A real-world Markov chain arising in recreational volleyball

Aldous, David J.; Cruz, Madelyn

doi:10.2140/involve.2021.14.829

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A real-world Markov chain arising in recreational volleyball

David J. Aldous and Madelyn Cruz

Vol. 14 (2021), No. 5, 829–852

DOI: 10.2140/involve.2021.14.829

Abstract

Card shuffling models have provided simple motivating examples for the mathematical theory of mixing times for Markov chains. As a complement, we introduce a more intricate realistic model of a certain observable real-world scheme for mixing human players onto teams. We quantify numerically the effectiveness of this mixing scheme over the seven or eight steps performed in practice. We give a combinatorial proof of the nontrivial fact that the chain is indeed irreducible.

Keywords

Markov chain, mixing time, sports

Mathematical Subject Classification

Primary: 60J10

Milestones

Received: 26 January 2021

Revised: 29 May 2021

Accepted: 16 June 2021

Published: 9 February 2022

Communicated by Jonathon Peterson

Authors

David J. Aldous
Department of Statistics University of California Berkeley, CA United States

Madelyn Cruz
Department of Mathematics University of the Philippines Diliman Quezon City Philippines

Vol. 14, No. 5, 2021