By Gordon Haverland and Tony Attwood
Is there really any evidence that Premier League matches are being rigged via referees? That is a question that we are often asked, and we have often replied that yes there is some evidence, but it is not definitive. However we also note how the PGMO which runs refereeing in the Premier League is set up, and ask, “if there is nothing amiss, why are they so incredibly secret?”
But now we have something new to offer which if you are interested in the subject, you may find slightly concerning.
Let’s imagine that one wanted to create a measurement of the various events that are introduced into football matches by referees and which can affect the outcome of a game. So not issues like goals, which are scored by players, but other things – the things that referees do.
What might we include?
We’d perhaps include yellow and red cards of course, penalty decisions, and the like. But if we wanted to evaluate the power of each decision, maybe we would include the amount of time involved – so that a red card on the 10th minute would be seen in our numbers as far more influential than a red card with one minute to go.
Now we know from the Italian experience that referees who are bent can become very adept at using cards and the like in manipulating of a game. The boss of Team A says to Referee Z, “you will probably get Team X five or six times this season – maybe more. When you do, if there is anything you can throw into the mix, I’d be very grateful. The odd yellow card early on perhaps, a dubious penalty given against them… And I don’t mean when we are playing them – but when other clubs are playing them. Let’s not have any suspicion pointing our way.”
So we’d be saying, do what you can to make it hard for Team X each time they get this ref. Not so that anyone would really notice, but the effect would be accumulative. The rivals of X are not involved, so the effect is harder to spot. It is known as Type III match fixing.
And the key point in the instructions is – “not so that anyone would notice.” In fact one would have to do quite a bit of fancy maths to start to note that what at first appears to be everyday events are in fact mounting up against some clubs in the top six but not others.
Now this is what we have gone out to look for, and in doing this we have looked for incidents which we have grouped under the word “Caution”. Caution is an event which does some harm to a team, and can be administered by referee engaging in Type III match fixing.
Here is a list of the relevant events that affect “Caution”.
First, the minutes of game time remaining (ignoring extra time) after a yellow is given. We can take it that the yellow card does really act as a warning to a player to reign in his more decisive behaviour and therefore fewer risks are taken by players once the yellow has been issued.
Second we could look at the number of minutes of game time remaining (ignoring extra time) after a second yellow is given. Clearly the second yellow to a player is a major disadvantage to a team, as they not only lose a player but also reorganise the team.
A similar problem arises when a red card is given, but since this comes as one straightforward effect we might consider the red card as being double the value of a yellow – if we are counting its impact. So if we are giving numbers to the system the red is worth twice the number of minutes of game time remaining (ignoring extra time) after a red is given.
Next we might want to look at the minutes of game time remaining if the referee gives a penalty (scored or not). This is certainly a way to influence a match and needs to be taken into account.
Our fifth point would be the minutes a team has to play short-handed because a player is receiving treatment. That is clearly something that can have an impact.
Next if a team has to finish the game short-handed because they ran out of substitutions, it is twice the short-handed time.
And finally if a team has to make a substitution due to a treatment, we might give it a value of 17% of the minutes remaining.
OK that is the “Caution list” – the events a referee could impose on a game to tilt it against a certain team if Type III match fixing was going on. A club that has a match fixing ref (or worse a set of match fixing refs) working against it will get a lot of these “Caution” points. A club that itself has its owners engaging in match fixing by influencing referees will have a very low number of points.
If there is no match fixing going on, there still be variance between one club and the next, but it will be modest.
We’ve come up an analysis for the top six clubs in the league to see how many Caution Points on our measurement they have gained. Here is the result, with the clubs with the most Caution Points at the top and the club with the smallest number at the bottom.
- Manchester United
- Manchester City
- Tottenham Hotspur
Interestingly, Liverpool is not only at the foot of the table with the least number of Caution Points but massively lower than the rest, and this difference is growing match by match.
Indeed if you are mathematically inclined you might like to note that recently Liverpool’s numbers were looking to be more than 3 standard deviations off expectations. They are getting far, far fewer caution points than anyone else.
But there is more for Newcastle, not shown on our table, and Chelsea, are also becoming exceptionally low on Caution points. Certainly more than we would expect.
One other factor of interest is that it is the Top 6 clubs that are driving the dispersion of Caution numbers in our tables. In other words, if something odd is happening, it is primarily happening with the top six.
And again if you are mathematically inclined you might be interested in this point. Liverpool are about 3 standard deviations off expectations with 15 more Game Days to go. If the process continues as it has been, Liverpool could be 6 standard deviations off expectations by the end of the season.
Now you may not be familiar with Standard Deviation points, and if not, don’t worry. But the chances of this sort of deviation of numbers turning up by chance is less likely than Leicester winning the league.
Of course as we know it can happen, and of course it did happen, but it is extremely unlikely. So you can see these figures and note them as a 1 in 2000 chance, but still one chance and it can happen. Or you can think that yes, it happened with Leicester, but that doesn’t mean that every other chance event can also be explained away as a one in 2000.
As we have said many times before, we don’t have the resources to look into this situation much further. But the fact that TV and radio never pick up on these oddities, the fact that PGMO is a fanatically secretive society, and the fact that the number of referees on active service is kept very low – which simply enhances the chance of Type III match fixing being carried out, all suggest that we should be taking these figures quite seriously.
After all, if we don’t, who will?
And here’s one more thing. The chance of these figures continuing on into next season are just so off the chart that my calculator blew a fuse. It will be interesting to watch.
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