Bayesian networks for unbiased assessment of referee bias in Association Football

Abstract

We present a novel Bayesian network model for assessing referee bias with respect to fouls and penalty kicks awarded. Unlike previous studies, our 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. The model is applied to the 2011-12 English Premier League season. Among our conclusions are that, in contrast to previous studies, being the home team does not in itself result in positive referee bias. 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.

Twelve eyes see more than eight. Referee bias and the introduction of additional assistant referees in soccer

“…Similarly, [10] showed that teams from the big five European competitions (English Premier League, Spanish Primera Division, French Ligue 1, German Bundesliga, and Italian Serie A) receive fewer yellow cards when playing against a team outside of the big five in European international club soccer, keeping team strength constant. Finally, [37] showed that in the 2011-2012 English Premier League, home favouritism in terms of penalty kicks occurred only for the top two teams (Manchester City and Manchester United).…”

A review of some emergent quantitative analyses in sport and exercise psychology

“…With the exception of one study, which employed Bayesian network analysis (Constantinou et al, 2014), SEP researchers have applied Bayesian statistics for the primary purpose of parameter estimation. The majority of this work has employed BSEM to examine the factorial validity of scores from questionnaires designed to assess constructs such as commitment (Jackson et al, 2014), sport motivation , walking motivation (Niven & Markland, 2016), and movement skill competence (Barnett et al, 2016).…”

“…Researchers have also employed BSEM to test theoretical sequences that encompass multiple antecedent, intermediary and outcome variables, such as the relations from self-efficacy beliefs to performance on endurance-based physical activity tasks via self-presentation motives and personal task goals (Howle et al, 2016); motivational pathways informed by self-determination theory (Chan et al, 2015); and the integration of basic psychological needs and the theory of planned behaviour (Gucciardi & Jackson, 2015). Other applications of Bayesian statistics include multilevel modelling (Doron & Gaudreau, 2014;Tamminen et al, 2016), latent growth modelling (Noordstar et al, 2016), and network analysis (Constantinou et al, 2014). Within and across each of the studies, researchers have drawn from theory and past empirical work to incorporate weakly informative and informative prior information, or employed the default non-informative prior.…”

Risk assessment and risk management of violent reoffending among prisoners

“…For instance, BNs have been employed for analysis and knowledge representation with success in diverse domains such as computational biology and bioinformatics (Friedman et al, 2000;Hohenner et al, 2005;Jiang et al, 2011), gaming (Lee & Park, 2010), computer science and artificial intelligence (de Campos et al, 2004;Pourret et al, 2008;, medicine (Heckerman et al, 1992;Diez et al, 1997;Nikovski 2000), and law (Fenton & Neil, 2011;Fenton et al, 2013;Taroni et al,2014). Especially relevant recent use of BNs include management of project maintenance delays based on expert judgments (de Melo & Sanchez, 2008), risk analysis in large projects to extend their understanding of project risks within the Korean shipbuilding industry (Lee et al, 2009), systematic development of causal interventional systems for prognostic decision support (Yet et al, 2011), qualitative examination and evaluation of service offered by the loan departments of Greek Banks (Tarantola et al, 2012), safety control decision support in dynamic complex project environments (Zhang et al, 2013), football match prediction (Constantinou et al, 2012; and inference of referee bias (Constantinou et al, 2014), detection of problems in software development project processes (Perkusich, 2015), and jointly monitoring internal and external performance of a Master's programme of an Italian University in a holistic approach (Di Pietro et al, 2015).…”