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HHP: Pythagorean record and the Gaussian Copula-Function: How I learned to stop worrying and love


cityknight

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I have a date w/ a Red Sox fan this weekend. Though, to be fair, she disdains Red Sox nation and the class-ascent of the Sox over the last few years. On the flip side, she didn't realize that O's fans loathe the Sox. It felt like Duke chanting "Not our rivals" at me all over again. ;)

I get it. I truly do.

WHAT!?!?!

...you got a date..???

:D

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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)

Maybe not famous enough. What 'proof' are you referring to?

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It's not possible to predict the rest of the season. Pythagorean, coin flips, the standings, asking Bernard the cat to pick playoff teams, in my view those are all valid ways to figure out what the rest of the season will look like. This team has defied expectations, weathered injuries and slumps. Who knows what'll happen. I don't, I don't believe anyone who says they do.

Oh why oh why can't people understand the concept of "probability?"

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Oh why oh why can't people understand the concept of "probability?"

Well, I think that a lot of people have had their mental equilibrium altered by the fact that the Orioles are 9 games over .500 in the middle of August ......... so, the concept of probability has really been hard to grasp, whether we are talking about the Pythagorean theory, ERA, batting average, or the likelihood of an experienced magician actually sawing a lady in half by accident.

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.

By the way, I just realized that I should probably credit Moose Milligan with my previous post. On several occasions, he has pointed out that he believes that a lot of Oriole fans are going a little batty and not knowing how to feel or act because the concept of the Orioles being a good team with a good record this late in the season is so foreign to them.

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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. It has been a joy to wake up every morning and read about win after win. It makes even my spreadsheets bearable.

Tl;dr: The Pythagorean record of a team is important, but accepting it as the end of the debate on what makes a team win and lose is as foolish as the subprime crisis.

Great post!!! Agree with most disagree with some but ultimately this is the kinda stuff I come to the OH for!!!

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I live in NYC. The hand you a woman when you exit the Lincoln Tunnel. It's not a testament to any skill or appeal on my part.

If I'd only known. Here in Southern Maryland you have to do a faithful real-time reenactment of The Odyssey before you're even allowed to gaze upon the women with teeth.

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I can't believe I actually convinced myself to read through another thread on this topic, but since I did: 1) While the subprime metaphor might not have been particularly apt, the bomb/Dr. Strangelove situation to Pythag-Orioles/OH situation is absolutely so. 2) I now understand Lucky Jim's name...I always thought he was just a guy named Jim who thought Lucky Jim had a nice ring to it. 3) The two posts above this one are pretty damn funny.

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I can't believe I actually convinced myself to read through another thread on this topic, but since I did: .

Ehh, not me. I've seen enough. Wake me up when someone does some actual coherent analysis related to run distribution and BP performance.

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I can appreciate the dichotomy of the Euclidean geometric within the Pythagorean expectation and the allusion of mathematical 'proofs in the Gaussian copula function expressed in the OP. But personally I prefer the simplicity of the game.

"This is a very simple game. You throw the ball, you catch the ball, you hit the ball. Sometimes you win, sometimes you lose, sometimes it rains." - from Bull Durham

The beauty of baseball is that you really don't have to think about the game to enjoy it.

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