Abstract
The Elo rating system is one of the most popular methods for estimating the ability of competitors over time in sport. The standard Elo system focuses on predicting wins and losses, but there is often also interest in the margin of victory (MOV) because it reflects the magnitude of a result. There have been few theoretical investigations and comparisons of Elo-based models. In the present study, we propose four model options for an MOV Elo system: linear, joint additive, multiplicative, and logistic. Notations and guidance for tuning each model are provided. The models were applied to men’s tennis for several MOV choices. The results showed that all MOV approaches using within-set statistics improved the predictive performance compared with the standard Elo system, but only the joint additive model yielded unbiased ratings with stable variance in the simulation study. This general framework for MOV Elo ratings provide sports modelers with a new set of tools for building systems to rate competitors and forecast outcomes in sport.
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