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Lookup NU author(s): Dr Pete PhilipsonORCiD
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
Scrutiny of referees in football is ever-increasing and likely at an all-time high. Is this fair? How consistent are modern day referees? In this work, the number of yellow cards given to the home and away teams over four seasons of data from 2018 to 2022 in each of the ‘Big 5’ European leagues in men’s football is modelled. This allows us to make an assessment of the heterogeneity amongst both referees, primarily, and teams, secondarily. The underdispersed nature of the data from the small counts, and likely dependence of the cards issued within a game, leads to a bivariate mean-parameterized Conway–Maxwell–Poisson copula model to analyse the data. We also model home advantage, and examine whether this was diluted during COVID-19, and league effects, allowing for an assessment of how consistent referees are across leagues and which league has the most heterogeneous ‘men in the middle’. We find that teams and referees are, perhaps surprisingly, similarly heterogeneous and that referees in Serie A appear to be the least variable. The underlying model has wider use in other fields when the researcher is analysing small multivariate counts with possible bidispersion.
Author(s): Philipson P
Publication type: Article
Publication status: Published
Journal: Journal of the Royal Statistical Society Series A: Statistics in Society
Year: 2026
Pages: epub ahead of print
Online publication date: 17/02/2026
Acceptance date: 14/01/2026
Date deposited: 29/06/2026
ISSN (print): 0964-1998
ISSN (electronic): 1467-985X
Publisher: Oxford University Press
URL: https://doi.org/10.1093/jrsssa/qnag014
DOI: 10.1093/jrsssa/qnag014
Data Access Statement: The code (for fitting and simulating) and data are available on GitHub at https://github.com/petephilipson/MPCMP_copula_yellow_cards.
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