When Do Sports Leagues Stop Being Competitive? Bayesian Detection of Competitive-Balance Eras from Match-Level Data
Abstract
Competitive balance shapes outcome uncertainty, fan interest, and league regulation, yet standard measures summarize realized standings and cannot separate structural ability differences from match-level randomness. We develop a Bayesian framework that infers structural competitive balance from longitudinal match outcomes. Team abilities are obtained by projecting Gaussian auxiliary variables onto a graph-fused l1 polytope whose radius measures total pairwise ability variation. The projection places positive probability on exact ties, so statistically indistinguishable teams form explicit rank tiers. The radius equals realized ability variation whenever the constraint binds, linking it to parity, detectability, and structural inequality. An adaptive finite-regime model lets competitive eras recur, emerge, and disappear while team hierarchies remain season specific. Simulations show accurate recovery of regimes, radii, abilities, and tiers. Applied to 25 English Premier League seasons, the model identifies a persistent shift to a more stratified league beginning in 2005/06, with 2010/11 the only later return to the compressed regime. It also shows that a close title race can coexist with wide league-wide separation and that head-to-head results can separate clubs level on points. The framework gives leagues a model-based measure of balance to inform debates on revenue sharing and financial regulation.
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BibTeX
@misc{li2026when,
title = {{When Do Sports Leagues Stop Being Competitive? Bayesian Detection of Competitive-Balance Eras from Match-Level Data}},
author = {Xinran Li and Maoran Xu and Guanyu Hu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07335},
eprint = {2611.07335},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07335},
}
RIS
TY - UNPB
TI - When Do Sports Leagues Stop Being Competitive? Bayesian Detection of Competitive-Balance Eras from Match-Level Data
AU - Xinran Li
AU - Maoran Xu
AU - Guanyu Hu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07335
UR - https://arxiv.org/abs/2611.07335
AB - Competitive balance shapes outcome uncertainty, fan interest, and league regulation, yet standard measures summarize realized standings and cannot separate structural ability differences from match-level randomness. We develop a Bayesian framework that infers structural competitive balance from longitudinal match outcomes. Team abilities are obtained by projecting Gaussian auxiliary variables onto a graph-fused l1 polytope whose radius measures total pairwise ability variation. The projection places positive probability on exact ties, so statistically indistinguishable teams form explicit rank tiers. The radius equals realized ability variation whenever the constraint binds, linking it to parity, detectability, and structural inequality. An adaptive finite-regime model lets competitive eras recur, emerge, and disappear while team hierarchies remain season specific. Simulations show accurate recovery of regimes, radii, abilities, and tiers. Applied to 25 English Premier League seasons, the model identifies a persistent shift to a more stratified league beginning in 2005/06, with 2010/11 the only later return to the compressed regime. It also shows that a close title race can coexist with wide league-wide separation and that head-to-head results can separate clubs level on points. The framework gives leagues a model-based measure of balance to inform debates on revenue sharing and financial regulation.
ER -