Comment by dhosek
3 years ago
Interesting take on the multiplayer ELO scoring. Another approach I've seen is to essentially treat an n-player game as an (n 2) set of two-player games, so, in the case where A>B>C>D, we have A wins three games (vs B, C and D), B wins two games (plus her loss against A), C wins one game (Plus losses against A and B) and D loses three games. The advantage of this over the model described in the article is that it more gracefully handles cases where there are what the author called multi-player zaps. In that instance, where say D is eliminated first and B and C simultaneously, A beats B, C and D still, but B and C are treated as being a tie¹ and both beat D.
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1. A tie is not a strictly neutral event in many ELO scoring systems: usually it means that the higher-ranked player loses some ELO while the lower-ranked player gains some, just not as much as in a straight victory.
For team-based play (like with Spades), on Board Game Arena, they treat the partners as having tied which is, I think, incorrect. A better approach is probably to treat it as a match between two players where each team's ELO is the mean of their individual member's averages. The tie approach means that a strong player is penalized for having a weaker partner.
That's an interesting approach for treating them as (n 2) sets, I might have to try modeling that out and applying that to the same data to see how it changes the numbers.
I have a number of table zaps recorded in subjective data, and I've considered a similar approach; treating a game recorded as a table zap as A winning a game against B, C, and D, however you're right, that doesn't handle the case of D being out, and then B and C being zapped at the same time. I think that's a subtle but important distinction.
Re: two player matches - That's a much better approach to my naive interpretation, definitely going to implement that sometime.