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

This paper introduces two novel methods for predicting ATP tennis match outcomes using data from 2000–2025. The first approach utilizes Topological Data Analysis (TDA) to analyze the competitive network of players. By applying lower-star filtration to player-match graphs, the authors extract topological features—such as connected components and loops—using four distinct summary methods (VAB, HNAV, HWNAV, and OW-HNPV). These features, combined with Modified Band Depth (MBD) scores and traditional graph-theoretic metrics, are fed into a Random Forest classifier. The second approach employs a modified Katz similarity index, which uses temporal edge weighting to account for the recency of player victories, allowing for a path-based assessment of competitive advantage.

The TDA-based Random Forest model achieved a 66.2% accuracy rate (AUC = 0.719) when incorporating rankings, centralities, and topological features. Notably, the authors found that topological features alone maintained a 63.56% accuracy rate, confirming that the underlying network structure of competitive tennis contains inherent predictive value independent of official rankings. Feature importance analysis indicated that while rankings remain the strongest predictor (36.3%), topological features contribute a significant 24.0% to the model's predictive power. The modified Katz index approach also performed well, achieving 62.48% accuracy on held-out test data.

This research is significant as it represents the first application of lower-star filtration to sports analytics. By demonstrating that TDA can capture complex, hierarchical competitive patterns that traditional statistical models might overlook, the study provides a new framework for sports forecasting. The ability to achieve above-chance predictions using only network topology suggests that these methods could be particularly useful in scenarios where traditional ranking data is sparse, noisy, or unavailable.