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Let's say I have 20 players [names A .. T] in a tournament. The rules of the tournament state that each player plays every other player twice [A vs B, B vs A, A vs C .. etc]. With 20 players, there will be a total of 380 matches.

In each match, there are three possible outcomes - player 1 wins, player 2 wins, or draw. There's a betting exchange which, ahead of each match, quotes the probabilities of each outcome occurring; so you might have 40% player 1 wins, 30% player 2 wins, 30% draw [probabilities sum to 100%]; I store these probabilities ahead of each match.

Fast forward one-quarter of the way through the tournament. I have collected probabilities for 95 games, with 285 still to go. What I want to know is -

Can the probability data from the 95 games be used to predict probabilities for the remaining 285?

For example, if I know A vs B and B vs C, can I use them to infer A vs C?

And if so, how do I do it?

1 Answer

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by (92.8k points)

Basically, you want to rank the players, such that a player of a higher rank will generally beat a player of a lower rank. One approach to your solution is that you can use simulated annealing to find these ranks. You can pick up some function of the ranks of the players for the game outcome, and let the fitness of a given rank assignment be the probability of the observed outcome given the chosen ranks. Repeat with different ranks, as per simulated annealing.

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