Methods for Detrending Success Metrics to Account for Inflationary and Deflationary Factors

European Physical Journal B, Vol. 79, pp. 67-78, 2011

24 Pages Posted: 21 Jul 2011

See all articles by Alexander Michael Petersen

Alexander Michael Petersen

University of California Merced, Ernest and Julio Gallo Management Program

Orion B. Penner

Ecole Polytechnique Fédérale de Lausanne

H. Eugene Stanley

Boston University - Center for Polymer Studies

Date Written: January 1, 2011

Abstract

Time-dependent economic, technological, and social factors can artificially inflate or deflate quantitative measures for career success. Here we develop and test a statistical method for normalizing career success metrics across time dependent factors. In particular, this method addresses the long standing question: how do we compare the career achievements of professional athletes from different historical eras? Developing an objective approach will be of particular importance over the next decade as major league baseball (MLB) players from the “steroids era” become eligible for Hall of Fame induction. Some experts are calling for asterisks (*) to be placed next to the career statistics of athletes found guilty of using performance enhancing drugs (PED). Here we address this issue, as well as the general problem of comparing statistics from distinct eras, by detrending the seasonal statistics of professional baseball players. We detrend player statistics by normalizing achievements to seasonal averages, which accounts for changes in relative player ability resulting from a range of factors. Our methods are general, and can be extended to various arenas of competition where time-dependent factors play a key role. For five statistical categories, we compare the probability density function (pdf) of detrended career statistics to the PDF of raw career statistics calculated for all player careers in the 90-year period 1920-2009. We find that the functional form of these PDFs is stationary under detrending. This stationarity implies that the statistical regularity observed in the right-skewed distributions for longevity and success in professional sports arises from both the wide range of intrinsic talent among athletes and the underlying nature of competition. We fit the PDFs for career success by the Gamma distribution in order to calculate objective benchmarks based on extreme statistics which can be used for the identification of extraordinary careers.

Keywords: MLB Baseball, Performance Enhancing Drugs, PED, Success Metrics

JEL Classification: D39, J24, J44, L83

Suggested Citation

Petersen, Alexander Michael and Penner, Orion B. and Stanley, H. Eugene, Methods for Detrending Success Metrics to Account for Inflationary and Deflationary Factors (January 1, 2011). European Physical Journal B, Vol. 79, pp. 67-78, 2011 , Available at SSRN: https://ssrn.com/abstract=1889427

Alexander Michael Petersen (Contact Author)

University of California Merced, Ernest and Julio Gallo Management Program ( email )

School of Engineering
Science & Engineering 2, Suite 315
Merced, CA 95343
United States

Orion B. Penner

Ecole Polytechnique Fédérale de Lausanne ( email )

Station 5
Odyssea 1.04
1015 Lausanne, CH-1015
Switzerland

H. Eugene Stanley

Boston University - Center for Polymer Studies ( email )

Boston, MA 02215
United States

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