The Premier League PINC season has been a goal fest so far. After Aston Villa hammered Champions Liverpool 7-2, and Spurs won 6-1 at Man United, many were wondering what was going on – was it to do with there being no crowds?
It wasn’t clear that it was, since the same pattern wasn’t happening elsewhere. It could have been that players thought to be very good, such as Harry Maguire, Man United’s £80m signing from Leicester, pictured above, may not be quite so good.
Since then, however, we’ve seen the most boring thing in all of statistics occur: mean reversion.
The first game week this season, in early September, saw on average 2.9 goals per game. Very close to the historical average goals per game since the very beginning of English football (2.97). The second gameweek there were 4.4 goals per game, followed by 3.6, followed by 4.1 in that famous week at the start of October.
It was going to be an extraordinary season, with loads of goals, breaking all sorts of records – for example, the number of hattricks scored.
One of the most basic, if boring, concepts in all of statistics is reversion to the mean. Data have a tendency to move back towards the average, given time. In other words, there’s nothing new under the sun.
Teams work each other out. In particular, the teams shipping goals work on their defences.
True enough, on the weekend of October 17, after the International Break (hence that bit more time for teams to sort out said defences), there was just 2.8 goals per game. And this last week, a mere 1.9. This is shown below. Each game week is a circle, and they are linked by a black line. The red line is the mean over all time (since 1888), the green line is the mean since 1970:
So, we had a few game weeks above average, and then we’ve settled right back down.
More broadly, here’s the pattern throughout history of game week goals:
So, a few unusual game weeks recently, but no great departure from trend. Alas, there appears to indeed be nothing new under the sun. But that said, the beauty of football is its ability to surprise…
Source: Forbes – Business