PEG (formerly xxG) Part 2

As always I should start with the credits. After I introduced this metric, I asked for better name suggestions than ‘expected expected goals’ and got many great suggestions, so thank you all. In the end I plumped for PEG (projected expected goals) and the credit to that one should go to Tom Worville (@Worville). Secondly, thanks for the comments and questions – they help to clarify my thinking and hopefully improve the metric. Finally, once again, thank you to Michael Caley (@MC_of_A) for publishing his expected goals numbers publicly and without whom this metric would not exist.

One of the problems that I had when publishing these figures is that because I only had match by match xG totals for the 15/16 season, I had to start each team at 0. This meant that we couldn’t do lots of cool stuff like looking at how the PEG rating of a team changed over the course of last season. We couldn’t investigate the impact of new managers using this metric. It meant we had to wait until next year. No longer! It’s a little bit of a fudge but I stumbled upon the expected goal totals for the 14/15 season (again, thanks to Caley!). This means we can use the average expected goal difference as the starting value for PEG, and investigate some interesting stories, like this one about Swansea (maybe sacking Garry Monk was a mistake, not that I’m complaining as a Leeds fan):

Secondly, we need to discuss the k-value (sensitivity) of PEG, in the graph above I’ve used k=0.075. Here, I’m trying to choose the lowest value that lets the end of season PEG to be relatively immune to the start of season PEG. This is because I’m unconvinced that information from more than a season ago is going to tell you much about future performance. So I tried three different sets of starting values – zero for all teams, the 14/15 average expected goals and the 15/16 expected goals. The lowest value where the end of season values converge to a large degree is k=0.075. This is the table showing final ratings and their sensitivity to starting values with k=0.075:

Finally, I want to answer a quick question about the predictive power of this metric. Firstly, we can look at the correlation between the pre-match PEG and both the actual goal difference and match expected goal difference:

To be honest, I’m not really sure how to interpret those R² values, but at least the direction is how we would expect. I think it is probably more illustrative to look at the number of games predicted correctly, and how well we did compared to odds. I took a PEG prediction as follows: anything greater than 0.25 was win for that team, the rest were considered draws. The number 0.25 comes from looking at the average number of draws from 05/06 to 14/15 (95) and choosing the PEG value that gives ~the expected number of draws. It predicted 178/380 results correctly, and would have made a £175 profit (on best odds, drops to £165 if I just use Bet365) by staking £1 on each game (46% ROI!). Caution abound since we only have one season of data, and that is not enough to draw conclusions, but I’ll be keeping track of this over the coming season.

Correction: I put the formula in wrong, it actual comes out about evens (£3.48 loss) against betting odds. With some k-values it makes a profit, mini-post coming later on optimising k. Dang, I knew it was too good to be true.

Where it comes to predicting the expected goals result, it does slightly better, as you would expect. I coded anything with a 0.3xG gap or smaller as a draw, and anything else as a win/loss and here PEG predicted 215/380 results correct. Not bad! I can’t tell you anything about it’s predictive power on a seasonal level, but we will know a little more in 12 months time.

So that’s part 2. If you keep an eye on my Twitter then I will be posting the stories of last season according to PEG. Until next time!