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# The Angels and Pythag

If you'll head over to Halo's Heaven and search for "Pythag", you'll be greeted with much disdain for the word.  The most recent example of that is a FanPost which laments the fact that, once again, the Angels are being called lucky this year.

The author of the FanPost is right; a lot of people consider the Angels to be getting lucky.  According to Justin's most recent Power Rankings, the Angels have been playing like a .529 W% team within league, compared to an actual W% of .609.  So I wanted to take a look at whether this was a skill, or if the Angels are just getting lucky.

First, how rare is the Angels current feat?  To answer I went into Baseball Databank and figured out the disparity between PythagenPat W% and actual W% for each team since 1960 (/random arbitrary date).  That's returned a total of 1236 separate teams, which seems like a pretty good sample.

The team that unperformed the most was the 1962 New York Mets, when they won a whopping 40 games and had a .248 W%.  PythagenPat thought that they should have had a W% of about .390, which would result in about 62 wins.  Conversely, the team that overperformed the most was the 2001 Mariners, winning about 20 games more than their Pythag suggested.

The standard deviation was .039 points of winning percentage, which is about 6.3 games over a full season of play.  Than means that 68% of teams with have an actual W% within .039 points of their Pythag, and 95% of teams will have be within .079 points.

UPDATE: Due to my SQL suckage, I screwed the pooch on this one.  The actual Stdev is about 3.9 wins.

The Angels spread this year is .08, which is over 2 standard deviations from the mean, and it means that their is only a 1/20 chance of this happening in a given year.

Based on that prior, we would naturally be inclined to dismiss it as simply luck, as the odds of a true skill are almost nil;  however, this isn't the first time the Angels have overperformed.  From Sky on the Halos Heaven FanPost:

##### 1, 2, 5, 4, 12, 7

Those are the number of games the Angels’ Win total has beaten their Pythag by over the last six years. ’04 and ’05 are nothing. ’06 and ’07 are solid, but nothing crazy. ’08 was crazy. ’09 is on pace to be crazy.

Baring that information, I have two questions for you guys:

• What are the mathematical odds of the Angels having an innate skill to beat their Pythag?
• What could be a possible explanation for the Angels beating their Pythag so much?

The first question probably entails some form of Bayesian math.  If we know the prior, which I believe would be the odds that a random team does what the Angels have done, then we just have to incorporate the information that we have about the Angels.  With me not being a statistician in any sense of the word, other people would be much better qualified to answer that question.

The second question is obviously open to a large range of possibilities.  Possible reasons I have heard include bullpen leveraging, "Mike Scosia is a genius", clutch hitting, aggressive base running, etc.; however, as far as I know, nobody has made a convincing case to support any of those notions.

So I'll ask your guys' help.  Are the Angels lucky or good?  I've already outlined two possible ways to look at it, and I'm sure there are others as well.