Probabilistic Completion of a Knockout Tournament

Abstract

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.