## How many Premiership goals should we have expected this weekend?

It’s been established by Mark Taylor (via simulations) and Simon Gleave (using a dataset stretching back 45 years) that the 74 and 78 goals scored through the first 39 and 40 Premiership games of the 2013-14 season, respectively, was low to the point of statistical significance. Generally I find the reasons given for this to be speculative and wishy-washy, as we simply don’t have numbers to back up the vast majority of explanations. However, Colin Trainor has put forward some evidence that the drop could be explained in part due to a drop in the number of shots being attempted, as well as the less favourable locations of those that are being taken.

I want to take a different slant on this, and look at whether statistically low goalscoring in the past is predictive of low goalscoring in the future. The sample I’m using is the 4940 Premiership games played between the 2000-01 and 2012-13 seasons (inclusive). To determine the predictive power of past goal scoring on future goal scoring I’ve split the data into 4891 spans, each of which comprises of 50 successive Premiership games (game numbers 1-50 being span 1, game numbers 2-51 being span 2, etc.). Each 50 game span is then split further, with the first 40 games henceforth known as the ‘preceding 40 games’ (i.e., the first 40 games played in the 50 game span) and the final ten games being named the ‘succeeding 10 games’ (i.e., the final ten games played during the 50 game span).

In the sample of 4891 ‘preceding 40 game’ spans, there are 68 which feature 78 or fewer goals. This equates to 1.39%, or roughly double the rate predicted by Taylor, and found by Gleave, however 78 goals is still 2.3 standard deviations below the 40 game mean of 105.5 goals. In other words we’re still looking at something that is statistically significant.

The plot below is kinda noisy, but it’s basically the number of goals in each 40 game span on the x-axis, with the corresponding number of goals scored in the succeeding ten games on the y-axis.

There’s two things to take away here. Firstly the correlation isn’t great, and secondly the line of best fit is very shallow. In other words the number of goals scored over a 40 game span is a pretty bad predictor of the number of goals that will be scored in the following ten games.

So lets take the 78 goals scored through the first 40 games (for reference that’s 19.5 goals per 10 games) and plug that into the equation to see what our best guess would have been as to the number of goals scored in the ten games last weekend. The line of best fit returns a predicted total of 25.1 goals. For comparison the average number of goals scored per ten games in the sample studied here is 26.35 – so we’d have predicted goal scoring to return almost to a historical average level, despite the fact that it’s been low to a statistically significant level in the prior 40 games.

One final note. I ran basically the same study, but with spans of 80 games, and compared goals in ‘preceding 40 games’ to goals in ‘succeeding 40 games’. Based on seeing 78 goals in games 1-40 of this Premiership season we’d expect to see 102 goals being scored in games 41-80, whilst the average for a 40 game span is 105 goals.

In summary, there isn’t a hell of a lot of predictive power in a small span of historical goals when trying to predict future goalscoring.