Predicting outcomes for games of skill by redefining what it means to win

TL;DR

This paper extends the Elo rating system to incorporate margin-of-victory data, enabling more detailed predictions of match outcomes beyond simple win-loss probabilities.

Contribution

It introduces a novel approach to redefine 'winning' in Elo ratings, allowing for prediction of full point spread distributions in games of skill.

Findings

Extended Elo ratings to include margin-of-victory information.

Able to predict full distribution of point spreads for unplayed matches.

Demonstrated improved outcome predictions over traditional Elo.

Abstract

The Elo rating system is a highly successful ranking algorithm for games of skill where, by construction, one team wins and the other loses. A primary limitation of the original Elo algorithm is its inability to predict information beyond a match's win-loss probability. Specifically, the victor is awarded the same point bounty if he beats a team by 1 point or 10 points; only the rating difference between the team and its opponent affects the match bounty. In this work, we explain that Elo ratings and predictions can be naturally extended to include margin-of-victory information by simply redefining "what it means to win." We create ratings for each value of the margin-of-victory and use these ratings to predict the full distribution of point spread outcomes for matches which have not yet been played.