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Methods for detrending success metrics to account for inflationary and deflationary factors

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  • A. M. Petersen
  • O. Penner
  • H. E. Stanley

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. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Suggested Citation

  • A. M. Petersen & O. Penner & H. E. Stanley, 2011. "Methods for detrending success metrics to account for inflationary and deflationary factors," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 79(1), pages 67-78, January.
    • Handle: RePEc:spr:eurphb:v:79:y:2011:i:1:p:67-78
    DOI: 10.1140/epjb/e2010-10647-1
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
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    1. Petersen, Alexander M. & Succi, Sauro, 2013. "The Z-index: A geometric representation of productivity and impact which accounts for information in the entire rank-citation profile," Journal of Informetrics, Elsevier, vol. 7(4), pages 823-832.
    2. Petersen, Alexander M. & Pan, Raj K. & Pammolli, Fabio & Fortunato, Santo, 2019. "Methods to account for citation inflation in research evaluation," Research Policy, Elsevier, vol. 48(7), pages 1855-1865.
    3. Seuront, Laurent, 2013. "Complex dynamics in the distribution of players’ scoring performance in Rugby Union world cups," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3731-3740.
    4. Petersen, Alexander M. & Penner, Orion, 2020. "Renormalizing individual performance metrics for cultural heritage management of sports records," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).

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