If we have a pool of players who's skill levelss are normally distributed, and we sample some number of players from that pool (not necessarily independently of their skill) for a "Tournament", how can we calculate the probability of a given set of standings for that tournament?
I.E. we have the final standings: Player A in first, Player B in second...Player Z in 26th.
The structure of the tournament uses 5 rounds of Swiss Pairings, such that the players are randomly pitted against each other in the first round, but after that everyone on 1 win will face each other, and then in the next round everyone on 2 wins, etc. And we assume that the more skilled player will win in an individual game.
How can we work out the probability of a given table of results?
This is part of a larger problem of trying to collate multiple tournament results of different subsets of players, and trying to combine those into a single ranking system.
Thanks!
EDIT: The pairing system will match players randomly if they are on the same number of wins in each round, if it is not possible to match everyone on the same number of wins then a player will be randomly picked who is as close to that number of wins as possible.