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:

Year Exponent PPG
1999 5.096 47.93
2000 5.274 49.52
2001 4.023 50.30
2002 6.782 49.48
2003 4.992 50.19
2004 4.796 49.21
2005 5.554 51.12
2006 4.930 50.93
2007 6.858 54.14
2008 6.555 54.83
2010 6.783 55.65
2011 5.191 53.43

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.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s