I have a problem where I have to predict the winner of a game. There could upto 10 players in each game and there is always one and only one winner. Each player also gets a rank in the game (the winner is obviously ranked 1 in the game).
I have a dataset with the history of hundreds of games and the winner of the game and the rank of each player in the game).
I've structured this problem as a pair-wise 1x1 comparison of players. So if there are three players A, B and C, I evaluate the winner in each pair (A-B, B-C and A-C).
I'm using classification techniques (Random Forest, SVM etc.) to predict the winner in each pair.
My problem is, how do I predict the winner of the game, given the pairwise results. I need to consider issues like:
- Pairwise comparison results might be inconsistent (ie. A>B, B>C but also C>A)
- High winning probability in all pairwise comparisons should lead to a higher probability of winning the match
- Winning against a "strong player" should influence the winning probability more than winning against a "weak player"