Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter March 18, 2014

Estimating the effects of age on NHL player performance

  • James A. Brander EMAIL logo , Edward J. Egan and Louisa Yeung


Using NHL data for the 1997–1998 through 2011–2012 seasons, we examine the effect of age on scoring performance and plus-minus for NHL skaters (non-goalies) and on save percentage for goaltenders. We emphasize fixed-effects regression methods that estimate a representative age-performance trajectory. We also use a method based on the best performances over time, a method based on the age distribution of NHL players, and a “naïve” specification that does not correct for selection bias. In addition we estimate individual age-performance relationships to obtain a distribution of peak ages. All methods provide similar results (with small but understandable differences) except the naïve specification, which yields implausible results, indicating that correcting for selection bias is very important. Our best estimate of the scoring peak age is between 27 and 28 for forwards and between 28 and 29 for defencemen. Both forwards and defencemen exhibit near-peak performance over a wide range, going from about 24 to 32 and 24 to 34, respectively. Goaltenders display little systematic performance variation over most of the age range from the early 20s to late 30s.

Corresponding author: James A. Brander, Sauder School of Business, University of British Columbia, 2053 Main Mall, Vancouver, BC, Canada V6T 1Z2, e-mail:

  1. 1

    Sabermetrics refers to the statistical analysis of baseball. The term was originally coined by Bill James and is derived from the acronym SABR, which stands for the Society for American Baseball Research.

  2. 2

    There is also related work by Kovalchik and Stefani (2013) that uses performances of Olympic medalists over time to assess time-related improvements in athletic performance.

  3. 3

    One very thoughtful effort to use statistical methods to compare players across eras in a variety of sports, including in the NHL, is provided by Berry, Reese and Larkey (1999).

  4. 4

    Addona and Yates (2010) provide a very interesting paper investigating the effects of birth month on NHL performance. They investigate the hypothesis that players born early in the year have an advantage due to being grouped with children several months younger than themselves throughout childhood and therefore exhibit better relative performance and get more attention, better coaching, etc.

  5. 5

    With even-strength play (also called five-on-five play) every goal results in an addition of 1 for all five skaters on the scoring team and a subtraction of 1 for all skaters on the other team, so the average is always zero. However, with shorthanded goals the four players on the penalty kill that scores the shorthanded goal record +1 while all five players on the powerplay scored against record -1. No pluses or minuses are given for powerplay goals. Therefore the average plus-minus is slightly negative as more players get a negative than get a positive for shorthanded goals. Given the very small relative number of shorthanded goals, this effect is very small.

  6. 6

    As of 2013–2014 a typical marginal player who will divide a season between an NHL team and its minor league American Hockey League (AHL) affiliate or “farm team” has a “two-way contract” that might pay $500,000 to $900,000 per year on a pro-rated basis for games played in the NHL, but perhaps only $70,000 or $80,000 per year on a pro-rated basis for games played in AHL. Salary data can be found on the website maintained by Matthew Wuest.

  7. 7

    See, for example, Henderson, Carroll and Li (2008).

  8. 8

    As Albert (1999) points out, quadratic age-performance provide a parsimonious and effective way of capturing individual trajectories sufficiently to estimate peak age functions even though they have the disadvantage of imposing symmetry – the assumption that players are assumed to improve at the same rate as they decline. See Albert (2009) for an application using the more flexible spline functions to capture individual trajectories.

  9. 9

    Among other things we confirmed that the individual aging functions estimated in this section exhibit a similar curvature to the common or representative aging function estimated in Section 5.


We are grateful to Jim Albert (the editor), an associate editor, and three reviewers for very helpful comments. We also thank Tom Davidoff, Keith Head, Jim Jamieson, John Ries, and Joanna Zhu for valuable discussions regarding this paper.


Addona, Vittorio, and Philip A. Yates. 2010. “A Closer Look at the Relative Age Effect in the National Hockey League.” Journal of Quantitative Analysis in Sports 6(4), Article 9:1–17.10.2202/1559-0410.1227Search in Google Scholar

Albert, Jim. 1999. “Comment.” Journal of the American Statistical Association 94(447):677–680.10.1080/01621459.1999.10474164Search in Google Scholar

Albert, Jim. 2002. “Smoothing Career Trajectories of Baseball Hitters.” Unpublished manuscript, Bowling Green State University, at in Google Scholar

Albert, Jim. 2009. “Is Roger Clemens’ WHIP Trajectory Unusual?” Chance 22:8–20.10.1080/09332480.2009.10722954Search in Google Scholar

Arkes, Jeremey. 2010. “Revisiting the Hot Hand Theory with Free Throw Data in a Multivariate Framework.” Journal of Quantitative Analysis in Sports 6(1):Article 2.10.2202/1559-0410.1198Search in Google Scholar

Berthelot, Geoffroy, Stéphane Len, Philippe Hellard, Muriel Tafflet, Marion Guillaume, Jean-Claude Vollmer, Bruno Gager, Laurent Quinquis, Andy Marc and Jean-François Toussaint. 2013. “Exponential growth combined with exponential decline explains lifetime performance evolution in individual and human species.” Age 34:1001–1009.10.1007/s11357-011-9274-9Search in Google Scholar PubMed PubMed Central

Berry, Scott, C. Shane Reese, and Patrick D. Larkey. 1999. “Bridging Different Eras in Sports.” Journal of the American Statistical Association 94(447):661–676.10.1080/01621459.1999.10474163Search in Google Scholar

Bradbury, J. C. 2009. “Peak Athletic Performance and Ageing: Evidence from Baseball.” Journal of Sports Science 27(6):599–610.10.1080/02640410802691348Search in Google Scholar PubMed

Broadie, Mark, and Richard J. Rendleman Jr. 2013. “Are the official world golf rankings biased?” Journal of Quantitative Analysis in Sports 9(2):127–140.10.1515/jqas-2012-0013Search in Google Scholar

Chen, Mike. 2010. “When is an NHL player’s prime age?” SB Nation Special Feature at in Google Scholar

Fair, Ray C. 2008. “Estimated Age Effects in Baseball.” Journal of Quantitative Analysis in Sports 4(1):Article 1:1–39.10.2202/1559-0410.1074Search in Google Scholar

Gramacy, Robert B., Shane T. Jensen, and Matt Taddy. 2013. “Estimating player contribution in hockey with regularized logistic regression.” Journal of Quantitative Analysis in Sports 9(1):97–111.10.1515/jqas-2012-0001Search in Google Scholar

Henderson, Daniel J., Raymond J. Carroll and L. Qi. 2008. “Nonparametric estimation and testing of fixed effects panel data models.” Journal of Econometrics 144:257–275.10.1016/j.jeconom.2008.01.005Search in Google Scholar PubMed PubMed Central

James, Bill. 1982. The Bill James Baseball Abstract. New York: Ballantine Books.Search in Google Scholar

Kovalchik, Stephanie Ann, and Ray Stefani. 2013. “Longitudinal analyses of Olympic athletics and swimming events find no gender gap in performance improvement.” Journal of Quantitative Analysis in Sports 9(1):15–24.10.1515/jqas-2012-0007Search in Google Scholar

Lavieri, M., M. Puterman, S. Tyldesley, and W. Morris. 2012. “When to Treat Prostate Cancer Patients Based on their PSA Dynamics.” IIE Transactions in Health Care Systems 2:62–77.10.1080/19488300.2012.666631Search in Google Scholar

Lepers, Romuald, Beat Knechtle, and Paul J. Stapley. 2013. “Trends in Triathlon Performance: Effects of Sex and Age.” Sports Medicine,, published online June 2013, forthcoming in print.10.1007/s40279-013-0067-4Search in Google Scholar PubMed

Macdonald, Brian. 2011. “A Regression-Based Adjusted Plus-Minus Statistic for NHL Players.” Journal of Quantitative Analysis in Sports 7(3):Article 4, 1–29.Search in Google Scholar 2013: The official website of the National Hockey League, in Google Scholar

Schulz, Richard, and Christine Curnow. 1988. “Peak Performance and Age Among Superathletes: Track and Field, Swimming, Baseball, Tennis, and Golf.” Journal of Gerontology: Psychological Sciences 43(5):113–120.10.1093/geronj/43.5.P113Search in Google Scholar PubMed

Schulz, Richard, Donald Musa, James Staszewski, and Robert S. Siegler. 1994. “The Relationship Between Age and Major League Baseball Performance: Implications for Development.” Psychology and Aging 9(2):274–286.10.1037/0882-7974.9.2.274Search in Google Scholar

Tiruneh, Gizachew. 2010. “Age and Winning Professional Golf Tournaments.” Journal of Quantitative Analysis in Sports 6(1): Article 5.10.2202/1559-0410.1209Search in Google Scholar

Vollman, Rob. 2013. Rob Vollman’s Hockey Abstract, in Google Scholar

Wooldridge, Jeffrey M. 2008. Econometric Analysis of Cross Section and Panel Data, 2nd ed. Cambridge, MA: MIT Pess.Search in Google Scholar

Wright, Vonda J., and Brett C. Perricelli. 2008. “Age-Related Rates of Decline in Performance Among Elite Senior Athletes.” Journal of the American Journal of Sports Medicine 36(3):443–450.10.1177/0363546507309673Search in Google Scholar PubMed

Wuest, Matthew. 2013. in Google Scholar

Published Online: 2014-3-18
Published in Print: 2014-6-1

©2014 by Walter de Gruyter Berlin/Boston

Downloaded on 6.12.2023 from
Scroll to top button