An analysis of Elo rating systems via Markov chains

19^th November 2024, 13:00 Ashton Lecture Theatre
Luca Zanetti
University of Bath

Abstract

We present a theoretical analysis of the Elo rating system, a popular method for calculating the relative skills of players (or teams) in sports analytics and particularly chess. We study Elo under the Bradley–Terry–Luce model and, using techniques from Markov chain theory, show that Elo learns the model parameters at a rate competitive with the state of the art. We apply our results to the problem of efficient tournament design and discuss a connection with the fastest-mixing Markov chain problem. This is joint work with Sam Olesker-Taylor.

Additional Materials

• https://arxiv.org/abs/2406.05869