On the distribution of winners' scores in a round-robin tournament

01/13/2022

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by   Yaakov Malinovsky, et al.

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In a classical chess round-robin tournament, each of n players wins, draws, or loses a game against each of the other n-1 players. A win rewards a player with 1 points, a draw with 1/2 point, and a loss with 0 points. We are interested in the distribution of the scores associated with ranks of n players after n 2 games, i.e. the distribution of the maximal score, second maximum, and so on. The exact distribution for a general n seems impossible to obtain; we obtain a limit distribution.