An Analysis of Elo Rating Systems via Markov Chains

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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Cite

Text

Olesker-Taylor and Zanetti. "An Analysis of Elo Rating Systems via Markov Chains." Neural Information Processing Systems, 2024. doi:10.52202/079017-4389

Markdown

[Olesker-Taylor and Zanetti. "An Analysis of Elo Rating Systems via Markov Chains." Neural Information Processing Systems, 2024.](https://mlanthology.org/neurips/2024/oleskertaylor2024neurips-analysis/) doi:10.52202/079017-4389

BibTeX

@inproceedings{oleskertaylor2024neurips-analysis,
  title     = {{An Analysis of Elo Rating Systems via Markov Chains}},
  author    = {Olesker-Taylor, Sam and Zanetti, Luca},
  booktitle = {Neural Information Processing Systems},
  year      = {2024},
  doi       = {10.52202/079017-4389},
  url       = {https://mlanthology.org/neurips/2024/oleskertaylor2024neurips-analysis/}
}