Topological Data Analysis and Graph-Theoretic Approaches for Tennis Match Prediction

2026-07-26

AI Summary

This study addresses the challenge of accurately predicting professional tennis match outcomes in the absence of conventional player rankings. Leveraging ATP singles match data from 2000 to 2025, the authors construct a competitive network among players and introduce the down-star filtration—a novel application in tennis prediction—while systematically evaluating four topological summary methods (VAB, HNAV, HWNAV, and OW-HNPV). By integrating persistent homology, refined band-depth analysis, centrality measures, an enhanced Katz similarity index, and time-weighted edges, their purely topological model achieves a prediction accuracy of 63.56% without any ranking information. A hybrid model incorporating additional features further improves performance to 66.2% accuracy (AUC = 0.719), demonstrating that network topological features provide significant complementary value for match outcome prediction.

Abstract

We present two approaches for predicting tennis match outcomes using topological data analysis and graph theory on ATP singles matches from 2000-2025. The first method applies lower-star filtration to player competitive networks, extracting topological features through persistent homology using four summary methods (VAB, HNAV, HWNAV, OW-HNPV) combined with Modified Band Depth analysis. Algorithmic optimizations including ego graph approximations and triangle elimination enable analysis of about 66k matches. Our Random Forest model achieves 66.2% accuracy (AUC = 0.719) using topological, graph-theoretic, and ranking features. Feature importance analysis reveals that rankings contribute 36.3%, centralities 25.5%, and TDA features 24.0%, with topological features providing complementary signal. When rankings are unavailable, the topology-only model maintains 63.56% accuracy, demonstrating that network-derived features alone capture meaningful competitive structure. The second method uses a modified Katz similarity index with temporal edge weighting, achieving 62.48% accuracy on held-out test data. This work represents the first application of lower-star filtration to tennis prediction, provides systematic comparison of four topological summary methods in sports analytics, and demonstrates that TDA can achieve above-chance prediction using network topology alone while providing additional value when combined with traditional features.

Problem

• tennis match prediction
• topological data analysis
• graph theory
• competitive networks
• persistent homology

Innovation

• Topological Data Analysis
• Lower-star Filtration
• Persistent Homology
• Graph-theoretic Features
• Tennis Match Prediction