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arXiv · 2406.05869

An Analysis of Elo Rating Systems via Markov Chains

Sam Olesker-Taylor·Luca Zanetti
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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.

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Sam Olesker-Taylor, Luca Zanetti. 2024-06-09. An Analysis of Elo Rating Systems via Markov Chains. https://arxiv.org/abs/2406.05869

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