by losses and cannot go below zero. You will simply stop receiving bonus points when your bonus pool is empty.


League and Division Modifiers

Blizzard has decided that players should not be compared across leagues and divisions (except the Master league). To prevent easy comparisons, each league has different modifiers to boost your DDP above your actual MMR. Also, to prevent comparisons across divisions, the various divisions within each league have different modifiers as well. One diamond division may add 63 to your MMR to get your DDP while another may add 315 (all known diamond modifier values are multiples of 63). A bronze player will gain a huge bonus to his MMR to determine his DDP. However, when he is promoted to silver, his league/division modifiers will shrink and he'll lose points as part of the process. The same is true of any other promotion. When trying to determine someone's MMR, you would have to subtract those modifiers out (but they are not published).


The Bonus Pool Modifier

Another modifier to your DDP is the amount of bonus pool you have (my own theory which explains a few cases, but is concerning as the bonus pool gets bigger. Can I get a confirmation/refutal on this?). Your final DDP will be your MMR plus division/league modifiers minus your bonus pool. For example, if you are a diamond player with a MMR of 2500 and a league modifier of +315, then your DDP would initially be 2815. However, let’s say you haven’t played very much and still have 2000 points sitting in your bonus pool. Your final DDP would then only be 815. Luckily, each win will decrease your bonus pool which will raise this final DDP. If your actual displayed points are higher than your final DDP, then you will gain fewer points when you win games and lose more when you lose games. If your actual displayed points are less than the DDP, then you will gain more from wins and lose less from losses. This system has the effect of having your points converge towards your DDP while your DDP runs parallel to your MMR. By doing it this way, the bonus pool will not create point inflation since your MMR is not effected by the bonus pool. However, with a large enough bonus pool and very small MMR, it is possible to get stuck at 0 points with each loss being huge and each win gaining little until you work off much of your bonus pool, but those cases are rare. In most cases, a rough estimate of your MMR can be determined by adding your bonus pool to your points and then removing division modifiers (unfortunately, these modifiers are not published).


Beginning Estimate vs Final One

The “Favored”, “Slightly Favored”, and “Even Match” notes at the beginning of the game are based on actual MMR comparisons. So those notes should be an accurate depiction of who Blizzard believes will win. However, due to other factors based around your actual points versus your DDP, the final amount of points that you gain or lose at the end of the match may not coincide. If your points are significantly lower than your DDP (especially prevalent at the beginning of a season when the bonus pool is small), you will gain more points for wins and lose less for losses. Therefore, against an “even match” opponent, you might gain 16 points as opposed to the 12 that you naturally would gain and therefore the final message will say that you were a “slight underdog” since you were awarded points that would normally be given to a slight underdog.


Team Games

No part of the ladder is more bemoaned than team games partially due to a lack of understanding on how the system works. In team games, each team has a hidden MMR just like in the 1v1 leagues. Likewise, when teams play other teams, the system tries to match based on their MMRs exactly like in 1v1. Unfortunately, there aren't as many people queueing for team games as in the 1v1 bracket, so team games tend to get more variety in MMR matchups. Luckily, the game will award more/less points for a win/loss to compensate as it was intended. However, and here's the tough part, arranged teams don't just play other arranged teams. Often, arranges teams get pitted against randomly paired partners. So, if you and your buddy go do a 2v2, you might be faced off against two people who have never spoken together before. The arranged team has some innate advantages such as being able to create racial synergy, being able to have a plan going into the game, and having an easier time communicating while in the game. Blizzard tries to compensate for these advantages.

When players are randomly paired together, Blizzard takes some sort of average of their MMRs and then subtracts an unknown amount from the combined MMRs before comparing it to an arranged team's MMR. So, what typically happens is that arranged teams will play against random teams of players who are in higher leagues such as an arranged silver team being considered an even match against two randomly paired platinum players (platinum in random 2v2, their 1v1 league is irrelevant). Teams can also play allied with random players in larger team games. So a 2v2 team can play in the 4v4 league and will get paired with two random people or another 2v2 team against four opponents. I would suspect that Blizzard compensates for this and subtracts a value from the combined MMR for each group or individual that is not part of an arranged team. When allowing for all the player combinations and the variety of skills and styles of each team, it is very understandable why many team games end up as roflstomps.

Finally, there is one last piece of bad news for team game balance. Every new team starts at the same relatively low MMR (even with all diamond 1v1 players). Swapping out just one new player creates a whole new team with a fresh MMR and five more placement matches to go. So, in team games, you will often be playing against teams playing their placement matches who haven't been able to get their MMR way above yours yet, but will do so very soon. As you can see, there are a lot of things stacked against Blizzard's ability to create even matches in team games. However, they've done a respectable job given the circumstances.


Conclusion

While I don’t guarantee that all this information is 100% correct, it should give you a good idea of the inner workings of Blizzard’s ladder system. If you’ve been wondering why you can’t seem to get promoted, then you’ve probably got a good idea why now. If it seems like the system is biased against you and is unfairly keeping your points low, then you should understand what you need to do to fix it (play a lot to get rid of your bonus pool or improve your MMR). I don’t endorse what Blizzard has done (it seems like there are some better ways to accomplish their goals), but at least we can make sense out of it.


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