Flexible marked spatio-temporal point processes with applications to event sequences from association football

TL;DR

This paper introduces a flexible family of marked spatio-temporal point processes tailored for modeling event sequences in football, enabling detailed inference and prediction of game dynamics and specific events.

Contribution

It develops a novel decomposition approach for marked Hawkes processes, allowing separate modeling of marks and times, with a Bayesian framework for inference and prediction.

Findings

Effective modeling of football event sequences

Extraction of team abilities from game data

Accurate predictions of key in-game events

Abstract

We develop a new family of marked point processes by focusing the characteristic properties of marked Hawkes processes exclusively to the space of marks, providing the freedom to specify a different model for the occurrence times. This is possible through the decomposition of the joint distribution of marks and times that allows to separately specify the conditional distribution of marks given the filtration of the process and the current time. We develop a Bayesian framework for the inference and prediction from this family of marked point processes that can naturally accommodate process and point-specific covariate information to drive cross-excitations, offering wide flexibility and applicability in the modelling of real-world processes. The framework is used here for the modelling of in-game event sequences from association football, resulting not only in inferences about previously unquantified characteristics of game dynamics and extraction of event-specific team abilities, but also in predictions for the occurrence of events of interest, such as goals, corners or fouls in a specified interval of time.