An Analysis of Elo Rating Systems via Markov Chains

Sam Olesker-Taylor, Luca Zanetti

Keywords: Elo ratings, Bradley–Terry–Luce model, tournament design, concentration

TL;DR: We present an analysis of Elo rating systems under the Bradley–Terry–Luce model

Abstract: We present a theoretical analysis of the Elo rating system, a popular method for ranking skills of players in an online setting. In particular, 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.

Primary Area: Probabilistic methods (for example: variational inference, Gaussian processes)

Submission Number: 2760