A Unified Server Quality Metric for Tennis

TL;DR

This paper addresses the need to isolate serving quality from holistic match performance in tennis. It introduces the Server Quality Score ($SQS$), a serve-specific metric estimated with logistic generalized linear mixed models that incorporate measured serve features and crossed server/returner random effects, producing a two-dimensional profile for first and second serves. Out-of-sample analyses across Wimbledon and the U.S. Open show that $SQS$ aligns strongly with serve efficiency (the likelihood of winning a point within the first three shots) and provides complementary information to weighted Elo ($wElo$), which performs less consistently for serve-centric outcomes. The results demonstrate that $SQS$ captures a distinct serve-driven component of performance with clear practical relevance for coaching, scouting, and matchup analysis, while acknowledging limitations and directions for future refinement.

Abstract

Traditional tennis rating systems, such as 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 to isolate serving quality from overall performance. For each tournament and gender, we fit logistic mixed-effects models using serve speed, speed variability, and placement features, with crossed server and returner random intercepts capturing unobserved server and returner-strength effects. We use these models to estimate Server Quality Scores (SQS) that reflect players' serving ability. In out-of-sample tests, SQS shows stronger alignment with serve efficiency (measured as points won within three shots) than weighted Elo. Associations with overall serve win percentage are smaller and mixed across datasets, and neither SQS nor wElo consistently dominates on that outcome. These findings highlight that serve-specific metrics complement holistic ratings and provide actionable insight for coaching, forecasting, and player evaluation.