The European Physical Journal B

, Volume 79, Issue 1, pp 67–78 | Cite as

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

  • A. M. PetersenEmail author
  • O. Penner
  • H. E. Stanley


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.


Maximum Likelihood Estimator Career Success Professional Sport Major League Baseball Baseball Player 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Supplementary material


  1. 1.
    J. Duch, J.S. Waitzman, L.A.N. Amaral, PLoS ONE 5, e10937 (2010) Google Scholar
  2. 2.
    G. Berthelot, V. Thibault, M. Tafflet, S. Escolano, N. El Helou et al., PLoS ONE 3, e1552 (2008) Google Scholar
  3. 3.
    F.D. Desgorces, G. Berthelot, N. El Helou, V. Thibault, M. Guillaume et al., PLoS ONE 3, e3653 (2008) Google Scholar
  4. 4.
    M. Guillaume, N.E. Helou, H. Nassif, G. Berthelot, S. Len et al., PLoS ONE 4, e7573 (2009) Google Scholar
  5. 5.
    G.C. Ward, K. Burns, Baseball: An Illustrated History (Knopf, New York, 1994) Google Scholar
  6. 6.
    G.J. Mitchell, Report to the Commissioner of Baseball of an Independent Investigation into the Illegal Use of Steroids and other Performance Enhancing Substances by Players in Major League Baseball (Office of the Commissioner of Baseball, 2007) Google Scholar
  7. 7.
    Sean Lahman's Baseball Archive:
  8. 8.
    D. Lazer et al., Science 323, 721 (2009) CrossRefGoogle Scholar
  9. 9.
    A.M. Petersen, W-S. Jung, H.E. Stanley, Europhys. Lett. 83, 50010 (2008) CrossRefADSGoogle Scholar
  10. 10.
    A.M. Petersen, W-S. Jung, J.-S. Yang, H.E. Stanley, Quantitative and empirical demonstration of the Matthew effect in a study of career longevity, accepted for publication, Proc. Natl. Acad. Sci. USA ArXiv preprint: 0806.1224 [physics] Google Scholar
  11. 11.
    V. Pareto, Cours d'Économie Politique (Droz, Geneva, 1896) Google Scholar
  12. 12.
    S. Redner, Eur. Phys. J. B 4, 131 (1998) CrossRefADSGoogle Scholar
  13. 13.
    R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 1999) Google Scholar
  14. 14.
    R. Albert, H. Jeong, A.-L. Barabási, Nature 401, 130 (1999) CrossRefADSGoogle Scholar
  15. 15.
    F. Liljeros et al., Nature 411, 907 (2001) CrossRefADSGoogle Scholar
  16. 16.
    J.A. Davies, Eur. Phys. J. B 27, 445 (2002) CrossRefADSGoogle Scholar
  17. 17.
    S. Sinha, S. Raghavendra, Eur. Phys. J. B 42, 293 (2004) CrossRefADSGoogle Scholar
  18. 18.
    M.E.J. Newman, Contemp. Phys. 46, 323 (2005) CrossRefADSGoogle Scholar
  19. 19.
    A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51, 661 (2009) zbMATHCrossRefADSMathSciNetGoogle Scholar
  20. 20.
    J.J. Koch, Pediatr. Rev. 23, 310 (2002) CrossRefGoogle Scholar
  21. 21.
    T.D. Noakes, N. Engl. J. Med. 351, 847 (2002) CrossRefGoogle Scholar
  22. 22.
    I. Waddington et al., Br. J. Sports Med. 39, e18 (2005) Google Scholar
  23. 23.
    J.C. Bradbury, What Really Ruined Baseball (New York Times, New York, 2007) Google Scholar
  24. 24.
    C.R. McHenry, Surgery 142, 785 (2007) CrossRefGoogle Scholar
  25. 25.
    R.G. Tobin, Am. J. Phys. 76, 15 (2008) CrossRefADSGoogle Scholar
  26. 26.
    B.J. Schmotzer, J. Switchenko, P.D. Kilgo, Journal of Quantitative Analysis in Sports 4, 4 (2008) CrossRefMathSciNetGoogle Scholar
  27. 27.
    J. Starks, Homers, homers, homers (, May 15, 2000) Google Scholar
  28. 28.
    E. Ben-Naim, F. Vazquez, S. Redner, Journal of Quantitative Analysis in Sports 2, 1 (2006) CrossRefMathSciNetGoogle Scholar
  29. 29.
    C. Sire, S. Redner, Eur. Phys. J. B 67, 473 (2009) CrossRefADSGoogle Scholar
  30. 30.
    S.C. Choi, R. Wette, Technometrics 11, 683 (1969) zbMATHCrossRefGoogle Scholar
  31. 31.
    P. Holme, C.R. Edling, F. Liljeros, Social Networks 26, 155 (2004) CrossRefGoogle Scholar
  32. 32.
    J.D. Farmer, M. Shubik, E. Smith, Physics Today 58, 37 (2005) CrossRefGoogle Scholar
  33. 33.
    B.F. de Blasio, A. Svensson, F. Liljeros, Proc. Natl. Acad. Sci. USA 104, 10762 (2007) CrossRefADSGoogle Scholar
  34. 34.
    M.C. González, C.A. Hidalgo, A.-L. Barabási, Nature 453, 779 (2008) CrossRefADSGoogle Scholar
  35. 35.
    C. Castellano, S. Fortunato, V. Loreto, Rev. Mod. Phys. 81, 591 (2009) CrossRefADSGoogle Scholar
  36. 36.
    A.M. Petersen, F. Wang, H.E. Stanley, Phys. Rev. E 81, 036114 (2010) CrossRefADSMathSciNetGoogle Scholar
  37. 37.
    J.E. Hirsch, Proc. Natl. Acad. Sci. USA 102, 16569 (2005) CrossRefADSGoogle Scholar
  38. 38.
    A.M. Petersen, H.E. Stanley, S. Succi, Statistical regularities in the rank-citation profile, under review Google Scholar
  39. 39.
    F. Radicchi, S. Fortunato, C. Castellano, Proc. Natl. Acad. Sci. 105, 17268 (2008) CrossRefADSGoogle Scholar
  40. 40.
    B. Maher, Nature 452, 674 (2008) CrossRefADSGoogle Scholar
  41. 41.
    B. Sahakian, S. Morein-Zamir, Nature 450, 1157 (2007) CrossRefADSGoogle Scholar
  42. 42.
    S. Saavedra, S. Powers, T. McCotter, M.A. Porter, P.J. Mucha, Physica A 390, 1131 (2010) CrossRefADSGoogle Scholar
  43. 43.
    J. Click et al., Baseball Between the Numbers.: why everything you know about the game is wrong (Basic Books, New York, 2006) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA
  2. 2.Complexity Science Group, Department of Physics and AstronomyUniversity of CalgaryAlbertaCanada

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