A Unified Server Quality Metric for Tennis

TL;DR

This paper introduces Server Quality Scores (SQS), a new metric derived from point-by-point tennis data that isolates serving impact from other factors, outperforming traditional Elo in predicting serve efficiency.

Contribution

The paper develops a novel serve-specific player metric using logistic mixed-effects models, providing a more precise measure of serve quality and its influence on short-point outcomes.

Findings

SQS correlates more strongly with serve efficiency than weighted Elo.

SQS captures serve-induced short-point advantage, offering actionable insights.

Model ablations show the incremental value of serve features and partial pooling.

Abstract

Traditional tennis rating systems (e.g., Elo) summarize overall player strength but do not isolate the independent value of serving. Using point-by-point data from Wimbledon and the U.S.\ Open, we develop serve-specific player metrics that separate serving quality from return ability and other latent factors. For each tournament and gender, we fit logistic mixed-effects models of point outcomes using serve speed, speed variability, and placement features, with crossed server and returner random intercepts to capture unobserved player strengths. From these models we derive Server Quality Scores (SQS): partially pooled, opponent-adjusted estimates of players' serving impact. In out-of-sample evaluation, SQS aligns more strongly with serve efficiency$\unicode{x2014}$the probability of winning points within three shots$\unicode{x2014}$than weighted Elo. We further benchmark SQS against task-aligned serve-stat baselines and model ablations, quantifying the incremental value of serve features and partial pooling. Associations with overall serve win percentage are smaller and dataset-dependent, and neither SQS nor weighted Elo consistently dominates that outcome. Overall, SQS is best interpreted as a measure of serve-induced short-point advantage (serve quality plus early-point conversion), complementing holistic ratings with actionable insight for coaching, forecasting, and player evaluation.