Vol. 14, No. 5, 2021

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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

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.

Markov chain, mixing time, sports
Mathematical Subject Classification
Primary: 60J10
Received: 26 January 2021
Revised: 29 May 2021
Accepted: 16 June 2021
Published: 9 February 2022

Communicated by Jonathon Peterson
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