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Testing equality of players in a round-robin tournament

par Bruss, F Thomas ;Ferguson, Thomas S.
Référence Mathematical scientist, 43, 2, page (125-136)
Publication Publié, 2018-12

Article révisé par les pairs

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Résumé :

In a round-robin tournament with n players, each player plays every other player once, resulting in (s) games. Let Xjj denote the score by which player i beats player j, with Xji =-Xjj for all (' 56 j. If we take Xu = 0 for all ; then S; = Xy denotes the total score of player 1 for 1 = 1, 2, ., n. To test the hypothesis, Ho, that the players are equally skillful, in the sense that the Xij for 1 < j are independent and identically distributed with mean 0 and common variance, we suggest rejecting Ho if V, = Yll=i is too large. We show that an associated statistic, W,, a generalization of the circular triads statistic of Kendall and Babington Smith (1940), is easier to work with and more stable. We establish the asymptotic normality of V, and Wn under general conditions. As an illustration, the results are applied to data from the Greek Soccer League 2016-2017.