Recently I explained the basics of regression to the mean and why I’m going to apply it to football. I want to briefly expand on it by explaining how it’s size is determined for a particular parameter.
It’s pretty simple to calculate and I’ll use the example of team points in consecutive years. The first step is to plot the points a team scores in the first year (on the x-axis) against the points the team scores in the following year (on the y-axis)
The R2 value here is 0.609 which is ok but not great. The % regression to the mean is calculated as follows
% regression to the mean = 100% x (1 – R) = 1 – (0.608)1/2 = 100 x (1 – 0.779) = 22.1%
Essentially this means that the number of points a team scores above or below the mean (of 52.1) is ~80% skill and ~20% luck.