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

With the rise of live sports betting in recent years, tennis forecasting has expanded from pre-match prediction to models that update win probabilities as a match unfolds. A central challenge in creating such a model is the constant need for models to adapt to score and performance changes. This study examines how pre-match and live information can be most effectively integrated into a model to produce accurate win-probability estimates. The analysis uses 8,222 Grand Slam matches containing a total of 1,505,355 points. Five models were evaluated using a chronological split, with matches from 2011-2021 used for training, 2022 for validation, and 2023-2024 for testing. Trace, a hybrid model, achieved accuracies of 76.06%, 82.15%, and 88.34% at 25%, 50%, and 75% match progress, suggesting that hybrid modeling is a practical approach to live tennis forecasting.

Sports-video understanding is moving beyond event recognition toward explaining how actions collectively shape match progression, however, existing tennis-video methods either perceive individual strokes without modeling their tactical dependencies or generate high-level analyses without grounding them in the underlying events. To bridge this perception-to-understanding gap, we formulate stroke-evidence-grounded tactical reasoning, a new rally-level task that requires models to jointly predict an open-ended answer, a hierarchical tactic label, an ordered sequence of supporting strokes, and decisive key actions, with each evidence stroke anchored to its racket-ball contact frame. We further introduce TRACE (Tactical Reasoning with Action-Chain Evidence in Tennis), a large-scale expert-annotated benchmark containing 11,189 rally videos, 41,485 stroke events, 25,429 tactical units, and 11,189 question-answer pairs, which unifies fine-grained stroke attributes, cross-stroke tactical relations, hierarchical tactic annotations, and evidence-grounded questions across factual perception, tactical understanding, and decision reasoning. Building on TRACE, we propose TennisVAR (Tennis Video Action-chain Reasoner), an evidence-grounded multimodal large language model that follows an "event-relation-evidence-tactic" reasoning paradigm, where an Event Parsing Module converts continuous rallies into explicit stroke-event sequences while a Tactical Graph-Guided Temporal Reasoner jointly models rally progression and same-player decision dependencies to identify question-relevant evidence and decisive actions.

In this paper, we study prediction problems for paired comparison data, for example, predicting the win probability between two unmatched players and ranking all the players according to the order of their strengths by using win probability data between two matched players. Paired comparison data are typically analyzed using Bradley-Terry and Thurstone-Mosteller models. These models predict the win probability by transforming the difference between learned rate parameters, which represent players';strengths, with a pre-specified inverse link function, and employ the order of learned rate parameters for player ranking. However, these models may suffer from model misspecification owing to the selection of a fixed inverse link function. Therefore, in this study, we propose to learn the rate parameters by a (sub-)gradient method and the inverse link function by an isotonic regression technique alternately. The proposed model guarantees monotonic improvement in training error, and is likely to yield an exact tie when the available data is insufficient to establish a strict ranking. We also verified that the proposed model could improve the win probability prediction and ranking performance through numerical experiments with synthetic data and real-world data of football Premier League, baseball MLB, and tennis ATP tour.