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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 Game Designer Pythagoras Explained )〕 The basic formula is: : where Win is the winning ratio generated by the formula. The expected number of wins would be the expected winning ratio multiplied by the number of games played. ==Empirical origin== 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 101.07 games. The 2002 Yankees actually went 103–58.〔(Baseball-reference.com | 2002 NY Yankees Statistics )〕 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.〔(Baseball-reference.com | What is pythagorean winning percentage? )〕 The updated formula therefore reads as follows: : The most widely known is the Pythagenport formula〔(Baseball Prospectus | Articles | Revisiting the Pythagorean Theorem )〕 developed by Clay Davenport of Baseball Prospectus: : He concluded that the exponent should be calculated from a given team based on the team's runs scored (R), runs allowed (RA), and games (G). By not reducing the exponent to a single number for teams in any season, Davenport was able to report a 3.9911 root-mean-square error as opposed to a 4.126 root-mean-square error for an exponent of 2.〔 Less well known but equally (if not more) effective is the Pythagenpat formula, developed by David Smyth.〔(W% Estimators )〕 : Davenport expressed his support for this formula, saying:
These formulas are only necessary when dealing with extreme situations in which the average number of runs scored per game is either very high or very low. For most situations, simply squaring each variable yields accurate results. There are some systematic statistical deviations between actual winning percentage and expected winning percentage, which include bullpen quality and luck. In addition, the formula tends to regress toward the mean, as teams that win a lot of games tend to be underrepresented by the formula (meaning they "should" have won fewer games), and teams that lose a lot of games tend to be overrepresented (they "should" have won more). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pythagorean expectation」の詳細全文を読む スポンサード リンク
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