Where did that  Pythagorean exponent of 2.37 really come from?

Football Outsiders has published their latest annual. You can get it in PDF form, and whatever gripes I have about the particulars of their methods, I’d also say just buy it and enjoy the writing.  I read something in the latest annual worth mentioning, that the Pythagorean exponent of 2.37 that Pro Football Reference attributes to a blogger named Matt on a blog named Statistically Speaking (via a link that no longer exists) is actually a result from Houston Rockets GM and former STATS inc employee Daryl Morey.

Not only does FO mention it in the 2011 annual, but Aaron Schatz mentions it in a pair of 2005 interviews (here and here) with Baseball Prospectus. The result is mentioned also in a 2005 New York Times article, and then in a 2003 article on the FO site itself, where he gives the link to Daryl Morey’s web site (the link no longer works). Chasing down the url http://morey.org leads to the MIT Sloan Analytics site (morey.org is now a redirect). If “morey.org” is used as a search term, then the search gives you a link to an article on the Harvard Business Review site by Daryl Morey, an important one.

The 2003 article, by  the way, makes it clear that the Pythagorean formula of Daryl Morey dates to 1990 and is thus 21 years old. In the Pro Football Reference article, a Stuart Chase (whose link in his name points back to the Football Guys site) says that the average Pythagorean exponent from 1990 to 2007 is 2.535, and I’ve posted results that show no, it sure isn’t 2.37 over the last decade. If one were to average my exponents, calculated annually, from 2001 to 2010, they would be much closer to 2.5 as well.

Also, note, my code is now part of the Perl CPAN library. You don’t need to believe me, get the data and do the calculation yourself.

In short, the use of 2.37 is an old, outdated 21 year old  trope.

I tend to like Pythagorean expectations because of all the scoring stats I’ve tested for predicting NFL playoff wins, this one comes closest to being reliable (p = 0.17, where p=0.05 or less desired).

Bashing on DVOA

I’ve posted a complaint previously about proprietary formulas, some issues being that they aren’t verifiable, and further, they aren’t falsifiable.  Some more gripes: back in the 2005 interviews on Baseball Reference, Aaron Schatz says that the average around which DVOA is based was based on a single season. In the 2011 annual, it’s made clear that the average on which DVOA is based is over more than one year. In other words, DVOA isn’t a single well defined commodity at all, the definition is changing over time. Of course, we only have FO’s word for  it, as (once again) the formula is proprietary (For all its faults, the NFL QBR is well understood, verifiable and falsifiable).

It’s the data, stupid.

This is where Daryl Morey comes in. The argument in his recent article is that analysts are becoming more common, their skills are high, the formulas and methods aren’t where the action is at. Who cares? The important element are the data sets themselves.

With the Moneyball movie set to open next month, the world will once again be gaga over the power of smart analytics to drive success. While you are watching the movie, however, think about the fact that the high revenue teams, such as the Red Sox, went out and hired smart analysts and quickly eroded any advantage the Oakland A’s had. If there had been a proprietary data set that Oakland could have built to better value players than the competition, their edge may have been sustainable.

If  data trumps formulas, why all these proprietary formulas? What’s the point?

These kinds of notions are one reason I’ve come to like Brian Burke and Advanced Football Stats more and more. He tends to give out small but useful data sets. He tends to strip the mystery off various proprietary formula bases. He tends to tell you how he does things. He’s willing to debunk nonsense.

I’m sure there are some cards hidden in Brian’s deck, but far less than the other guys. I’m really of the opinion that formulas are meant to be verified and falsified. Data sets? Gather those, sell those, work was involved in collecting and creating  them. Analysis based on  those data sets? Sell that too. Formulas? Write in Python or Perl or Ruby, write in the standard required by the common language library (either PyPI or CPAN or RubyForge) and upload your code for all to use. Since the code then gets put through a stock test harness, the reliability of  the code also becomes more transparent.

We’ll start on a small, pretty blog called “Sabermetrics Research” and this article, which encapsulates nicely what’s happening. Back when sabermetrics was a “gosh, wow!” phenomenon and mostly the kind of thing that drove aficionados to their campus computing facility, the phrase “sabermetrics” was okay. Now that this kind of analysis is going in-house (a group of  speakers (including Mark Cuban) are quoted here as saying that perhaps 2/3 of all basketball teams now have a team of analysts), it’s being called “analytics”. QM types, and  even the older analysts, need a more dignified word to describe what they do.

The tools are different. There is the phrase logistic regression all over the place (such as here and here). I’ve been trying to rebuild a toolset quickly. I can code stuff in from “Numerical Recipes” as needed, and if I need a heavyweight algorithm, I recall that NL2SOL (John Dennis was a Rice prof, I’ve met him) is available as part of the R language. Hrm. Evidently, NL2SOL is also available here. PDL, as a place to start, has been fantastic. It has hooks to tons of things, as well as their built-ins.

Logistics regression isn’t a part of PDL but it is a part of PDL::Stats, a freely available add on package, available through CPAN. So once I’ve gnawed on the techniques enough, I’d like to try and see if Benjamin Morris’s result, combining winning percentage and average point spread (which, omg, is now called MOV, for margin of victory) and showing that the combination is a better predictor of winning than either in basketball, carries over to football.

I suspect, given that Brian Burke would do a logistic regression as soon as tie his shoes, that it’s been done.

To show what PDL::Stats can do, I’ve implemented Brian Burke’s “Homemade Sagarin” rankings into a bit of code I published previously. The result? This simple technique had Green Bay ranked #1 at the end of the 2010 season.

There are some issues with this technique. I’ll be talking about that in another article.