Stochastic Extensions of the Elo Rating System

Abstract

This work studies how the Elo rating system can be applied to score-based sports, where it is gaining popularity, and in particular for predicting the result at any point of a game, extending its statistical basis to stochastic processes. We derive some new theoretical results for this model and use them to implement Elo ratings for basketball and soccer leagues, where the assumptions of our model are tested and found to be mostly accurate. We showcase several metrics for comparing the performance of different rating systems and determine whether adding a feature has a statistically significant impact. Finally, we propose an Elo model based on a discrete process for the score that allows us to obtain draw probabilities for soccer matches and has a performance competitive with alternatives like SPI ratings.