PEG – Optimising K

In part 2 of PEG I wrote briefly about choosing a k value. I chose it pretty much on a hunch, that some level of stability is good, so that the metric isn’t just blowing with the wind. Alongside that, I wanted to pick the k that made end of season values roughly immune to the starting point, on the hunch that performances from over a season ago wouldn’t tell us much about future performance. Ben Torvaney (@Torvaney) had the great suggestion that I should test different k values and choose the one with the best predictive power, and I did. So here’s a quick mini-post run down.

So, I looked at three metrics: the number of correct results predicted, the mean average error in predicted goal difference and the betting profit/loss over the course of the season. I looked at these both with actual results and the expected goals ‘results’. The curious thing is that it really depends on whether you want to optimise to predict future results, or future expected goals. Let’s have a look:

Looking at those three together, it seems that for predicting future results the optimal k is somewhere from 0.09-0.14, whilst for predicting future expected goals the optimal k is 0.05-0.1. Taking those together, a sensible compromise seems somewhere in the region of to be k=0.09.