The original purpose behind the Soccer Pythagorean was to determine, in mid-season, whether a team was performing above or below its (statistical) expectations. I've already done some work on developing Pythagorean exponents for various European leagues, and if you've read my paper in the previous post, you would find out that the exponents of the various leagues are surprisingly close to each other. There needs to be more work to determine whether this exponent is some kind of universal constant, but it makes calculations a lot easier.
Let's look at the usefulness of the metric by collecting some data. I collected some mid-season tables for a number of European football leagues and applied the Soccer Pythagorean formula to determine the expected points and table placement. The English Premier League always gets a lot of attention, so I decided to start there. At this point of the season (shortly after New Year's Day I think), all clubs had played between 18-20 matches. The first two numerical columns are the goals scored and allowed, followed by columns for actual points, projected points, and difference in league placing. I think the position difference is a better indicator of under/overperformance than difference in projected points (the current version of the Soccer Pythagorean overpredicts league points).
I used a league Pythagorean exponent of 1.70. The table is after the jump.
||+/- League Standing
|West Ham United
So if you believe the veracity of the Soccer Pythagorean and the predictive quality of the goals scored/allowed statistics, it is possible to see which teams have underperformed and overperformed relative to expectations. The sides at the very top are performing exactly as you would expect teams of their goal-scoring records to perform. That is definitely true of Chelsea, Manchester United, and to a lesser extent Arsenal, although at this point in the season Tottenham appear to have trailed off a bit. The rest of the top ten sees teams that are marginally better or worse than expectations, with the exception of Manchester City. I do find it interesting that Liverpool and Birmingham City, despite what the pundits and fans believe, were not having seasons at wide variance with their statistical expectations.
The bottom ten consists of teams that are either performing much better than expectations or much worse. The three promoted sides, at the halfway mark, are all having extremely good seasons, and some teams that might have been expected to fight against relegation are comfortably away from the relegation zone. (In light of Burnley's recent swoon, it could be argued that Burnley had overachieved and were due for a fall.) The three worst performing sides relative to their statistical expectations are all in or near the relegation zone: West Ham, Bolton, and Portsmouth. The only side in the bottom four actually performing in line with expectations has been Hull City. And that's about right, as most critics felt that they were in for a season-long fight against relegation.
In the coming days, I'll present tables on the German, French, and Turkish leagues and discuss them.