The geometry of touching: optimal transport to cluster playing styles and match outcomes in soccer

2025/11/12 by Alessandro Spelta, Paolo Pagnottoni, Nicoló Pecora · 1 voice
Economics, Econometrics and Finance · Medicine · Social Sciences · #Evolutionary Game Theory and Cooperation #Sports Analytics and Performance #Sports Performance and Training

paper · pdf · doi:10.1093/jrsssc/qlaf060

openalex created_date 2025/11/12 · openalex publication_date 2025/11/12 · openalex updated_date 2026/08/01

Abstract

Abstract Touching distributions, represented as spatial maps of where players interact with the ball during a match, play a fundamental role in shaping team strategy and influencing match outcomes in soccer and other sports. In this work, we propose a novel approach based on optimal transport theory to quantify and compare the spatial distributions of players’ touches across matches. By leveraging both balanced and unbalanced optimal transport formulations, we capture not only the spatial structure of touching patterns but also their volumetric differences. Our analysis shows that touching distributions effectively discriminate between match outcomes, with teams exhibiting more consistent patterns in victories than in draws or defeats. Furthermore, we cluster team touching distributions using Wasserstein barycentres and identify dominant playing styles that, while largely stable within outcomes, exhibit notable variations between wins, draws, and losses. Finally, we evaluate the predictive accuracy of the clustering method, demonstrating that spatial touching distributions, reflecting distinct on-field playing styles, have predictive power in discriminating match outcomes.

Citations

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• How often does the best team win? A unified approach to understanding\n randomness in North American sport
• On Wasserstein Two Sample Testing and Related Families of Nonparametric\n Tests
• Iterative Bregman Projections for Regularized Transportation Problems
• Competing Process Hazard Function Models for Player Ratings in Ice Hockey

Discussions

• "The geometry of touching: optimal transport to cluster playing styles and match outcomes in soccer" by Paolo Pagnottoni, Nicoló Pecora (U. Cattolica di Piacenza), Alessandro Spelta (U- di Pavia) publ [bsky, 0 points, 1 comments]