The Shrinkage of the Pythagorean exponents

Journal of Sports Analytics

article

John Chen¹  Tengfei Li¹ 

[1] King George V School

关键词: Team strength;    prediction;    least squares;    mean squared error;   

DOI  :  10.3233/JSA-160017

来源: IOS Press

【 摘 要 】

The Pythagorean expectation is a formula designed by Bill James in the 1980s for estimating the number of games that a baseball team is expected to win. The formula has since been applied in basketball, hockey, football, and soccer. When used to assess National Basketball Association (NBA) teams, the optimal Pythagorean exponent is generally believed to be between 14 and 17. In this study, we empirically investigated the accuracy of the formula in the NBA by using data from the 1993-1994 to 2013-2014 seasons. This study confirmed the results of previous studies, which found that the Pythagorean exponent is slightly higher than 14 in the fit scenario, in which the strengths and winning percentage of a team are calculated using data from the same period. However, to predict future winning percentages according to the current evaluations of team strengths, the optimal Pythagorean exponent in the prediction scenario decreases substantially from 14. The shrinkage factor varies from 0.5 early in the season to nearly 1 toward the end of the season. Two main reasons exist for the decrease: the current evaluated strengths correlate with the current winning percentage more strongly than they do with the future winning percentage, and the scales of strengths evaluated in the early or middle part of a season tend to exceed those evaluated at the end of the season because of the evening out of randomness or the law of averages. The prediction accuracy decreases with time over a season. Four measurements of strength were investigated and the ratio of total points scored to total points allowed was the most useful predictor. Point difference exhibited nearly the same accuracy, whereas the ratio of games won to games lost was somewhat less accurate. An explanation of Dean Oliver’s choice of 16.5 as the Pythagorean exponent is offered.

【 授权许可】

Unknown