The curious case of the uneven effect of referee activity in the PL. Part 2

Caution and Liverpool Part 2 – Some Details

By Gordon Haverland

This article continues from the previous post  The curious effect of referee actions on the top six clubs this season.

Treatments

There are two kinds of treatments, the ones where a physio does not come on to the field to bring the player off the field to receive attention the player, and those where the player is taken off the field to receive extended attention and the game is restarted. The treatments mentioned here, are the treatments where a player ends up being removed from the field for an extended period of time (and the game becomes restarted), and perhaps at some point the player who was injured seeks permission from the referee to come back onto the field, or a substitution is made.

The referee doesn’t cause the treatment directly.  Referees practice “man management”; they create the environment where some players become frustrated, who think they might get away with something or various other things.  The fact that few referees call fouls associated with these events, let alone card a player (either rough play or simulation) in one of these events, means they regard these events as not worthy of consideration.  I believe we lost 2 (or perhaps three) players to serious injury in these kinds of events this season (Maitland-Niles was the first).

The reason to include things derived from treatment data, is to get the tabulation of that data out of the hands of the PGMO.  If the PGMO issue a lot of cards to a team, supposedly the reason is that the team is dirty.  But the PGMO can, potentially, issue a lot of cards to a team that is not dirty.  In doing so, most people will start to think that is a dirty but there is a perfectly valid alternative explanation.

Thus PGMO can’t “cook” the books by having more treatments in a game.  But they can “cook” the books by calling more fouls, issuing cards or granting penalties.

Dispersion

Dispersion is a common sort of word, which talks about the width of something.  Standard deviation is a term used to describe dispersion in a very particular way.

I plotted up “trajectories” of Caution over the season so far.  Let’s pretend we are standing on the moon (low gravity and no air) with a shotgun.  We shoot the shotgun at say 10 degrees above the horizon.  As the pellets travel down range, they tend to get further away from the average trajectory of all the particles.  How wide the pattern is, is a measure of dispersion.  A second shot with the shotgun, will not have the pellets travelling the same paths as the first shot, but how the dispersion changes with distance should be about the same.

If there were 100 pellets in a load, and 99 of the pellets were within 20 inches of the average trajectory at some point, what would you think of there being a single pellet that was 30 inches off?  You might think it is possible, but unlikely.  What if it was 60 inches off? The further this outlier gets from the average, the more likely it is that some strange circumstance not involving any of the other pellets is affecting that one pellet.

And in footballing terms this season, that’s Liverpool!   Their results are way out of line with everyone else when we consider the concept of Caution (which we defined in the previous article), and what we are looking for is an explanation.

Conclusions

“Pure chance” isn’t an explanation for what we are seeing here because it doesn’t tell us about any mechanics that have caused this variation.   Nor is the “law of averages” which isn’t a law at all, but just suggests that there will be a normal distrubition of results – without one really weird outlying statistic at one end.   So we still need to look for something else.

But we are hampered in our search by two things: the secrecy of the PGMO and the way they insist on only having a small number of referees avaialble so that the same referee can run matches by certain teams multiple times in the season.

The problem here is twofold.  First, if there is a rotten apple among the referees, he is going to have undue influence.   The second is that there is no good reason to have such a tiny number of referees and combine this with the ultra secrecy of PGMO.   We are constantly left asking the question: why run the show in a way that can raise these questions, when you could run refereeing in a way that would work hard to ensure that refereeing was harder to manipulate.