|
Abstract:
|
Originally developed to rate chess players, the Elo rating system is now a popular approach to track player and team ratings across a variety of sports. Its simple form is intuitive but lacks a probabilistic justification. With no theory as a guide, modellers have to rely on intuition and empirical comparisons when extending the algorithm. We clarify the close relationship between the Elo update and approximate posterior mode estimation as well as extended Kalman filtering. Crucially, we show how this connection can be used to extend Elo, giving rise to a simple recipe for constructing new estimators. Using tennis as an example, we derive variants of Elo that incorporate the margin of victory and allow players' abilities to vary by court surface. We evaluate the resulting models on the 2019 season of men's professional tennis matches (2,589 matches). We find that, compared to Elo, predictive accuracy improves from 63.6% to 65.7% and log loss improves from 0.634 to 0.620, demonstrating the ability to improve predictions. While we chose tennis as an example, we highlight that the derivation is completely general and suggest how the approach could be applied to other sports.
|
