Ranking football teams via the higher-order decomposition of performance networks

Abstract

Official league standings summarize match outcomes but overlook the underlying performance structure. To address this, we propose a network-based framework to rank football teams through the higher-order decomposition of performance networks, using data from the 2017–2018 major European leagues. Metric-specific weighted graphs yield team ratings from their gradient component, which we compare with official standings. We show that local cyclic flow, quantified by the solenoidal-to-total flow energy ratio, constrain ranking reconstruction and provide a topological signature of league competition styles. This provides evidences for the existence of distinct regimes, ranging from hierarchical structures in England and Italy to loop-driven parity in Germany and more localized dynamics in France and Spain. Finally, a league-specific LASSO composite rating improves predictive performance while identifying the relative importance of indicators. Although comparable in ranking accuracy to classical approaches such as Bradley–Terry, our higher-order network framework additionally exposes latent structural features of competitive performance, offering a general diagnostic tool for oppositional sports.