Abstract
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.
- 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
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
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
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
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
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 capgeek.com maintained by Matthew Wuest.
- 7
See, for example, Henderson, Carroll and Li (2008).
- 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
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.
Acknowledgments
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.
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