Research On the Role and Influencing Factors of Momentum in Tennis Matches Based on Linear Conditional Probability Model and Support Vector Machine

Abstract

This research investigates the role and influencing factors of momentum in tennis matches using a Linear Conditional Probability Model (LCPM) and Support Vector Machine (SVM). The study begins with data preprocessing to address outliers and standardize scoring notations, followed by an analysis of the momentum's role in tennis, which is defined in relation to consecutive points, games won, and service breaks. The principal component analysis (PCA) is employed to synthesize key factors reflecting momentum, including consecutive scores, untouchable shots, aces, and net points, with a focus on their Markovian properties. A momentum formula is constructed, accounting for the sliding average of scoring differentials and the mutual cancellation of momentum between players. The study further examines the stochasticity of swings in play and runs of success, challenging the notion that these elements are random. The results of the Wald Wolfowitz Run Test and Granger Causality Test indicate that momentum significantly influences the probability of winning points and is not a random phenomenon. A PCA-SVM-SHAP model is developed to predict momentum fluctuations, achieving an 81.26% accuracy rate in the validation set. The model identifies net skills, serving skills, and untouchable shots as the most influential factors on momentum changes. The research extends the model's application to unknown tennis matches and other sports events, demonstrating its generalization ability with varying degrees of accuracy.