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Bayesian networks for unbiased assessment of referee bias in Association Football

机译：贝叶斯网络对协会足球中裁判偏见的无偏评估

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摘要

To assess referee bias with respect to fouls and penalty kicks awarded by taking explanatory factors into consideration. Design: We present a novel Bayesian network model for assessing referee bias with respect to fouls and penalty kicks awarded. The model is applied to the 2011-12 English Premier League season. Method: Unlike previous studies, the model takes into consideration explanatory factors which, if ignored, can lead to biased assessments of referee bias. For example, a team may be awarded more penalties simply because it attacks more, not because referees are biased in its favour. Hence, we incorporate causal factors such as possession, time spent in the opposition penalty box, etc. prior to estimating the degree of penalty kicks bias. Results: We found fairly strong referee bias, based on penalty kicks awarded, in favour of certain teams when playing at home. Specifically, the two teams (Manchester City and Manchester United) who finished first and second appear to have benefited from bias that cannot be fully justified by the explanatory factors. Conversely Arsenal, a team of similar popularity and wealth and who finished third, benefited least of all 20 teams from referee bias at home with respect to penalty kicks awarded. Conclusions: Among our conclusions are that, in contrast to many previous studies, being the home team does not in itself result in positive referee bias. More importantly, the model is able to explain significant discrepancies of penalty kicks bias into non-significant after accounting for the explanatory factors.
机译：通过考虑解释性因素来评估裁判在犯规和罚球方面的偏见。设计：我们提出了一种新颖的贝叶斯网络模型，用于评估裁判对犯规和罚球的偏见。该模型适用于2011-12英超联赛​​赛季。方法：与以往的研究不同，该模型考虑了解释因素，如果忽略这些因素，可能导致对裁判偏见的评估出现偏差。例如，一支球队可能会因为其进攻次数更多而被判处更多罚金，而不是因为裁判偏爱它。因此，在估算罚球踢偏见的程度之前，我们将诸如占有率，在对方罚球盒中花费的时间等因果因素纳入考虑范围。结果：基于判罚点球，我们发现相当强烈的裁判偏颇感，对某些球队在主场比赛时有利。具体来说，第一名和第二名的两支球队（曼彻斯特城队和曼联队）似乎已经从偏见中受益，而偏见并不能完全由解释性因素证明。相反，阿森纳（Arsenal）是一支知名度和财富相近的球队，并获得第三名。在判罚点球大战中，阿森纳（Asenal）受益于主裁判偏向于全部20支球队。结论：与许多先前的研究相比，我们的结论是，作为主队本身并不会导致积极的裁判偏见。更重要的是，该模型在解释了解释因素之后，能够解释罚踢偏向非显着的重大差异。

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