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Pythagorean Expectation

What is Pythagorean Expectation?

Pythagorean expectation (or record) is based on a formula created by Bill James that estimates how many games a baseball team should (or expected) to have won based on the number of runs they scored and allowed.

Sporting Charts explains Pythagorean Expectation

The basic formula Bill James is as follows:

Win = runs scored² /(runs scored² + runs allowed²)  = 1 / 1 + (runs scored + runs allowed)²

There have been several different versions of this formula that have been honed over the years by other great baseball statiscian minds like Clay Davenport of Baseball Prospectus and David Smyth. Despite this, Bill James' formula remians the standard bearer, though staticians have now change each squared number to 1.83 to compensate for a constant error of about 3 wins. So, now the formula looks like this: 

Win = runs scored to the 1.83 power /(runs scored to the 1.83 power + runs allowed to the 1.83 power) 

To use it in an example for the 2012 New York Yankees:

Win = 804 to the 1.83 power / (804 to the 1.83 power + 668 to the 1.83 power) 

Win = 207309.20/ (207309.20 + 147686.54) 

Win =  207309.20/ 354995.74 

Win = .584 = 94.6 wins = According to, the 2012 Yankees Pythaogrean Expectation was 95-67. Actual record, 95-67 

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