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

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.