Different formations, different patterns: An integrated approach combining entropy, machine learning, and XAI to analyze passing networks in soccer

This study examined the differences in passing network between two- and three-center-back (2-CB and 3-CB) formations and their predictive relevance for match outcomes using machine learning models. The dataset comprised 256 matches (7328 player observations) from FIFA Soccer World Cups from 2010–2022. A novel subgroup entropy metric was introduced to quantify the distribution of ball circulation within positional units (defenders, midfielders and forwards). Results showed that conventional network metrics failed to distinguish formation-specific features, whereas the subgroup entropy metric revealed significant differences: 2-CB formations exhibited higher forward- and defender-entropy but lower midfielder-entropy compared with 3-CB formations (p < 0.001). Among the tested models, XGBoost achieved the best performance (accuracy = 0.599 ± 0.040, F1 = 0.737 ± 0.033). SHAP-based explainability analysis indicated that the key network metrics associated with match success varied by formation: midfielder-entropy and forward-entropy were most influential in 2-CB formations, while average weighted degree, average path length, and Density dominated in 3-CB formations. These findings suggest that different formations shape distinctive patterns of passing flow and team coordination. The proposed subgroup entropy provides a novel framework for linking network structure, tactical organization, and match outcomes in football analytics.