Quantifying Momentum and Performance Dynamics in Tennis: A Point-Level Study Using Logistic Regression, Momentum Scoring, and Random Forests

Abstract

Does a tennis player’s momentum influence match outcomes, and if so, how can it be quantitatively measured? This study investigates the role of momentum in tennis matches using statistical modeling and machine learning methods. A binary logistic regression model was first constructed to predict the probability of a player winning a point, with ten performance indicators as independent variables and point outcome as the dependent variable. The predicted winning probability was used to evaluate point-level performance, and the model achieved an accuracy of 64.7%. A momentum score function was then proposed to quantify players’ momentum throughout matches. Pearson correlation analysis between momentum scores and match outcomes revealed a significant positive correlation, indicating that momentum plays an essential role in determining match results. To further explore the factors driving shifts in match situations, a random forest model was applied to predict match outcomes and identify key influencing variables. The results show that first-serve success, distance traveled, serve error rate, and point spread are among the most important factors affecting match outcomes. Finally, four additional matches were used to validate the proposed framework, demonstrating that the binary logistic regression model can effectively predict match outcomes and evaluate player performance. Overall, this study provides a quantitative approach to measuring momentum and analyzing performance in tennis matches.