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Referee bias in Scottish football

a statistical analysis of penalties conceded, 2016-2023


  • Michael Garrett University of Manchester



football, soccer, bias, referee


This study presents a statistical analysis of penalties conceded in the top tier of the Scottish Professional Football League (SPFL) from seasons 2016/2017 - 2022/2023. In particular, claims in the media that the number of penalties conceded by Glasgow Rangers is statistically anomalous are considered. A t-test analysis of the penalties conceded by Rangers versus other SPFL premier league clubs, reveals a statistically significant difference, with Rangers conceding fewer penalties. This result is even more pronounced for Rangers if the analysis is restricted to penalties conceded at home. By comparison, the number of penalties conceded by Glasgow Celtic do not diverge significantly from the league's average, despite their dominant playing style and high possession rates. The study concludes that the number of penalties conceded by Rangers over this period is formally a statistical outlier, lending significant weight to concerns over the impartiality of match officiating in Scottish football.


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