A few days ago I presented Pythagorean projections for this year's English Premiership, based on the formula that I developed. I didn't like the fact that the projection overestimated league points, but felt that perhaps the estimated league position might be useful.
Over the weekend, I took a much closer look at the derivation of the Pythagorean formula and made some necessary corrections to it. I am very pleased to say that the new version is a huge improvement on the original. I am not pleased to say that the resulting formula is extremely complicated and not as simple as the baseball Pythagorean, but that is the price to be paid for three possible outcomes to a match. I'll give more details in a separate post.
After the jump I present the mid-season tables for this year's Premier League with Pythagorean estimated points. I used a league Pythagorean exponent of 1.70.
||+/- Point Diff
|West Ham United
As you can see, the point spread between the Soccer Pythagorean and reality is down to a mere +/- 5 points. A difference of one to two wins, or a win and a draw or two, essentially. This is a much better metric, and as commenters have said, it's more useful to say something about points than league placement.
The teams with the large point spreads attract the most attention — on New Year's Day, Birmingham City and Wolverhampton Wanderers have outperformed relative to their statistical expectations, while West Ham and Portsmouth have underperformed significantly.