I would like to use ELO to track player rankings between matches of a certain game, however the game can be played with up to four players in a match. I have seen games like Carcassonne use ELO with more than two players playing, but I am not familiar with ELO beyond a 1-1 matchup.
From the wikipedia article the two-player equations I would like to extend are:
Ea = 1/(1 + 10(Rb - Ra) / 400)
Eb = 1/(1 + 10(Ra - Rb) / 400)
Rxnew = Rxold + 32 * (W – Ex), where W=1 if X wins and W=0 if X loses.
How would the computation for Ex and W change given more than two players?