Is this crowd pressure?

This will be part VI in my series looking at referees. These are the links for parts I, II, III, IV and V.

This time I’m going to move on and look at how much more likely each referee is to produce a card when an away player commits a foul compared to a home player.

The calculation will yield a ratio for each referee and is carried out as follows

Home fouls per card / Away fouls per card

Basically the resulting ratio tells you how much more likely the away team is to be shown a card after a foul than the home team. A value of 1 would mean that both teams are equally likely to receive a card whereas a value of 2 means that the away team is twice as likely to be shown a card following a foul than the home team. All of the referees actually fall between these two numbers and I’ve included the values for all 23 referees studied in the table below.

Referee # of games Ratio Referee # of games Ratio
J Winter 84 1.718 P Durkin 88 1.285
M Halsey 224 1.445 Average 155 1.268
N Barry 95 1.440 L Mason 80 1.259
S Bennett 243 1.394 A D’Urso 99 1.253
P Dowd 203 1.387 G Barber 80 1.236
D Gallagher 127 1.329 M Riley 205 1.223
C Foy 177 1.325 R Styles 211 1.186
H Webb 203 1.311 A Wiley 253 1.181
P Walton 150 1.310 M Atkinson 151 1.169
A Marriner 110 1.290 M Dean 247 1.159
G Poll 186 1.286 U Rennie 116 1.105
S Dunn 99 1.286 M Clattenburg 139 1.098

The first things to point out are that on average the away team is ~25% more likely to receive a card than the home team and that every single referee gives more cards per foul to the away team than the home team. As I mentioned in part V I think there are certain things that can account for this (I think time-wasting and bias due to crowd pressure are the major factors) and I’m sure there are more that I haven’t thought of.

Amongst the referees there’s a pretty wide spread of numbers but one stands out a long way from the others. To put into context just how unlikely Jeff Winter’s ratio is I’ve plotted the distribution for a sample with an average of 1.268 and a standard deviation of 0.133. This is shown below (blue bell curve) along with the accompanying cumulative probability line (red line).

So to summarise the plot it says that 99.96% of the population will have a ratio of 1.718 or lower. Therefore in a typical sample of 2,500 referees we’d expect to see an average of one who has a ratio of 1.718 or higher. The sample size here is a mere 23 so probability dicates it’s highly unlikely (~1 in 130) that Jeff Winter’s number is that high due to chance alone. It’s worth mentioning here that he is one of the most lenient referees in terms of producing cards but I still can’t think of an alternative explanation for these numbers other than keeping the cards in his pocket when a home player commits a foul. The sample size in terms of the number of games he officiated could be questioned but there’s still over 2,000 fouls and over 200 cards and his ratio is so far above any of the other referees (who are all comfortably within the bounds of the normal distribution above) that there has to be something behavioural in there. If anyone can point me to a freak set of games that he officiated where the away sides consistently made dirty challenges and wasted massive amounts of time I’d love to see them.

Amongst active referees there’s a pretty wide spread, going from Mark Halsey, who ranks second behind Jeff Winter, all the way down to Mark Clattenburg right at the bottom. Next time I’m going to have a short further look at Jeff Winter’s numbers but beyond that I think I’ve reached the logical end of this little series on referees.

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