SciSports: Learning football kinematics through two-dimensional tracking data

TL;DR

This paper explores machine learning methods, including Kalman filters and deep generative models, to analyze and interpret football players' movement trajectories from two-dimensional match data, aiming to extract meaningful insights.

Contribution

It introduces novel applications of Kalman filters, GANs, and VAEs to model and distinguish football player trajectories, advancing sports analytics techniques.

Findings

Kalman filter provides an interpretable model with player-specific parameters.

GANs show potential but limited by computational resources.

VAEs generate trajectories similar to real data, indicating learned underlying structures.

Abstract

SciSports is a Dutch startup company specializing in football analytics. This paper describes a joint research effort with SciSports, during the Study Group Mathematics with Industry 2018 at Eindhoven, the Netherlands. The main challenge that we addressed was to automatically process empirical football players' trajectories, in order to extract useful information from them. The data provided to us was two-dimensional positional data during entire matches. We developed methods based on Newtonian mechanics and the Kalman filter, Generative Adversarial Nets and Variational Autoencoders. In addition, we trained a discriminator network to recognize and discern different movement patterns of players. The Kalman-filter approach yields an interpretable model, in which a small number of player-dependent parameters can be fit; in theory this could be used to distinguish among players. The Generative-Adversarial-Nets approach appears promising in theory, and some initial tests showed an improvement with respect to the baseline, but the limits in time and computational power meant that we could not fully explore it. We also trained a Discriminator network to distinguish between two players based on their trajectories; after training, the network managed to distinguish between some pairs of players, but not between others. After training, the Variational Autoencoders generated trajectories that are difficult to distinguish, visually, from the data. These experiments provide an indication that deep generative models can learn the underlying structure and statistics of football players' trajectories. This can serve as a starting point for determining player qualities based on such trajectory data.