ArticleEntropy (Basel, Switzerland)2026
Empirical Analysis of Hierarchy and Shared Macroscopic Organization in Soccer Leagues.
Article in Entropy (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
This paper presents a coarse-grained framework for analyzing the long-term structural evolution of soccer leagues. This framework draws on ideas from non-equilibrium statistical physics. It combines latent-strength modeling, interaction rules, and large-scale observables to explore the rise of hierarchical organization in competitive leagues. Teams interact based on a Bradley-Terry-type stochastic model. This model relies on teams' latent competitive strengths, which are derived from match outcomes employing maximum-likelihood estimation. Experiments on 38 soccer leagues around the world show persistent hierarchical organization. This is evident in varied latent strengths, uneven competitive balance, and stable macro-state organization from season to season. Even with differences in history, geography, and competition format, many leagues display surprisingly similar large-scale structural patterns. These findings support the idea of shared principles that guide the evolution of competitive leagues and highlight the value of using a statistical physics perspective to describe how macro-level organization arises from repeated team interactions.
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