  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.
