An Analysis of Elo Rating Systems via Markov Chains
Sam Olesker-Taylor · Luca Zanetti
2024 Poster
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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