Relegation, promotion and the components of scoring in water polo
Abstract
Relegation, not the championship, decides the outcome of many European water polo leagues: one club has won every recent national title in Italy, Spain and Hungary. We make the relegation decision our object of inference. Serie A1 relegates one club for finishing last and a second through a three-match play-out, and we ask at each stage how much can be known and when. Promoted clubs arrive with no top-flight record, so we also compare four ways of setting their prior. These analyses rest on the first Bayesian hierarchical model of water polo, which splits scoring into even-strength, man-up and penalty components, models opportunities and conversions separately, and lets abilities evolve between seasons. Treating the components as independent proves untenable, since they compete for a common budget of possessions. Fitted to a new dataset of 940 matches, the model identifies the directly relegated club from the ninth round, before the league table does, predicts the play-out field better than the table, and shows the play-out itself to be close to a coin toss. Promoted clubs start below the league on every component except drawing exclusions: knowing a club was promoted improves forecasts; knowing how does not.
Related
BibTeX
@misc{leonelli2026relegation,
title = {{Relegation, promotion and the components of scoring in water polo}},
author = {Manuele Leonelli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25894},
eprint = {2609.25894},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25894},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relegation, promotion and the components of scoring in water polo
AU - Manuele Leonelli
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25894
UR - https://arxiv.org/abs/2609.25894
AB - Relegation, not the championship, decides the outcome of many European water polo leagues: one club has won every recent national title in Italy, Spain and Hungary. We make the relegation decision our object of inference. Serie A1 relegates one club for finishing last and a second through a three-match play-out, and we ask at each stage how much can be known and when. Promoted clubs arrive with no top-flight record, so we also compare four ways of setting their prior. These analyses rest on the first Bayesian hierarchical model of water polo, which splits scoring into even-strength, man-up and penalty components, models opportunities and conversions separately, and lets abilities evolve between seasons. Treating the components as independent proves untenable, since they compete for a common budget of possessions. Fitted to a new dataset of 940 matches, the model identifies the directly relegated club from the ninth round, before the league table does, predicts the play-out field better than the table, and shows the play-out itself to be close to a coin toss. Promoted clubs start below the league on every component except drawing exclusions: knowing a club was promoted improves forecasts; knowing how does not.
ER -