The path to a goal: Understanding soccer possessions via path signatures

TL;DR

This paper introduces a novel method using path signatures to predict soccer actions by encoding entire possessions, outperforming benchmarks and reducing computational costs, with new evaluation metrics and detailed season analysis.

Contribution

It proposes a path signature-based framework for soccer action prediction that captures complex spatio-temporal data without manual feature engineering, outperforming existing models.

Findings

Outperforms transformer-based benchmarks in prediction accuracy.

Reduces computational costs compared to existing methods.

Introduces a new, more reliable possession evaluation metric.

Abstract

We present a novel framework for predicting next actions in soccer possessions by leveraging path signatures to encode their complex spatio-temporal structure. Unlike existing approaches, we do not rely on fixed historical windows and handcrafted features, but rather encode the entire recent possession, thereby avoiding the inclusion of potentially irrelevant or misleading historical information. Path signatures naturally capture the order and interaction of events, providing a mathematically grounded feature encoding for variable-length time series of irregular sampling frequencies without the necessity for manual feature engineering. Our proposed approach outperforms a transformer-based benchmark across various loss metrics and considerably reduces computational cost. Building on these results, we introduce a new possession evaluation metric based on well-established frameworks in soccer analytics, incorporating both predicted action type probabilities and action location. Our metric shows greater reliability than existing metrics in domain-specific comparisons. Finally, we validate our approach through a detailed analysis of the 2017/18 Premier League season and discuss further applications and future extensions.