Using The Usage-Efficiency Distance Metric to Create Aging Curves for the NBA

An age-old question  — see what I did there? — among APBRmetricians is trying to understand how aging affects players. Consider this post my first contribution to the discussion.

I calculated the that I introduced in a recent post for the 10,000 or so player seasons since the 3-pt shot was instituted. I then divided these seasons into four groups by age, as follows:

  • "very young" (18-21)
  • "young" (22-25)
  • "prime" (26-29)
  • "old" (30+)

For each group, I used the lme4 package to create a mixed-effects model. Here is an example for the first group:

Linear mixed model fit by REML 
Formula: Dist ~ Age + (1 | Player) 
Data: subset(usage_big, Age >= 18 & Age < 22) 
AIC BIC logLik deviance REMLdev 3129 3146 -1560 3108 3121 
Random effects: 
Groups Name Variance Std.Dev. 
Player (Intercept) 0.00010698 0.010343 
Residual 0.02807594 0.167559 
Number of obs: 482, groups: Player, 312 
Fixed effects: 
Estimate Std. Error t value 
(Intercept) -2.5396933 0.0117872 -215.5 
Age 0.1189821 0.0005701 208.7 
Correlation of Fixed Effects: (Intr) Age -0.998

You can see that there were 482 observations (player-seasons) and 312 unique players. The intercept and slope that were found was -2.54 and +0.119, respectively. The positive slope represents improvement in terms of the distance metric as a function of age.

I repeated this analysis for each group, and compiled the following table of intercepts and slopes:

very young -2.540 0.119
young -0.900 0.033
prime 0.429 -0.019
old 1.610 -0.057

I then used these to create data points for each age. Essentially, I broke up a nonlinear function into four separate linear functions. I then used these to construct a smoothed version of an aging curve:

Distance is the scoring metric developed in a previous post.

What this shows is that on average there is significant improvement from age 18 to about 25, a plateau period that lasts until age 30, and then fairly rapid decline afterwards. Not so unexpected based on what has been shown previously, but it's always good to see confirmation using alternative approaches. For good measure, I thought I would show a bunch of individual aging curves. Of course, not everyone follows exactly this pattern. Some players are age-defying, while others decline much more rapidly. You can click on the plots to enlarge them.

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19 pts

It would be interesting to see these plotted on the same graph so the comparisons are immediate. I think I superimposed your Kobe and Jordan together correctly here: if correct, it seems telling.

19 pts

Great analysis, can you throw one up for Joe Johnson now of the Nets. That would be interesting given his contract.

This is interesting Evan, but my first thought is that it's slightly misleading. Unless I'm misunderstanding -- and that's possible, given that sometimes I need to read your equations twice for comprehension -- this is only a curve of recorded scoring (measured as TS% in relation to usg). My issue with that is that I believe most players peak on offense later than what the public, or their scoring stats suggest, and they do so precisely by curbing their own scoring for a more team-centric, balanced (or global) court game.

This is purely about scoring, so if older players are contributing in ways that don't have anything to do with their own scoring, then this won't capture that. I also think this is capturing "ability to score effectively" and not just player altruism (i.e. giving up his own scoring for the sake of the team). If that's a good thing, then should Kevin Durant do so right now?

Well, I don't think Durant is a good enough passer/creator to do so. It is possible (and hopeful) that after some more time in this role he will learn how to use his teammates better...


  1. says:

    [...] under-23 rule.  Two words for you: age curve.  Basketball players don’t appear to hit their peak until around 25.  So if you still dedicate the US team to NBA players, we won’t even be [...]