Intransitive Player Dominance and Market Inefficiency in Tennis Forecasting: A Graph Neural Network Approach

TL;DR

The paper tackles intransitive player dominance in tennis and associated market inefficiencies by building gender- and surface-specific temporal directed graphs of players, where edges encode dominance through $D_n^s(u,v)$. A MagNet-based model on the normalised magnetic Laplacian with $q=0.25$ learns from directed cycles to predict match outcomes, with walk-forward validation ensuring realistic dynamic learning. Out-of-sample accuracy is 65.7% with a Brier score of 0.215, competitive with baselines, though Pinnacle odds often outperform in overall predictive power. A targeted betting strategy that bets on highly intransitive matchups yields statistically significant profits (Kelly ROI $3.26 ext{ extpercent}$, over 1,903 bets), illustrating a market inefficiency that the graph-based approach can exploit, while also highlighting the superior general performance of bookmaker odds in many contexts.

Abstract

Intransitive player dominance, where player A beats B, B beats C, but C beats A, is common in competitive tennis. Yet, there are few known attempts to incorporate it within forecasting methods. We address this problem with a graph neural network approach that explicitly models these intransitive relationships through temporal directed graphs, with players as nodes and their historical match outcomes as directed edges. We find the bookmaker Pinnacle Sports poorly handles matches with high intransitive complexity and posit that our graph-based approach is uniquely positioned to capture relational dynamics in these scenarios. When selectively betting on higher intransitivity matchups with our model (65.7% accuracy, 0.215 Brier Score), we achieve significant positive returns of 3.26% ROI with Kelly staking over 1903 bets, suggesting a market inefficiency in handling intransitive matchups that our approach successfully exploits.

Figures (8)

• Figure 1: Overview of the graph construction process.
• Figure 2: The walk-forward validation process. After each pass, predictions are generated and the model is retrained; the historical graph grows as matches are added. For illustration, the schematic is not to scale: in practice, the historical graph and sliding training window span several hundred snapshots.
• Figure 3: Brier scores from 300 parameter optimisation trials, with Pareto-optimal trials highlighted. Colour indicates receptive field size ($K \times L$ hops).
• Figure 4: Calibration curves for the men's and women's predictions, showing predicted probabilities versus observed frequencies. Perfect calibration would align with the diagonal $y=x$ line.
• Figure 5: An intransitive triangle among Federer, Nadal, and Davydenko. The edge weights are evaluated at the end of the 2009 ATP season for the hard-court surface graph, with Equation \ref{['eq:dominance_decay']} and optimised graph construction parameters detailed in Table \ref{['tab:paramtuning']}. Each directed edge indicates a consistent head-to-head advantage.