## The Annals of Mathematical Statistics

### Probabilistic Completion of a Knockout Tournament

J. A. Hartigan

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177699533

Digital Object Identifier
doi:10.1214/aoms/1177699533

Mathematical Reviews number (MathSciNet)
MR185727

Zentralblatt MATH identifier
0144.40803

JSTOR