An Analysis of Elo Rating Systems via Markov Chains

Sam Olesker-Taylor, Luca Zanetti
6/1/2024

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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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Cite this paper

@article{oleskertaylor2024analysis,
  title  = {An Analysis of Elo Rating Systems via Markov Chains},
  author = {Sam Olesker-Taylor and Luca Zanetti},
  year   = {2024},
  eprint = {2406.05869},
  archivePrefix = {arXiv},
  doi    = {10.52202/079017-4389},
  url    = {https://arxiv.org/abs/2406.05869},
  journal = {NEURIPS 2024 2024}
}

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