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Pythagorean expectation, baseball game

작성자 Uploader : ezmath 작성일 Upload Date: 2016-05-30변경일 Update Date: 2016-05-30조회수 View : 658

Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team "should" have won based on the number of runs they scored and allowed. Comparing a team's actual and Pythagorean winning percentage can be used to evaluate how lucky that team was (by examining the variation between the two winning percentages). The name comes from the formula's resemblance to the Pythagorean theorem.

The basic formula is:

W = S^2 / (S^2 + A^2)
W : Winning ratio
S : Runs scored
A : Runs allowed

Empirically, this formula correlates fairly well with how baseball teams actually perform. However, statisticians since the invention of this formula found it to have a fairly routine error, generally about three games off. For example, in 2002, the New York Yankees scored 897 runs and allowed 697 runs. According to James' original formula, the Yankees should have won 62.35% of their games.
Based on a 162-game season, the Yankees should have won 101.01 games. The 2002 Yankees actually went 103-58.
In efforts to fix this error, statisticians have performed numerous searches to find the ideal exponent.
If using a single-number exponent, 1.83 is the most accurate, and the one used by baseball-reference.com. The updated formula therefore reads as follows:

W = S^1.83 / (S^1.83 + A^1.83)


*** 참고문헌[References] ***

https://en.wikipedia.org/wiki/Pythagorean_expectation
W = S^1.83 / (S^1.83 + A^1.83)
변수명 Variable 변수값 Value 변 수 설 명 Description of the variable


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