View Full Version : Pythagorean Wins

ondafarm

05-10-2005, 01:01 PM

It's been asked a few times about what the formula for Pythagorean wins is and I found this article.

http://www.baseballprospectus.com/article.php?articleid=342

In short, the formula for expected win percentage is: the square of runs scored divided by the sum of the square of runs scored and the square of runs allowed.

When the Sox offense heats up and a few more blowouts occur the Pythagorean wins will return to the actual wins. And Pythagoras couldn't even hit a curveball.

For propeller heads only, the article also describes an alternative poisson based formula. However, after a bit of experimentation, I believe that altering the value of e provides a better basis for manipulating the model. The article does mention that the spread of values is way too low. An issue I had to deal with while working on a doctoral thesis (not mine.)

santo=dorf

05-10-2005, 01:16 PM

For propeller heads only, the article also describes an alternative poisson based formula. However, after a bit of experimentation, I believe that altering the value of e provides a better basis for manipulating the model. The article does mention that the spread of values is way too low. An issue I had to deal with while working on a doctoral thesis (not mine.)

That's what sabermetrics is all about. Manipulate the data as much as possible so you can come up with your own conclusions.

Even www.baseballreference.com (http://www.baseballreference.com) says it's more approximate if you take the runs to the 1.83 power instead of 2.

ondafarm

05-10-2005, 01:48 PM

That's what sabermetrics is all about. Manipulate the data as much as possible so you can come up with your own conclusions.

Even www.baseballreference.com (http://www.baseballreference.com/) says it's more approximate if you take the runs to the 1.83 power instead of 2.

Actually by varying the power thru the 1.8ns they show the R-squared minimizes at 1.87.

Ol' No. 2

05-10-2005, 01:56 PM

Actually by varying the power thru the 1.8ns they show the R-squared minimizes at 1.87.But if you look at the RMS errors, it's a pretty shallow minimum. The practical significance of the differences between those exponents is practically nil. Instead of an error of 4.126 games it's 4.039 games. Am I supposed to be impressed by that?

ondafarm

05-10-2005, 02:00 PM

But if you look at the RMS errors, it's a pretty shallow minimum. The practical significance of the differences between those exponents is practically nil. Instead of an error of 4.126 games it's 4.039 games. Am I supposed to be impressed by that?

Well, the short answer is no. That's why the author circumvents Bill James and applies the Poisson methodology. Even that seems fairly flawed by the spread problem, which I believe could be corrected with an alternate base value.

Ol' No. 2

05-10-2005, 02:17 PM

Well, the short answer is no. That's why the author circumvents Bill James and applies the Poisson methodology. Even that seems fairly flawed by the spread problem, which I believe could be corrected with an alternate base value.But in the end, is he significantly reducing the RMS error? There is a certain random element in baseball. Not everything can be modelled. If the remaining sum of squares is due to true error and not lack of fit, there's no model that will reduce it. I have a strong suspicion that's the case.

ondafarm

05-10-2005, 02:31 PM

But in the end, is he significantly reducing the RMS error? There is a certain random element in baseball. Not everything can be modelled. If the remaining sum of squares is due to true error and not lack of fit, there's no model that will reduce it. I have a strong suspicion that's the case.

Well personally, I think that manager skill and team intelligence have to be taken into account. Smart teams know when you can give up a few runs safely and still win the game and when playing for only one run really pays. It's hard to put team intelligence in a single number though and manager skill is one of the most resistant to stat analysis that I'm aware of.

Ol' No. 2

05-10-2005, 02:40 PM

Well personally, I think that manager skill and team intelligence have to be taken into account. Smart teams know when you can give up a few runs safely and still win the game and when playing for only one run really pays. It's hard to put team intelligence in a single number though and manager skill is one of the most resistant to stat analysis that I'm aware of.If that's true, then some managers should consistently outperform their Pythagorean win%. I, frankly, have no idea if this is true.

Flight #24

05-10-2005, 03:08 PM

If that's true, then some managers should consistently outperform their Pythagorean win%. I, frankly, have no idea if this is true.

Not sure, but I know I read a piece not too long ago that said some managers can impact a game and something that showed certain managers consistently winning close games. In that article, Ozzie had a better start in 1-run games than either Torre or Bobby Cox. It was linked here not too long ago.

Edit: here it is http://www.whitesoxinteractive.com/vbulletin/showthread.php?t=48635&highlight=cox+torre+guillen

Here' the base article: http://nwitimes.com/articles/2005/04/22/sports/top_sports/a574bf6ce97b663e86256fea007fb2da.prt

ondafarm

05-10-2005, 07:40 PM

Teams that score lots of runs seem to have an advantage in Pythagorean wins. Managers like Tommy Lasorda or Sparky Anderson supposedly have an advantage over Pythagoras.

ma-gaga

05-10-2005, 09:46 PM

Hell, I don't even watch games any more. I just simulate them and let the team with the higher Pythagorian record win.

:cool:

Daver

05-10-2005, 09:52 PM

Hell, I don't even watch games any more. I just simulate them and let the team with the higher Pythagorian record win.

:cool:

I'm gonna have to ask WU to make a propellerhead tag.

ondafarm

05-10-2005, 09:58 PM

I'm gonna have to ask WU to make a propellerhead tag.

Can I get a sig like that?

ma-gaga

05-10-2005, 10:00 PM

I'm gonna have to ask WU to make a propellerhead tag.

That's cool. I didn't know where that term originated from, but I read that Bill James was called that at some point in the 80's. Again, the origin escapes me, but it is definitely on point.

I'm curious, when and where have you heard that term used??

ondafarm

05-11-2005, 08:04 AM

That's cool. I didn't know where that term originated from, but I read that Bill James was called that at some point in the 80's. Again, the origin escapes me, but it is definitely on point.

I'm curious, when and where have you heard that term used??

I'd always thought that propeller head came from the propeller equipped beanies that certain new students were required to wear. It's supposed to be a greater insult than stathead.

voodoochile

05-11-2005, 08:18 AM

But if you look at the RMS errors, it's a pretty shallow minimum. The practical significance of the differences between those exponents is practically nil. Instead of an error of 4.126 games it's 4.039 games. Am I supposed to be impressed by that?

Those extra .087 games can really make a difference in the standings. :tongue:

An error factor of 4 games? Essentially a team with an expected Pythagorean win total of 87 should finish between 85 and 89 wins (or is it 83 and 91?).

But what does it tell us when a team finishes outside the error range? Are they smart? Lucky?

Would a major trade or two late in the trading season alter a teams win total or only if they were exceeding it or failing to meet it before the trade?

Where did they come up with this forumula and how accurate is it from past seasons?

1951Campbell

05-11-2005, 08:45 AM

The best formula to measure a team's performance is to multiply their wins by 1, and then do the same for losses.

:D:

voodoochile

05-11-2005, 08:49 AM

The best formula to measure a team's performance is to multiply their wins by 1, and then do the same for losses.

:D:

I prefer wins divided by wins + losses. :D:

daveeym

05-11-2005, 09:52 AM

:bs: :drunken: :kukoo: :yup: :smokin: :thud: :help:

Edit: Maybe I should take out the 4th smiley. Him and propeller heads don't mix.

Ol' No. 2

05-11-2005, 09:54 AM

Those extra .087 games can really make a difference in the standings. :tongue:

An error factor of 4 games? Essentially a team with an expected Pythagorean win total of 87 should finish between 85 and 89 wins (or is it 83 and 91?).

But what does it tell us when a team finishes outside the error range? Are they smart? Lucky?

Would a major trade or two late in the trading season alter a teams win total or only if they were exceeding it or failing to meet it before the trade?

Where did they come up with this forumula and how accurate is it from past seasons?It's plus or minus 4 wins, so it would be 83-91 wins in your example. And the RMS error is analagous to a standard deviation. You can expect roughly one-third of the teams to be outside that error band. About 5% will lie outside a window twice as large.

The formula, like a lot of the sabermetric stuff, is entirely empirical. You just get a bunch of data and try to come up with a mathematical equation that fits. It's not like an equation which is derived from basic principles.

voodoochile

05-11-2005, 10:02 AM

It's plus or minus 4 wins, so it would be 83-91 wins in your example. And the RMS error is analagous to a standard deviation. You can expect roughly one-third of the teams to be outside that error band. About 5% will lie outside a window twice as large.

The formula, like a lot of the sabermetric stuff, is entirely empirical. You just get a bunch of data and try to come up with a mathematical equation that fits. It's not like an equation which is derived from basic principles.

This doesn't seem like much of a predictive tool. I mean there is a large difference between 83 and 91 wins (as Sox fans have become all too keenly aware of recently). 83 is nothing special, but 91 is potentially a playoff team. It's a 50 point swing in win percentage (permillage technically :D: ).

I mean most of the guys at WSI could probably peg the Sox W/L total this season within a range like that without any need to look at numbers at all.

Edit: by the time you get to that 5% bracket, it gets really silly. I mean what is the good of being able to say, "The Sox will win between 79 and 95 games this season"?

Flight #24

05-11-2005, 10:03 AM

It's plus or minus 4 wins, so it would be 83-91 wins in your example. And the RMS error is analagous to a standard deviation. You can expect roughly one-third of the teams to be outside that error band. About 5% will lie outside a window twice as large.

The formula, like a lot of the sabermetric stuff, is entirely empirical. You just get a bunch of data and try to come up with a mathematical equation that fits. It's not like an equation which is derived from basic principles.

I love it. I can't remember who, but some writer recently said "Twins are performing 2 games below their pythagorean total, Sox 1 game above, so you can expect that gap to close".

Translation: The Twins are well within the 8 game window around their pyth. total, as are the Sox.....and in any case, only 67% of teams end up with records within that window.

I.e. Here's a stat that really doesn't say much. But since it doesn't say much I can make it out to mean whatever my :smokin: tells me is the correct meaning.

Ol' No. 2

05-11-2005, 10:41 AM

This doesn't seem like much of a predictive tool. I mean there is a large difference between 83 and 91 wins (as Sox fans have become all too keenly aware of recently). 83 is nothing special, but 91 is potentially a playoff team. It's a 50 point swing in win percentage (permillage technically :D: ).

I mean most of the guys at WSI could probably peg the Sox W/L total this season within a range like that without any need to look at numbers at all.

Edit: by the time you get to that 5% bracket, it gets really silly. I mean what is the good of being able to say, "The Sox will win between 79 and 95 games this season"?Unfortunately, the same can be said for an awful lot of these things. But they rarely publish (and often don't even consider) the error bands. PECOTA projections generally predict a players OPS not significantly better than taking the average of the previous three years.

It makes me laugh when they get all worked up over changing the exponent and "improving" the fit by 0.087 when the error band is 4 games.

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