Pythagorean exponents in the 2008-09 English Premier League
Categories: Goalscoring Models, Soccer Pythagorean: Theory, Team Performance
A couple of nights ago I presented goal distributions for all twenty teams in the 2008-09 English Premier League season, in an attempt to calculate the exponent that would be used for my expansion of the Pythagorean. I realized after my calculation that I needed to consider the sum of the squares of both the error from the goals scored data and the goals allowed data, instead of separately like I had done before. Fortunately that correction was easy to fix, so now I'd like to present the alpha and gamma terms for all 20 teams in last year's Premiership:
Club |
Alpha_GF | Alpha_GA | Exponent |
---|---|---|---|
Arsenal | 2.7560 | 1.5805 | 1.5030 |
Aston Villa |
2.2955 | 2.1485 | 1.4849 |
Blackburn | 2.0192 | 2.6941 | 1.4604 |
Bolton |
2.0961 | 2.3750 | 1.3561 |
Chelsea |
2.6428 | 1.2474 | 1.4092 |
Everton |
2.3008 | 1.6886 | 1.4051 |
Fulham |
1.9156 | 1.7100 | 1.3650 |
Hull City |
1.9233 | 2.3686 | 1.8368 |
Liverpool |
2.9020 | 1.3778 | 1.4974 |
Manchester City |
2.4678 | 2.2673 | 1.6112 |
Manchester United |
2.4407 | 1.1003 | 1.6722 |
Middlesborough |
1.6117 | 1.9444 | 1.6419 |
Newcastle United |
1.9951 | 2.4601 | 1.8405 |
Portsmouth |
1.9960 | 2.3075 | 1.4803 |
Stoke City |
1.8209 | 2.3877 | 1.5949 |
Sunderland |
1.7685 | 2.2380 | 1.5820 |
Tottenham |
1.9768 | 1.9093 | 1.6944 |
West Brom |
1.8442 | 2.9093 | 1.3816 |
West Ham |
2.0579 | 2.0006 | 1.5762 |
Wigan |
1.7025 | 1.9550 | 1.3951 |
The mean of the exponent is 1.5394 (median 1.5002), with a standard deviation of 0.1457. The numbers that I've seen on the web for the exponent term are right in the 1-sigma range of this estimate. It was also close to my guess of 1.5, which was more of a gut instinct than anything else.
I suppose that if I want to make a stronger claim that this curve-fit is the right one, I would perform a chi-square goodness-of-fit test, but I'll leave that for later or as an exercise for someone more enterprising.
My solution approach is described in this document. I implemented it using a script in Scilab. If you'd like a copy of the script I can send it to you, but you will have to download Scilab.