The Annals of Mathematical Statistics

Probabilistic Completion of a Knockout Tournament

J. A. Hartigan

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A knockout tournament is a procedure for selecting the best among $2^n$ players by, in the first round, splitting the $2^n$ players into $2^{n - 1}$ pairs who play each other; the $2^{n - 1}$ winners proceed to the next round and repeat the process; finally the one player left is declared the best. A method is given for estimating a complete ranking of the $2^n$ players given the results of the $(2^n - 1)$ matches in the tournament; the method is based on the assumption that all $(2^n)$! orderings of the players are equally probable before the tournament begins.

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Ann. Math. Statist., Volume 37, Number 2 (1966), 495-503.

First available in Project Euclid: 27 April 2007

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Hartigan, J. A. Probabilistic Completion of a Knockout Tournament. Ann. Math. Statist. 37 (1966), no. 2, 495--503. doi:10.1214/aoms/1177699533.

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