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
- Arsenal
- Manchester City
- Tottenham Hotspur
- Chelsea
- Liverpool
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.
Interesting. And worrying.
Perfect summery. The influence of Epl ref on matches is huge and it does have great effect on which team gets into top 4 and relegation.
Their influences is far becoming damaging and toxic for the brand plus the sport’s channel delibrate ignorance towards PGMO action on mismanagement of Epl is appalling.
We can see how spurs gets David Dean often over the last few season couple with dubious penalties plus multiple caution against their opponents which gives their players freedom and licence to attack constantly until they brake the deadlock.
Man city had lots of support from Epl ref over the last 2-3 season in a row but then when they gets to European league they struggle, just because they are not as great as been propagated by our media and Epl ref.
Can’t remember the last time Arsenal had a player been sent off earlier in a game against us in a genuine incident t or earlier penalty been awarded in many obvious situation .
Personally, I think PGMO have decided their top 4 already and they can then use their sport pundits to execute their agenda.
Moreover, still have my doubts with a free and fair usage of VAR from Epl ref because of their insecure and obsessive culture to influence matches but next season will be highly interesting with a battle between VAR and Epl magic finger.
Perfect summery. The influence of Epl ref on matches is huge and it does have great effect on which team gets into top 4 and relegation.
Their influences is far becoming damaging and toxic for the brand plus the sport’s channel delibrate ignorance towards PGMO action on mismanagement of Epl is appalling.
We can see how spurs gets David Dean often over the last few season couple with dubious penalties penalties plus multiple caution against their opponents.
Man city had lots of support from Epl ref over the last 2-3 season in a row but then when they gets to European league they struggle, just because they are not as great as been propagated by our media and Epl ref.
Can’t remember the last time Arsenal had a player been sent off earlier in a game against us in a genuine incidence or earlier penalty been awarded in many obvious situation .
Personally, I think PGMO have decided their top 4 already and they can then use their sport pundits to execute their agenda.
Moreover, still have my doubts with a free and fair usage of VAR from Epl ref because of their insecure and obsessive culture to influence matches but next season will be highly interesting with a battle between VAR and Epl magic finger.
That the degree of dispersion of Caution figure is being driven by the so-called top six premiership clubs, according to your analysis, there is thus a suggestion of a degree of sophistication arising within the PGMOL in the way that matches are officiated. Obviously this hypothesis would need further testing through some experimental procedure, if indeed such procedure(s) would be allowed or supported by those organisation(s) most affected by the results or general findings. There could be a PhD in the offing perhaps for somebody out there to investigate this phenomena further. If only…..
Well done Gordon and Tony with your initial attempt to try and rationalise this through the use of a statistical process. It would be most instructive if this could be looked at in more depth.
As Pat observes, it is most interesting and very worrying………..
I seldom look at the Telegraph, but someone one thinks Moss is a lousy referee.
https://www.telegraph.co.uk/football/2019/01/26/accrington-stanley-vs-derby-county-fa-cup-fourth-round-live/
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There should be a second article to follow this article, which hopefully has a couple of graphics in it.
I have felt for a long time that Type III match fixing has been going on. It is amazing how when a “non-favoured” team starts winning all of a sudden they have a run of yellow and or red cards to stop them.
I also notice that the VAR “tests” (as PIGMOB call them) have been disastrously bad again this weekend. I do not hold out much hope for VAR being used correctly by PIGMOB next season.
It is funny how I watch Spanish and German football and see VAR being applied correctly. This means that it can be done to benefit football.
Referees in Spain and Germany can talk to the media and they are not bound to secrecy like their PIGMOB counterparts.
One cant help thinking that PIGMOB secrecy is used for neferaious purposes. After all if they have nothing to hide why dont they share things with us
@Gord isnt it amazing how Moss seems to be in the news every week. It is almost as if he is imcompetent, I think the word corrupt is more apt.
“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.” I’m sorry, I don’t understand the relevance of 17%. Please can you elaborate.
i have even noticed one when reefs deny penalty and balance it with a tackle out side penalty area, some thing which is un called for and cann make fans loose hope on reefs and football matches they orficiate.
Our Women have just finished their game against Reading winning by three goals to nil. A poor referee I’m afraid and a very stop start game as a result. Also very poor commentating by the BBC. Praise for every Reading touch and snide comments about every Arsenal touch. A clear penalty for Arsenal, which the referee got absolutely correct, was rubbished despite the obvious push on our player who , according to the commentators, tripped over the ball. Of course she did having been pushed over!
Bad news before the game with another two players out with knee injuries. So we are even shorter in terms of players. We even had our assistant manager in the Doug out as Joe has been laid up all week with some kind of illness.
Our third goal was a stunning left foot shot by Katie ZmcCabe from just outside the area. It was about the last kick of the game.
The original idea about substitutions was to allow teams to continue with a full squad of 11, in the event of injuries. However, I think most managers would prefer to be able to use substitutions solely for tactical reasons.
If a team is forced into making a substitution because a player who needed treatment can’t continue, it removes one possible substitution for tactical reasons. Hence, it has some influence on the ability of a team to play the manager would like them to play.
The number 17% is taking the remaining minutes and arbitrarily dividing that remainder by 6.
I do wish the two graphics were still present.
The first graphic shows how the median Caution changes from game to game over the entire season, and it has the Caution “trajectories” for the Top-6 plotted. Finally, it has the MAD (the median absolute deviation from the median) for the entire EPL plotted.
The graph is a semi-log plot (the log of Caution is plotted). You can see that the plot of MAD is approximately parallel to the plot of the median with the most recent data. That means that both quantities are growing at the same rate.
The second graphic has the same median of the EPL and MAD of the EPL, plotted against the median of the 14 teams not in the Top-6 (Rest Of The Pack – ROTP) and the MAD for the ROTP. The median of the ROTP very closely follows the median of the EPL, as it should as it constitutes almost 75% of the data.
What is interesting to me, is that at about Game Day 9, the MAD of the ROTP stops growing. Instead, it is doing a sort of random walk, some Game Days it is a bit higher and some days it is a bit lower.
Sort of like a ROTP team gets on a bit of a run of acquiring Caution in every game at a higher rate than the median (or average), and then the manager has a talk to them and tells them to quit getting Caution, and so that team “falls away” from the high side, to be replaced by some other team from the ROTP on a run of acquiring Caution takes over.
I don’t think the ROTP Caution data stopped growing at Game Day 9, I think it changed from a linear growth rate, probably to a logarithmic growth rate. It was experiencing linear growth while the system was “coming to equilibrium, and then switched over to a slower growth curve after it got to steady state. The data from the Top-6 hasn’t switched to a slower growth rate, because it is constantly being perturbed by the PGMO representatives.
Mikey
If you had arguments as to how much someone should weight individual data, I’m all ears. Dividing by 6 for substitutions is just as arbitrary as multiplying by 2 for red cards.
I didn’t want to get into a curve fitting exercise, so I just picked numbers that seemed reasonable.
Very interesting! Thanks Gord and Tony
Looking at the Caution data was easy, in that it is similar to engineering statistics.
I’m slowly picking my way through combining a bunch of data to look at principle components analysis and factor analysis (which seems to be a subset of data mining, which is new to me). The last time I did it, I had 42 variables, no useful predictions could come out (no convergence). I am adding all the card data, all the penalty data, the attendance at the game, the capacity of the stadium, the fractional attendance, where the game is being played (Lat/Long), the Lat/Long of the visiting team, the Lat/Long of the referee (born and lived), how many “weeks” it has been since the referee last worked, and some other stuff. Probably be up around 80 variables (more?). But it is hard entering some of this data, as it is all manual. And I don’t want to make mistakes.
With some of this stuff, I will probably put reports on the Untold Arsenal Github site. For those people that want something more technical, or who want to either look at code or write code.
As an aside on Mikey’s question about where 17% comes from, if I do principle components analysis I get eigenvalues. Sometimes these things are called ‘loadings’, which seems to be the language used in factor analysis. A person may be able to come up with better weight factors for Caution, by looking at the eigenvalues or loadings.
To do this is still just an exercise in curve fitting, as this is just one league and one season.
Some people might run out of computer in doing this. I’m not likely to. I’ve got 2 computers with 12 cores, one with 32 GB of RAM and 6 or 7 TB of disk. I’ve got other computers with 8 cores, and only 8 GB of RAM. I’m in the middle of some hardware upgrades, and after I should be up around 20TB of disk across the LAN.
When there was no VAR untold was screaming for it, but I always knew when it came to be untold would be one of its biggest critic, because when you refuse to accept truth, you will always find excuse for failure. So no VAR? Let’s blame the refs call for var. VAR in place? Let’s blame the refs, scrap VAR
Unrelated to this article.
Rule changes.
I still like the idea that you need to score to get points. Hence a 0-0 final score should be 0 points to both teams.
There are entirely too many cards in extra time. And they are so late in the game, they really don’t apply Caution to anybody. Mostly I think they are a way for the referee to “even up” the card count, without affecting the game (in their opinion).
I would like to see all yellows assigned in the 90th minute, to count as 2 yellows as far as discipline goes. That would at least give some meaning to a yellow so late in the game.
Unrelated to this article.
Rule changes.
In terms of Type III match fixing, Arsenal would get screwed over even worse with that yellow card change. We already get early cards for eating garlic. If referees could give us cards in extra time and they count double towards bans, that would just have our players getting lots of yellows in extra time.
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In terms of type III match fixing, if some team was looking for favours in terms of “punishing” a third team; I would think a likely after effect of this request could be a reduction in how many cards the requesting team gets in regular play. If that is reasonable, then it might point to Liverpool!!, and possibly Newcastle and Chel$ea as teams requesting that officials make things difficult for other Top-6.
Other than moaninho being an a**hole, I see no reason why ManU should be in the Caution position it is in. But as everyone seems to hate Arsenal, it explains what happens to us. The other Top-6 teams are either at the median, or below. With Liverpool!!! and Chel$ea being quite a bit below.
I’ve no idea why Newcastle figures into this, as I think their owner is almost as hated as the Blackpool owner. PGMO trying to be smart, and throw some noise into people like me looking for patterns?
Extremely interesting, looks like at least some of the usual suspects doing well and seems to confirm what we see with our own eyes with Liverpool .
After all, they have to at least try and make this league look competitive up against a team that has largely been financed by a state, would be embarrassing for our authorities if they just let city win everything
On another note, nice to see is in our usual negative penalty balance, quite extremely negative at the moment, isn’t it something like 1 for and 4/5 against!
Maybe we need the Kroenkes to have a few words and give us the kind of officials intervention that the Rams clearly benefited from at the end of the game that got them to the Super Bowl!
Enough of a reason to look at football in the premier league as dead.
Untold you are in the right ball park and the link below to which i believe you are familiar with the bloggers, gives all some more incite into why things look so weird.
I expect alot of people will ignore or not understand what is posted in this link and and i will get i am a conspiracy theorist with a tin foil hat while ignoring whats in front of their face.
https://footballisfixed.blogspot.com/2019/01/the-prevention-of-var-by-uk-mafia.html?m=1
We have had only one penalty this season and that was for as blatant a handball as one could ever see. None for a foul.
We must have had nearly 10 against us at least. C.palace and Liverpool had 2 each and there have been lots more I am sure.
I think you ought to consider the history of what we have said about referees in the past.
For the record, I have checked, we have conceded 5 penalties. Apart form the ones mentioned by me there was the one awarded to the scum for a dive.
Tony – Has there been any changes to how City are being given cards since they had their meeting with the PGMOL?
why not have articles about how players are continually trying to deceive referees. seems to me referees are guilty on the wholr of human frailties, tring to even things up, making mistakes ans being aware of past reputations
why not have articles about how players are continually trying to deceive referees. seems to be referees are on the whole guilty of human frailties, trying to even things up, making mistakes and being aware of past reputations
Well Ron, the point about Untold Arsenal is in both parts of its name “Untold” and “Arsenal”. For 11 years we have been running the stories that no one else likes to run – and we have repeatedly said we’re not really interested in running stories that other people are running. The issue of players trying to deceive referees is regularly run, so we don’t bother. Our interest is in uncovering stories the media don’t run.
Great job guys. Well done. And some fine supporting links and comments.
Also note that there are those who still are very comfortable with their heads in the sand. Am looking forward to the day all this corruption blows up in the faces of the crooks.
Every season there is many a plot twist , especially in the final fortunes of the top clubs. I do believe that sometimes human errors /karma causes overturning of the apple cart. Case in point , those unfortunate slips by Steven Gerrad and by John Terry .
Am quite interested and intrigued on how this Ole Solskjaer/ Man Utd love fest will end . Its like a plot from so many sports movies – a returning former hero ,comes to the aid of his ailing club , the crowds embrace him and with their support , all their failings are corrected and the club rides/glides over stormy waters , to finally …….. ( fill in your ending here !).
I am not surprised by the findings above. I am Interested as to what their motivation is? What is clear is that they are doing a huge dis-service to the game of football. I would be interested to know the chart for when Leicester City won the premier league, was that 2015-2016?