A Real-World Markov Chain arising in Recreational Volleyball
David J. Aldous, Madelyn Cruz

TL;DR
This paper introduces a realistic Markov chain model for mixing players in recreational volleyball, analyzing its effectiveness and proving its irreducibility through combinatorial methods.
Contribution
It presents a novel Markov chain model based on real-world volleyball team mixing, with numerical analysis and a combinatorial proof of irreducibility.
Findings
The chain effectively mixes players within 7-8 steps.
The model accurately reflects real-world volleyball team changes.
The chain is proven to be irreducible.
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 7 or 8 steps performed in practice. We give a combinatorial proof of the non-trivial fact that the chain is indeed irreducible.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsSports Analytics and Performance
