Cheaty Divers

Based on last weekend's match between Liverpool and Man City, one would have to say that Luis Suarez's reputation for diving is well deserved. He appears to hit the ground in response to any attempted tackle by opponents, successful or not. At one point, during this match, he actually went studs up into the defender (Vincent Kompany) and then fell on the ground as if he had been fouled!

The individual efforts of Suarez probably explain much of the difference in fouls received in the match (11 v 15). However, there were other notable refereeing decisions that went Liverpools way. In particular, goalkeeper Reina not receiving a card for deliberately handling outside his penalty box and Mario Balotelli's second yellow card. A few in the media have agreed with the latter decision; however, on average, those in the media have suggested it was harsh. All together, there were plenty of reasons for Man City fans to feel aggrieved.

That said, it seems unlikely that any of this, aside from Reina receiving a card, would have changed the outcome of the match. However, deliberate attempts to draw cards either by diving (Suarez) or surrounding the referee (the rest of the Liverpool squad) is not what any fan wants to see. As Roberto Mancini said after the match, "this is not football."

I was left wondering whether this was a one-off for Liverpool or rather a general strategy. In other words, is diving and surrounding the referee now part of the Liverpool way?

To try to understand this, I analyzed fouls in matches using the same technique as I would model goals. Each team gets an "attack" score, which measures how much they foul, and a "defense" score, which measures how much they draw fouls for the other team.*

What do the statistics tell us then?

Broadly, they show that most teams foul at about the same rate. There are a few teams that foul less than usual: Swansea, Norwich, and Man United. Swansea, in particular, foul very little, while the other two foul only a tiny bit less than usual. At the other end, Blackburn and Wigan foul a bit more than usual.

That describes how much each team fouls. The more interesting part is how much each team draws fouls from their opponent.

First off, the statistics do not show that Liverpool are cheaty divers. While they may have displayed some unsporting behavior in this match versus Man City, the model does not suggest they draw fouls any more than other teams in general.

However, some teams do appear to draw fouls. Chelsea, Wolves, and Newcastle draw a few. But the leader in this department, by a huge margin, are Queen's Park Rangers. The amount of fouls they draw is about the same as the difference in fouls between Swansea and an average team, which is quite big. In other words, when Swansea plays against QPR, we would expect them to receive as many fouls as an average team. An average team, on the other hand, should receive quite a few more fouls than usual when playing against QPR.

There is one more possibility afforded by the model, which we have not yet discussed. It's possible for a team not to draw fouls from their opponent but somehow to suppress them. In other words, are there teams whose opponents systematically receive fewer fouls than they should?

It turns out this does indeed happen to one team: Man City. Somehow, when teams play Man City, either they choose not to foul as much as usual or the referee chooses not to call them as often as usual. Furthermore, the effect is not small. It's the third largest effect in the model after Swansea's not fouling and QPR's drawing fouls.

So are teams especially timid when playing against Man City or are the referees biased against them? I'll leave that to you to decide.

(*) As usual, I "regularized" my model, which means I only allowed new variables if the improvement in fit outweighs the extra complexity they add to the model. I.e., Occam's razor was applied.

4-4-2 versus 4-2-3-1

We have previously discussed on the fact that no top team plays a traditional 4-4-2 today and that the current version of the 4-4-2 played by, say Manchester United, is not especially different from a 4-2-3-1. Zonal Marking, in his review of Napoli v Man City, strikes the same note:

Of course, when you play with two attack-minded wide players plus one striker dropping off into the hole, 4-4-2 and 4-2-3-1 are, if not interchangeable, not significantly different.

Beware of Hindsight Bias

The book "Future Babble", which I'm just finishing at the moment, mentions a new type of cognitive bias that I had not heard of before: hindsight bias. This can be seen, for example, when fans say after a match that the outcome was inevitable, say, as a result of the tactics used by the manager or his player choices.

The bias is not simply that people become more convinced after-the-fact that this outcome was always going to occur. People actually become more convinced that they knew beforehand that this was going to happen. Numerous experiments, comparing people's memories of their certainty with recordings made before the event, have shown this effect to be quite strong.

Further experiments showed that typical post-match analysis actually makes this bias worse. Two psychologists from Northwestern University studied fans at American college football matches and asked some of them to analyze the match in certain ways. (Their paper is called "Perceptions of Purple: Counterfactual and Hindsight Judgments at Northwestern Wildcats Football Games" in case you want to look it up.)

Before the match, fans gave what would be the actual outcome of the match a less than 15% chance of occurring. After the match, fans recalled their own predictions were of a 30% chance of occuring. Amazingly, fans who were asked to analyze the match — in terms of what could have been done differently or what caused the result — recalled their own predictions were higher than 50%!

Clearly, most fans who think about football as much as we do are doing exactly the sort of analysis performed in the experiment. Hence, we are quite likely to fall victim to hindsight bias.

In my mind, this highlights once again the importance of looking at football statistics. Of course, statistics can't eliminate hindsight bias, but they can do two things.

First, they can suggest that some inevitability arguments are implausible. For example, a claim that the team lost because one player started in place of another would seem suspect if statistics show the one who played created just as many chances, had just as many successful tackles, etc. as would have been predicted for the other player.

Second, and perhaps more importantly, statistics can remind you that football involves a lot more chance than most people are willing to admit.