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On the distribution of winners’ scores in a round-robin tournament

Part of: Graph theory Nonparametric inference

Published online by Cambridge University Press:  06 August 2021

Yaakov Malinovsky Open the ORCID record for Yaakov Malinovsky [Opens in a new window]
Yaakov Malinovsky*
Affiliation:
Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, MD 21250, USA. E-mail: yaakovm@umbc.edu
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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 ${{n \choose 2}}$ 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.

Keywords

ExtremesNegative correlation

MSC classification

Primary: 62G32: Statistics of extreme values; tail inference
Secondary: 05C20: Directed graphs (digraphs), tournaments

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 4 , October 2022 , pp. 1098 - 1102
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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