Graphic: hot shots

It’s one of my favourite facts. After watching Jaws, holidaymakers became significantly less likely to swim in the sea. They massively overestimated their chance of being killed by a man-eating shark.

The reason for this is something called availability bias. Dramatic events stick in the mind and we overestimate the chances that they will happen again.

So when Arsenal lost to Hull City and Stoke City, what were we witnessing? A real tendency for poor teams to lift their game when playing good ones? Or a couple of games that may tell you a little about Arsenal’s weaknesses, but are essentially just the sort of thing we tend to see in football?

The Fink Tank is on the case. The basic model developed by Dr Henry Stott and Dr Ian Graham allows us to establish the probability of different outcomes in different games.

We take past results and weight them so that the most recent counts most heavily.

When we started we just used goals as a measure of the quality of teams. Then we established that shots on target mattered, too. Putting it very crudely - if two equal teams played each other on a neutral ground and the game ended in a draw, we would regard the team that had a better record with shots on target as the favourite if the teams were to replay their game immediately.

Why? Because there are more shots than goals. Therefore they provide more data, eliminating some of the luck involved in whether the ball actually goes in the net.

When we started using shots on target, it significantly improved our predictions. The shots data can help with simple analysis – the graphic, for instance, shows which teams are more on the front foot in games. From the shots on target made by each team, we subtracted the shots on target that they allow on their own goal.

But Dr Mark Latham has done something altogether more sophisticated. He has used the shots data over the past three seasons to establish whether underdogs lift their game when playing the big teams and whether the big teams, thinking that they have secured victory against a minnow, take their foot off the gas towards the end of a match.

The first step is to establish the number of shots on target that you would expect a team to make and to concede in particular games. This can be done by running our computer model on match outcomes. Then this data is compared to the actual match outcomes.

What we were looking for was a pattern. Was there a systematic difference between our expectations and reality? And if there was, did it vary by the type of match being played? If it is true that poor teams up their game against big ones, we would expect to see the difference between expectations and reality at its greatest when those big teams were playing them and we would think the poor teams would shoot on target more. If we did not find that, we would know that the whole idea was another footballing myth.

So what did we find? The Fink Tank analysed with each team whether the gap between expectation and reality changed depending on the difficulty of the game. We found only a handful of statistically significant results and they were in varying directions.

In a nutshell, the idea that underdogs up their games against the big teams is a myth. And so is the idea that big teams drop their standards after thinking that they have secured victory against small teams.

Another two bite the dust.