Calculating elo ratings between 2 players is fairly straightforward. See http://pastebin.com/9sjQyxiU.
3rd place = -1 which is loass
Hmm.. Wouldn't it be better if 2nd place got 0.5 and 3rd place got -0.5 in a 4-player match? This way, in a 5-player match, the 3rd place would get 0 and 4th place would get -0.5?
well there would be a 1 point gap between 2nd and 3rd.....and then only half point gap between 1st and 2nd ...and 3rd and 4th. Could do it like that but makes more mathematical sense doing 1/3 of a point and negative 1/3 of a point.
How about this? For each player, sum the Elo points that would be won/lost across all 1-1 pairs with that player.
For example, suppose Players A, B, C, D come in 1st, 2nd, 3rd, 4th. A gains points equal to the points he would gain for beating B, C, and D in individual 1v1s; B would gain/lose points equal to the points he would gain for beating C and D minus the points he would lose for losing to A; etc.
Reduces to 1-1 Elo in boundary cases - Suppose there are three players, A B C, and C has a rating of -Inf. We can assume that C will always lose. A and B will not gain any points from beating C. Hence, the system reduces to 1-1 Elo between A and B.
This is actually how the rating was calculated - I recently modified it so that the the highest ratings, of the players you beat and lost to, are used. This allows for more 'positive' rating changes :)
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