Last time I looked at how much more likely referees were to give out cards to players on the away team than those playing at home. I found that one referee in particular, Jeff Winter, was an outlier as he was almost twice as likely to give a card to a player on the away side than the home side. The plot below shows the normal distribution of ‘away cards ratio’ which is a measure of how many cards an away team receive per foul for every one card the home team receives.
Basically there is a 1 in 2,500 chance that a referee will have an away cards ratio of 1.718 or higher (Jeff Winter’s value is 1.718). So what happens if we remove him from the sample on the basis that he is an outlier? Well the average drops to 1.262 and the standard deviation falls to 0.097 as the remaining referees are more tightly grouped. Below is the normal distribution for those values.
The chances of a referee having an away cards ratio of 1.718 through luck alone are now much slimmer, around 1 in 15,000. It’s also worth bearing in mind that whilst he gave 52.3% of fouls against the away team (league average is 51.3%) they received a massive 65.3% of the cards distributed. Even with the small sample size (more games would obviously give more reliable results) I’ve reached the conclusion that it is basically inconceivable that crowd pressure played no part in Jeff Winter’s decision making process when it came to giving out cards.