Capturing Intransitive Dominance in Tennis Forecasting: A Graph Neural Network Approach

A graph neural network that models tennis matches as a temporal directed graph can capture intransitive dominance patterns that conventional rating systems miss, according to research posted to arXiv [1]. The model achieved 65.7% accuracy and a 0.214 Brier score, performing competitively with the established Weighted Elo system [2]. The approach, submitted to arXiv on 23 October 2025 and revised on 18 June 2026, represents players as nodes and historical match outcomes as directed edges [1][2]. Intransitive dominance — where player A defeats B, B defeats C, but C defeats A — is common in professional tennis, yet few forecasting methods explicitly incorporate it [2]. The authors, including John Cartlidge, constructed temporal directed graphs to encode these cyclical relationships [1][2]. While the model did not improve on the Weighted Elo baseline in unconditional accuracy, a forecast-encompassing test demonstrated that it carries complementary information [2]. A combined forecast that merges the graph neural network output with Weighted Elo significantly outperformed Weighted Elo alone, and the gain appeared stronger on the intransitive matchups the model was designed to target [2]. The paper argues that a graph-based representation captures a forecasting signal that transitive rating systems discard, even between players who share no common opponents [2]. The research appears on arXiv, a preprint platform that has integrated community-built machine learning demos through a collaboration with Hugging Face Spaces, allowing readers to interact with models directly from a paper’s abstract page [3][4]. Hugging Face Spaces, launched in October 2021, hosts over 12,000 open-source machine learning demos built with tools such as Gradio and Streamlit [3]. The integration lets users navigate to a Demos tab on an arXiv paper to find and run interactive applications without writing code [5]. The tennis forecasting paper’s abstract page includes links to code, data, and media through services such as CatalyzeX, DagsHub, and Hugging Face [1]. The broader machine learning landscape has seen rapid shifts, including the January 2025 debut of DeepSeek-R1, a large language model developed by the Chinese firm DeepSeek that rivaled OpenAI’s GPT-4 and o1 at a reported training cost of US$6 million — roughly one-sixteenth the cost of GPT-4 — using approximately one-tenth the computing power of Meta’s Llama 3.1 [6]. Large language models are defined as machine learning models with many parameters, trained with self-supervised learning on vast text corpora [7]. The retrieval-augmented generation technique, foundational to many modern AI systems, was introduced in a 2020 paper co-authored by Douwe Kiela, who later served as Head of Research at Hugging Face and now directs research at Google DeepMind [8].