## The variance of goals scored and conceded in a Premiership season

Following the methodology set out in this post which, once more, is taken from the comments to this post on Phil Birnbaum’s wonderful site, I’m going to look at the variance of goals in the Premiership.

So first, the sample – each of the 4,940 games played in the last 13 Premiership seasons. In essence there were 9,880 ‘team’ matches (as each match has two teams), in which a total of 13,044 goals were scored, or 1.32, per team, per match. Below is the frequency of the number of goals scored split by home and away teams, and the total.

So, the average team season would look as follows in terms of goals scored (and conceded) per game:

Now that the average number of goals scored, and the frequency of each, is known, the standard deviation of the number of goals scored per season can be calculated, and it comes to 1.53 goals. The variance is then calculated by multiplying the standard deviation by the number of games played in a season (38), and taking the square root of that number.

In all, the variance of goals in a Premiership season is 7.63 goals. A model predicting next seasons goals should be aiming to get as close to that figure as possible.

Finally, as mentioned at the end of the my prior post on the variance of points, home advantage is likely to drag this number down a little, but I think it’s a pretty good ballpark figure to work with for now.