On the distribution of winners' scores in a round-robin tournament. Issue 4 (October 2022) - Malinovsky, Yaakov
Abstract : 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, that is, 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.