The trade-off between model flexibility and accuracy of the Expected Threat model in football

TL;DR

This paper analyzes the trade-off between flexibility and accuracy in the Expected Threat model for football analytics, providing theoretical bounds, simulations, and practical guidelines for practitioners.

Contribution

It offers a theoretical analysis and simulation-based characterization of the Expected Threat model's error, along with practical advice for balancing flexibility and accuracy.

Findings

Established an upper bound on model error for different flexibilities

Provided simulation-based error characterization surpassing theoretical bounds

Developed practical guidelines for model parameter selection

Abstract

With an average football (soccer) match recording over 3,000 on-ball events, effective use of this event data is essential for practitioners at football clubs to obtain meaningful insights. Models can extract more information from this data, and explainable methods can make them more accessible to practitioners. The Expected Threat model has been praised for its explainability and offers an accessible option. However, selecting the grid size is a challenging key design choice that has to be made when applying the Expected Threat model. Using a finer grid leads to a more flexible model that can better distinguish between different situations, but the accuracy of the estimates deteriorates with a more flexible model. Consequently, practitioners face challenges in balancing the trade-off between model flexibility and model accuracy. In this study, the Expected Threat model is analyzed from a theoretical perspective and simulations are performed based on the Markov chain of the model to examine its behavior in practice. Our theoretical results establish an upper bound on the error of the Expected Threat model for different flexibilities. Based on the simulations, a more accurate characterization of the model's error is provided, improving over the theoretical bound. Finally, these insights are converted into a practical rule of thumb to help practitioners choose the right balance between the model flexibility and the desired accuracy of the Expected Threat model.