Rating System for multiple competitors [closed]

Question

I have been doing a research on various rating systems. I have found some good ones like Elo Rating system and Glicko Rating system. But all of these system are designed for a games which involve 2 competitors. ( chess, go)

I would like to know if there are any algorithms available for games involving N players, or if there is a way above systems can be extended to support N player games.

This is the closet thing I have found so far: http://sradack.blogspot.com/2008/06/elo-rating-system-multiple-players.html

Saidee

The Elo rating system is also in use in games like Starcraft 2 and League of Legends (see leagueoflegends.wikia.com/wiki/Elo_rating_system), where games involves two teams of 2,3,4 or 5 players. – Enate

Yes but in those games as well, there are parties of 2 who are playing against each other. Essentially 2 teams playing against each other is a fancy version of 2 players playing against each other. I'm talking about games where everyone is competing against each other. e.g., a swimming competition. – Saidee

@Saidee I find the question interesting, but this isn't a typical algorithm question -- you aren't trying to optimize for time or space (I don't think). Are you looking for more conceptual answers? (For some discussion about the meta topic of conceptual vs. practical, see discussion at meta.stackexchange.com/questions/108695/…) – Tutorial

@Saidee I didn't vote to close, but I can see why people did. You might take a look at Condorcet methods to start; there is great insight on voting methods on Wikipedia! – Tutorial

Answer 1

Assuming the game results in a ranking of all players (rather than just determining a single winner, say), you could treat the single game as N(N-2)/2 individual two-player games in which 1st place beat everyone else, 2nd place beat 3rd, 4th, and so on. You can then apply one of the 2-player algorithms to each of these individual games.

You would probably want to reduce the weighting of rating changes because this gives many "games" worth of ratings changes for each game played. Perhaps the changes should be reduced by a factor of N since each player is rated as having played N games, then again, maybe it makes sense to weight games among more players more heavily.

I have no idea whether this produces a rating system that is actually useful, but it is certainly possible to extend 2-player systems to the N-player case.

Upraise

breaking each N player game into N(N-2)games of 2 players sounds like a good idea but does not seem practical. I'm sure there is simpler solution to this. – Saidee

@Saidee One key insight of many voting algorithms is indeed to break things down into simpler problems, namely pairwise comparisons. I'd suggest designing the result you want (intuitively) then, only later, see if the performance is not acceptable. – Tutorial