Stumbling on Wins: Do coaches not understand how players age?

On page 118 of "Stumbling on Wins," authors David Berri and Martin Schmidt argue that NBA coaches don't understand how players age. That's because, according to Berri and Schmidt, coaches give players more and more minutes until age 28. But, they, report, player productivity actually peaks at age 24. Therefore,

"... the allocation of minutes suggests the age profile in basketball is not well understood by NBA coaches."

Geez, that doesn't follow at all.

First, I don't understand how the authors figure that minutes played peak at 28. If you look at actual minutes played by age, the peak appears to be earlier. These are minutes by age for the current 2009-10 season, on the day I'm writing this:

19: 1512
20: 10932
21: 38198
22: 37283
23: 52626
24: 52653
25: 47297
26: 34481
27: 43339
28: 29843
29: 48955
30: 37756
31: 27852
32: 14336
33: 20376
34: 11677
35: 12976
36: 5333
37: 4516
38: 0
39: 122

The curve appears to reach its high point at 23 and 24, then diminishes irregularly down to age 39. There are a couple of blips, notably at 29, but you certainly wouldn't put the minutes peak at anything other than 23-24.

So why do the authors say 28 is the peak? I'm not sure. In a footnote, they say the details can be found on their website, but there's nothing posted yet for that chapter (seven).

I suspect the issue is selective sampling. If you look at only players who had long careers, you could very well come up with a peak of 28. As has been discussed repeatedly here and at Tango's site in the context of baseball aging, when you look only at players with long careers, you're sampling only those who aged more gracefully then others. And so your peak will be biased high.

Also, a player with a long career is probably a full-time player for most of it. Suppose someone comes up at 23 and plays until 33. His first couple of seasons and last couple of seasons, he might be a part-time player; the middle seasons, he's full-time, with only minor variations in minutes. So his minutes curve looks like: low horizontal line, high horizontal line, low horizontal line. If you try to draw a smooth curve to that, it'll peak right in the middle, which, for our example, is age 28.

The idea is: there's only so much playing time you can give to a good player. You might give him 40 minutes a game at age 28, when he's still very, very, good ... but you can't give him 50 minutes a game when he's 24 and brilliant. So the curve is roughly flat in a good player's prime, and the off-years at the beginning and the end will artificially make it look like there's a peak in the middle.

Anyway, this is all speculation until Berri and Schmidt post the study.

The average minute in the above table occurs at age 26.6 -- below the 28 that Berri and Schmidt talk about, but above the 24 that they say it should be. It makes sense that it should be well above 24. A good player might still be in the league ten years after the peak, at age 34 -- but there's no way he'd be in the league ten years before the peak, at age 14. If a player can play when he's old, but not when he's young, that, obviously, will skew the mean above the peak of 23-24.

There are probably other reasons, too, but I think that's the main one.

Berri and Schmidt think that NBA minutes peak later than 24 because coaches don't understand how players age. It seems obvious that there's a more plausible explanation -- that it's because players like Shaquille O'Neal are able to play NBA basketball at age 37, but not at age 9.