Friday, April 06, 2012

Arena Football Pythagorean Exponents

A couple years ago, I went through and calculated the Pythagorean exponent for the NFL over various years. I promised a week ago that if I won the Mega Millions lottery jackpot, I'd spend time developing advanced statistics for Arena Football. Alas, I didn't win the lottery, but I did spend a little bit of time tonight working on calculating the ideal Pythagorean exponent for Arena Football anyway, at least for the past dozen seasons.

The methodology for this was pretty simple: I took every AFL 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. The findings:


YearExponentPPG
19995.09647.93
20005.27449.52
20014.02350.30
20026.78249.48
20034.99250.19
20044.79649.21
20055.55451.12
20064.93050.93
20076.85854.14
20086.55554.83
20106.78355.65
20115.19153.43

As I did for the NFL chart, I added points per game, to see if there was any trend that more scoring meant a higher exponent. As you can see, there is no apparent strong pattern that that is indeed the case. Arena Football has also expanded the season length from 14 to 16 and then to 18 games over the course of this sample; no great pattern is apparent there either. Ditto the number of teams, which has also varied.

In addition to the exponent for each year, I also figured out the average exponent (based on each year), and came up with 5.400. If you want to use a Pythagorean exponent over time, then I suggest that be the one you use.

When Aaron wrote the first FO article discussing the use of Pythagorean exponents in football back in 2003, one of the things he used it for was to predict how teams would do the next season. I have not yet done that for Arena Football; I suspect it tends to be a lot less consistent than the NFL. Looking solely at the 2011 standings, based on Pythagorean standings, I would expect Milwaukee and Philadelphia to improve, while Pittsburgh and Tampa Bay get worse.

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