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

A. Chacoma; J. I. Perotti; O. V. Billoni

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arXiv · 2606.21814

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

A. Chacoma·J. I. Perotti·O. V. Billoni

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Abstract

We propose a unified methodological framework to quantify team performance in elite football by combining event-level performance metrics, higher-order network representations, and algebraic ranking methods. Using data from the 2017--2018 season of the five major European leagues, we construct metric-specific weighted graphs in which teams are connected through relative performance indicators. These graphs are analyzed via Hodge decomposition, and the gradient component is used to derive metric-based team ratings. The resulting rankings are systematically compared with the true league standings using Pearson and Kendall correlation measures, revealing strong metric- and league-dependent effects. Furthermore, by analyzing the ratio between solenoidal and total flow energies, we show that local cyclic dynamics structurally limit the gradient component's capacity to reconstruct the ranking. This topological inconsistency acts as a structural fingerprint of each league's ``competition style'' successfully mapping the studied systems into distinct regimes: highly hierarchical structures (England and Italy), tactical parity driven by generalized loops (Germany), and pockets of localized chaos (France and Spain). Lastly, we introduce a composite rating obtained as a parsimonious linear combination of metric-based ratings, optimized separately for each league. This composite approach significantly improves predictive power and allows the relative importance of different performance indicators to be quantified in a league-specific manner. Our results demonstrate how higher-order network methods provide a flexible and interpretable framework to uncover latent performance structures in football, offering a complementary perspective to outcome-based rankings and a general approach applicable to other oppositional sports.

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A. Chacoma, J. I. Perotti, O. V. Billoni. 2026-06-20. Ranking football teams via the higher-order decomposition of performance networks. https://arxiv.org/abs/2606.21814

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