Fouls and Cards Awarded by the Referee
by Andrew Crawshaw
Some of our readers have noted that there seem to be some anomalies this season between the number of fouls committed by teams in the Premier league and the numbers of cards issued. I have looked at the official web site of the Premier League and abstracted the relevant numbers for each season back to 2006/7 and will be seeing what sense (if any) I can make of the numbers.
Now we all are aware from the work by Walter and his team of referee reviewers over the past few years that the number of fouls and cards awarded by referees does not necessarily bear any resemblance to the numbers that should be awarded and I will try in future articles to compare Walter’s figures with those actually given.
For the first 9 games of the season here is the table of referee awarded fouls and cards :-
|Team||Fouls conceded (as awarded by Referee)||Yellow Cards||Red Cards||Average fouls per card|
The average number of fouls committed per card awarded across all games is 5.8. In the above table all teams from Aston Villa downwards can be said to be doing better than average, the further down the table the better they have done.
Teams from West Brom upwards can be said to have done worse than average, the further up the table the worse they have done.
Clearly Arsenal have been treated more harshly than any other team this year, Leicester and Southampton noticeably more leniently. The real question is are these numbers statistically meaningful or not?
I am not a expert in statistics, but have had occasion to use such analysis many times in my career. My understanding is that within a number sequence a particular value is likely to be “NORMAL” if it lies between the 5 and 95 percentile values for that sequence. If a value lies outside those values it is statistically unlikely. I am assuming that the numbers can be said to have a normal distribution.
I am sure that there will be someone better at Statistics than I am reading this so if I have got it wrong then I’m sorry and will be glad to be corrected.
So what are the ‘magic’ numbers :-
|Average number of Fouls per Card||5.80|
|5 Percentile value||4.68|
|95 Percentile value||9.01|
I would contend that statistically speaking the Arsenal value of 3.79 and the Southampton value of 9.25 are both “odd”, the Leicester City value of 9.00 is just within normal limits.
What is also apparent is that all teams are being carded more than in previous years, again something I want to look at further.
- The home and away scandal: ignorance, or cover up?
- The reason why Liverpool and Man C are ahead of Arsenal.
- How which referee a club gets has a major impact on the result of each game
- The statistical evidence that shows PGMO are biased against Arsenal
- How European football has taken up the fight against clubs breaking FFP