@inproceedings{
olesker-taylor2024an,
title={An Analysis of Elo Rating Systems via Markov Chains},
author={Sam Olesker-Taylor and Luca Zanetti},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=kLiWXUdCEw}
}
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.
An Analysis of Elo Rating Systems via Markov Chains
Sam Olesker-Taylor Luca Zanetti