arXiv subjects

Mirjam Bruinsma

Publications and source records attributed to Mirjam Bruinsma.

2 recordsLinked to original sources

arXiv2026

Model quality in football: Quantifying the quality of an Expected Threat model

The recent growth in data availability in football has increased the risk of incorrect use of data-driven models, making guidelines on their validation and application necessary. The Expected Threat (xT) model is an accessible option for football organisations that start building in-house methods, yet little is known about how to assess its quality. The aim of this study is twofold: to examine how the model quality depends on the number of game states and the number of training points, and to translate these results into guidelines for constructing and applying the model. Using the Markov chain underlying the model, we perform theoretical analyses and simulations to study the estimation error. These show that the estimation error is approximately lognormal for a given number of training points and game states. Additionally, we combine the simulations with expert consultation to establish the estimation error beyond which player evaluations based on the Expected Threat model become unreliable for scouting applications. From this, we derive rules of thumb to ensure the quality of an Expected Threat model before application, and we illustrate through an example how a validated model can be applied in practice. Because the approach generalises to Expected Possession Value models, this paper illustrates a framework to systematically quantify model quality, despite the ground truth being unobservable in football analytics.

stat.AP↗

arXiv2025

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

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.

stat.AP↗