How to extend Elo: a Bayesian perspective

Metro Toronto Convention Centre 

The Elo rating system, originally designed for rating chess players, has since become a popular way to estimate competitors' time-varying skills in many sports. The self-correcting Elo algorithm is simple, intuitive, and often makes surprisingly accurate predictions. But, as it lacks a probabilistic justification, it is unclear how to extend it to include information beyond wins and losses. I will present a close connection between steady-state Kalman filtering and the Elo update. This connection both provides a probabilistic interpretation of Elo in terms of an approximate Bayesian update and a straightforward procedure for modifying it. I use this connection to derive versions of Elo incorporating margins of victory and correlated skills across different playing surfaces in tennis, and show that this improves predictive accuracy compared to both Elo and Glicko.