Reading and Thinking Football

Football, including books thereon and idiosyncratic thinking thereabout

Pythagorean exponents over time

with 2 comments

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:

table.tableizer-table {border: 1px solid #CCC; font-family: Arial, Helvetica, sans-serif; font-size: 12px;} .tableizer-table td {padding: 4px; margin: 3px; border: 1px solid #ccc;}.tableizer-table th {background-color: #104E8B; color: #FFF; font-weight: bold;}

Year Exponent PPG
1970 2.280 19.26
1971 1.885 19.36
1972 2.312 20.25
1973 2.131 19.45
1974 2.249 18.18
1975 2.637 20.59
1976 2.205 19.15
1977 2.251 17.18
1978 2.437 18.33
1979 2.875 20.06
1980 2.603 20.49
1981 2.215 20.67
1982 2.607 20.16
1983 2.609 21.81
1984 2.679 21.21
1985 2.690 21.40
1986 2.888 20.52
1987 2.567 21.60
1988 2.740 20.30
1989 2.178 20.61
1990 2.520 20.12
1991 2.547 18.98
1992 2.417 18.73
1993 1.968 18.70
1994 2.617 20.26
1995 2.321 21.49
1996 2.566 20.43
1997 2.798 20.74
1998 2.596 21.70
1999 2.370 20.89
2000 2.140 20.67
2001 2.696 20.21
2002 2.423 21.67
2003 2.681 20.83
2004 2.781 21.48
2005 2.804 20.62
2006 2.401 20.70
2007 2.508 21.69
2008 2.620 22.03
2009 2.196 21.47

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.

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Written by Tom Gower

April 15, 2010 at 04:04

Posted in General NFL

2 Responses

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  1. Fascinating

    Your wikipedia link is broken

    joe football

    April 16, 2010 at 01:37

  2. Oops, thanks.

    Tom

    April 16, 2010 at 02:17


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