An Analysis of Elo Rating Systems via Markov Chains
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 8 of its 42 references that are in the map. First posted on arXiv 9 Jun 2024.
Builds on
8 of 42 references.
References · 8
- 2017Bridging the Gap between Constant Step Size Stochastic Gradient Descent and Markov Chainscited by 88
- 2015Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependencecited by 61
- 2014Minimax-optimal Inference from Partial Rankingscited by 24
- 2021ℓ∞-Bounds of the MLE in the BTL Model under General Comparison Graphscited by 9
- 2017Lifting Markov Chains To Mix Faster: Limits and Opportunitiescited by 3
- 2022Learning to Identify Top Elo Ratings: A Dueling Bandits Approachcited by 2
- 2023A State-Space Perspective on Modelling and Inference for Online Skill Ratingcited by 2
- 2020Zig-zag sampling for discrete structures and non-reversible phylogenetic MCMCcited by 1
Built on by
Citing papers per year: 2026: 1.
1 paper.