Methods for detrending success metrics to account for inflationary and deflationary
factors* |
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Authors: | A M Petersen O Penner H E Stanley |
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Institution: | (1) Center for Polymer Studies and Department of Physics, Boston University, Boston, 02215, Massachusetts, USA;(2) Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, T2N 1N4, Canada |
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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. |
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