Investigating Fouling Efficiency in Football Using Expected Booking (xB) Model

TL;DR

The paper introduces the Expected Booking ($xB$) metric to quantify the likelihood that a foul results in a yellow card, focusing on non-dangerous fouls and defensive tactics. It builds an ensemble-based predictive framework using StatsBomb event and 360 data, enhanced by VAEP and spatial features, and validates the approach through three iterative experiments that show substantial performance gains with more data and features. Application to FIFA World Cup 2022 demonstrates that $xB$ aligns with actual defensive performance and reveals team- and player-level fouling strategies, with notable findings such as Morocco's high foul rate paired with relatively few bookings. The work highlights a gap in fouling efficiency analysis and suggests future improvements via more comprehensive data and improved spatial features, potentially informing tactical analysis and referee-style decision studies.

Abstract

This paper introduces the Expected Booking (xB) model, a novel metric designed to estimate the likelihood of a foul resulting in a yellow card in football. Through three iterative experiments, employing ensemble methods, the model demonstrates improved performance with additional features and an expanded dataset. Analysis of FIFA World Cup 2022 data validates the model's efficacy in providing insights into team and player fouling tactics, aligning with actual defensive performance. The xB model addresses a gap in fouling efficiency examination, emphasizing defensive strategies which often overlooked. Further enhancements are suggested through the incorporation of comprehensive data and spatial features.

Figures (9)

• Figure 1: VAEP values for each action in a sequence of plays
• Figure 2: Dummy instance to show feature values
• Figure 3: ROC Curve from Different Classifiers
• Figure 4: ROC Curve from Gradient Boosting & XGBoost
• Figure 5: ROC Curve for Experiment 4.3