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I'm trying to modify the ELO ranking system formulas to adapt them to eSport (electronic sports, but more specifically Starcraft II).

(The reason I'm using ELO, is the straight forward concept and the pretty easy maths it is using. I might change though if I find a solution that can't be implemented in ELO.)

One of the big problems I have is the following :

  • How do you rank two separate populations that encounter each other very rarely (basically players from different geographical regions), in the same raking ?

Little explanation. Imagine that you have one player from England and one player from South-Korea, both have say "2700" rating.

Now the problem is that you can't say that they have the same "skill" since they play in two different environments populated with different players that have a different level of skill.

(In this particular use of the system (Starcraft II), about 10% of the games correspond to "cross-population" games. And in those 10%, I would say that the players are generally the same and correspond to roughly 20% of the total number of players in the population they are part of.)

I looked at quite a lot of other ranking systems like Chessmetrics and Glicko I-II, but none of them seem to solve the problem. Most likely because they were designed for a more "global" game (Chess) and thus don't have this issue with "separated populations".

  • The only potential solution I could think of was to inflate the "K" factor in the ELO formula for those particular "cross-population" games. This would increase the "weight" of this particular case.

But honestly, I don't really like this solution ...

Thank you a lot in advance !


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There is an area of statistics that deals with paired comparisons. Systems that rank teams such as the BCS for American College Football base the rankings on wins and loses with their opponents. In the ranking if two teams have never played each other they may share common opponents and those results are used to help. One model commonly used to rank is called the Bradley-Terry model. A monograph from the 1960s that gives a thorough accounting of these methods is called "The Method of Paired Comparisons" by H. A. David.

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Hum, didn't thought of this at all ! So basically, you are trying to maximize the number of games "related" to both those teams so that you have a statistically more representative data pool. Seems pretty cool ! =) Thank you very much I will look into this. – Awake Zoldiek May 27 '12 at 0:43
I will let this question open for a few hours to see if other people can add things on the topic and then I will "check" your answer. (Hum, ... can't even up vote ...) – Awake Zoldiek May 27 '12 at 0:44
You can do all that when you have something like 16 reputation points. – Michael Chernick May 27 '12 at 2:15

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