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

arXiv: https://arxiv.org/abs/2508.12930 · HTML: https://mlsanity.com/paper/2508.12930/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 43 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Builds on (most cited first, 8 of 8)

- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [A framework for the fine-grained evaluation of the instantaneous expected value of soccer possessions](https://mlsanity.com/paper/2011.09426/) (2020)
- [Developing the Path Signature Methodology and its Application to Landmark-based Human Action Recognition](https://mlsanity.com/paper/1707.03993/) (2017)
- [Learning stochastic differential equations using RNN with log signature features](https://mlsanity.com/paper/1908.08286/) (2019)
- [Classification of Passes in Football Matches using Spatiotemporal Data](https://mlsanity.com/paper/1407.5093/) (2014)
- [Detecting early signs of depressive and manic episodes in patients with bipolar disorder using the signature-based model](https://mlsanity.com/paper/1708.01206/) (2017)

## Built on by (most cited first, 1 of 1)

- [Semi-Supervised Bayesian GANs with Log-Signatures for Uncertainty-Aware Credit Card Fraud Detection](https://mlsanity.com/paper/2509.00931/) (2025)

## Abstract (arXiv)

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.