Beyond Winning: Margin of Victory Relative to Expectation Unlocks Accurate Skill Ratings

TL;DR

This paper introduces MOVDA, a new framework that improves skill ratings by incorporating margin of victory deviations, leading to more accurate and faster convergence in competitive systems like NBA basketball.

Contribution

MOVDA is a novel, domain-specific method that models expected margin of victory and uses deviations for enhanced skill rating updates, outperforming traditional approaches.

Findings

Reduces prediction error by 1.54% over TrueSkill

Increases outcome accuracy by 0.58%

Speeds up rating convergence by 13.5%

Abstract

Knowledge of accurate relative skills in any competitive system is essential, but foundational approaches such as ELO discard extremely relevant performance data by concentrating exclusively on binary outcomes. While margin of victory (MOV) extensions exist, they often lack a definitive method for incorporating this information. We introduce Margin of Victory Differential Analysis (MOVDA), a framework that enhances traditional rating systems by using the deviation between the true MOV and a $\textit{modeled expectation}$. MOVDA learns a domain-specific, non-linear function (a scaled hyperbolic tangent that captures saturation effects and home advantage) to predict expected MOV based on rating differentials. Crucially, the $\textit{difference}$ between the true and expected MOV provides a subtle and weighted signal for rating updates, highlighting informative deviations in all levels of contests. Extensive experiments on professional NBA basketball data (from 2013 to 2023, with 13,619 games) show that MOVDA significantly outperforms standard ELO and Bayesian baselines. MOVDA reduces Brier score prediction error by $1.54\%$ compared to TrueSkill, increases outcome accuracy by $0.58\%$, and most importantly accelerates rating convergence by $13.5\%$, while maintaining the computational efficiency of the original ELO updates. MOVDA offers a theoretically motivated, empirically superior, and computationally lean approach to integrating performance magnitude into skill rating for competitive environments like the NBA.