Wednesday, April 14, 2010

Pythagorean exponents over time

So, over at Football Outsiders, we've been using 2.37 as the proper exponent when calculating a team's Pythagorean record. That number was in one of FO's first articles, and I was wondering (a) whether or not that exponent, which was calculated by a then-obscure STATS, LLC employee by the name of Daryl Morey, was still valid, and (b) whether that exponent was valid for past years, particularly in the lower-scoring era before the 1978 passing rules liberalization.

To that end, I went ahead and calculated the proper exponent for every year since the merger. The methodology for this was pretty simple: I took every NFL team's points scored and points allowed, put them in a spreadsheet, and used Excel's Solver function to calculate the proper exponent as determined using the least squares method. This is not a particularly sophisticated way of doing the calculation, as it doesn't take into account consistency, and other, more complicated techniques are likely to produce better results. But, I thought the results were fairly interesting, so here they are:



YearExponentPPG
19702.28019.26
19711.88519.36
19722.31220.25
19732.13119.45
19742.24918.18
19752.63720.59
19762.20519.15
19772.25117.18
19782.43718.33
19792.87520.06
19802.60320.49
19812.21520.67
19822.60720.16
19832.60921.81
19842.67921.21
19852.69021.40
19862.88820.52
19872.56721.60
19882.74020.30
19892.17820.61
19902.52020.12
19912.54718.98
19922.41718.73
19931.96818.70
19942.61720.26
19952.32121.49
19962.56620.43
19972.79820.74
19982.59621.70
19992.37020.89
20002.14020.67
20012.69620.21
20022.42321.67
20032.68120.83
20042.78121.48
20052.80420.62
20062.40120.70
20072.50821.69
20082.62022.03
20092.19621.47

There you go. For grins, I added another column, that of points per game, to see if the exponent really was different in the pre-1978 era. The evidence does suggest that points per game and the proper exponent were both lower in the post-merger, pre-1978 era, but that it wasn't a particularly strong correlation. See, for instance, 1970 and 1971 with virtually identical points per game totals and greatly differing exponents. See also 1991-1993, again with similar PPG totals and differing exponents, both greater and lower than the 5-year running average.

Keep in mind, though, that this was done in a particularly simple way. A more sophisticated, smarter analysis, taking into account all the intelligent factors people have done in baseball would almost certainly result in a different number. My understanding, moreover, is that somebody who's able and capable of doing that work (i.e., someone other than me) is actually doing it, but I thought I'd slap this up on here all the same.

2 comments:

joe football said...

Fascinating

Your wikipedia link is broken

Tom said...

Oops, thanks.