The Pythagorean record and the Gaussian Copula-Function: or, How I learned to stop worrying and love...the O's
I don't post, basically ever. But I feel compelled to comment on a common debate around here. What does the Pythagorean record mean to the 2012 Orioles?
I work with numbers. I would not say that I am good at statistics or math in general. I am not mathematically illiterate, but I am no PhD either. I may be completely wrong with this little spiel, and if I am, please tell me why so I may understand. But here it goes:
1. The Pythagorean expectation for a baseball team is the best easily accessible metric that baseball fans have available to them that allows them to accurately predict the future performance of a club most of the time. The Pythagorean expectation relies on a Weibull distribution for its mathematical derivation. This means that the 'proof' famously published by Professor Miller in 2006 makes the following assumption 'runs scored and runs allowed per game are statistically independent,' (stolen gladly from Wikipedia)
2. A common criticism of the record is that sometimes teams have 'pluck' or a 'great manager' who allows you to beat the statistical averages, thus the Pythagorean expectation is merely the hand-waving of nerds who don't understand 'real' baseball. I think this is a poor explanation. I'm a massive nerd who has loved baseball on the field, in the stands, and from my sofa since I was a young boy. I think that I understand real baseball. Don't dismiss the nerds.
3. However, the reverse applies as well: the hubris of mathematical 'proofs' is well documented. A rather apt comparison relates to the subprime mortgage crisis and what is commonly known as the Gaussian copula function. I'm not getting political here, so please read carefully. When the financiers were building the complicated mathematical equations and algorithms that allowed them to bundle up mortgages, repackage them and sell them later, one of the justifications that they used was based on a model built by a young man far removed from the buying and selling of homes. The 'Gaussian copula' was not a model or an equation that allowed one to predict the future, it was merely a good way to describe a relationship between disparate assets, like a bunch of houses in some part of the world. This was not the problem. The problem came when the limitations of the function were ignored by people who were so eager to believe the results that it seemed to spit out that they did not bother to learn what the function actually did. Many individuals took what they thought to be a concrete theory, and used it to create a value narrative that ended up being dramatically wrong. Some of these individuals probably did it out of pure greed, but I would posit that most thought they were just much cleverer than those old fashioned folks who did not use the fancy formula. But they were ignoring one of the great pieces of wisdom from the older generation: understanding half of something can be far worse than having the wisdom to admit that you do not understand it at all.
4. This brings me to my conclusion. The Orioles are outperforming their Pythagorean record by a significant margin. Luck is a factor. That is to be celebrated, not bemoaned. But, is there something more? Is the Weibull distribution a fair representation of how the game is played out? Could it be that Buck?s bullpen management means that scoring and allowing runs are more related than one would initially think? If certain poorer pitchers are only used in certain situations, then the mathematical foundations of the proof are themselves flawed. I'm not sure. But if I have time I'm going to find out.
Ultimately, there are so many smart passionate people writing about the Orioles as fans of the team and baseball alike. I hope that:
a. We recognize that the Pythagorean record of a team is fundamentally important
b. It has its limitations
c. Using it as a tool to close off debate and hiding behind the handwaving of math is boring. Break out the figures, learn some statistics, and let's figure out how to enjoy the game even more.
Pythagoras, the man, is a bit of an apocryphal character in history. He is variously a mathematician, a religious leader, and a fictional combination of a few disparate characters. The mythology tells us that the Pythagorean neophytes were the akousmatikoi ("listeners"). This is absolutely essential; we need to listen to one another. But that is not enough. Just because some guy on SI told me that the Orioles were doomed to failure does not mean that I have to believe him. We should all aspire to be like the Pythagorean inner circle, the mathematikoi ("learners"). Listening without questioning does not get us anywhere. I have been out of the country for a very long time, but I get back in just a few weeks. I hope with all of my soul that I will witness my first meaningful Orioles game in fifteen years
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