## Wednesday, March 31, 2010

### 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.

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At Wednesday, April 07, 2010 1:29:00 PM,  Don Coffin said...

I think we may have an issue here about *what* we're measuring. The data you present is aggregate minutes played for all players of a particular age. Berri and Schmidt may be (I'm not sure about this because I haven't yet read their book) looking at average minutes played per player, or even average minutes per game by player age, which is something still different.

So that's three possible measures of playing time and age, and we might have three different expectations for which of these will be larger.

(a) If there is a larger number of 23 or 24 year-old players than of 27, 28, or 29 year old-players, then aggregate minutes played may be greater for the younger age groups.

(b) If younger players play more games per season, then, again, average seasonal minutes per player may be greater for younger players.

(c) But, then, there's minutes per game per player of different ages.

The question is, in looking at an aging pattern, which of these measures is most important? I'm not sure that I know what the answer to that is, but I suspect it's average player-minutes per season. I could be convinced that it's one of the other two measures, but that would take an argument for why something else is correct.

(Incidentally, did you wonder why aggregate minutes of 28-year-olds fell by about a third, compared with 27-year-olds in your table, and then rose, for 29-year-olds back to a higher level than for 27-year-olds? That pattern would make me wonder if there weren;t something weird about this year's data...)

At Wednesday, April 07, 2010 1:51:00 PM,  Phil Birnbaum said...

Right ... as I wrote, I'm not sure how Berri and Schmidt came up with 28. They do imply that they're following the trajectory of an individual player -- players get more minutes up to 28, and then start dropping.

If that's the case, then, I think, there's definitely selective sampling going on. Because, how else could 24-year-olds get more minutes than 28-year-olds? Couldn't happen unless the players with shorter careers are being dropped from the study.

That is: suppose (without loss of generality) that there are 100 players in the 24 group. That's 526 minutes each. And suppose that five years later the chart hasn't changed, and so they play 489 minutes each. That's a drop, not an increase! The only way you get an increase is if you count only players still active at 29. And that biases your results.

As for the 28-29 blip in the chart ... you're right, and I wonder what's going on there. It shouldn't affect any of the conclusions, I don't think.

At Wednesday, April 07, 2010 2:24:00 PM,  Don Coffin said...

Phil, I'm still not sure what you're using as your choice of a valid measure--aggregate minutes by age, average minutes per season by age, or average minutes per game by age.

Assume it's the last of there. Assume 100 players at age 24, averaging 24 minutes per game, appearing in an average of 60 games. That's:
(a) 144,000 aggregate minutes for 24-year-olds;
(b) an average of 1,440 per season for 24-year-olds; and
(c) an average of 24 minutes per game for 24-year-olds.

Now, if the best of those players remain in the league, there will be fewer (say, 60) players at age 28. If those players average 32 minutes per game and 75 games at age 28, then what would we observe:
(a') 135,000 aggregate minutes;
(b') an average of 2,250 nimutes per season;
(c') an average of 32 minutes per game.

Which of those three measured to you want to use? Two of them say 28-year-olds play more, one says they play less. (A result that I admitedly selected numbers to generate...these are NOT actual numbers.) We need to justify which measure we decide to use, don't we? Which measure lets understand the effect of aging on playing time better?

I think it's measure (b), but the argument that it's an artifact of better players surviving is a valid concern. But what if we observed only those players at age 24 and at age 28--if we constructed age-playing-time profiles for players? Is that a better of worse approach than simply aggregate minutes by age? Why or why not?

At Wednesday, April 07, 2010 2:26:00 PM,  Don Coffin said...

Er, that should be 30 minutes per game at age 28. Sorry about my typing ability...

At Wednesday, April 07, 2010 4:16:00 PM,  Phil Birnbaum said...

Hi, Doc,

The chart shown is aggregate minutes.

In your example, I would argue that you have to divide by 100, not 60. Why would you eliminate the guys who are out of the league at 28?

If you don't eliminate them, you could wind up with misleading results. Suppose your 100 guys are 99 bums and Michael Jordan. Jordan winds up having played 45 minutes at 24, and 44 minutes at 28. The other 99 guys play 25 minutes at 24, and zero at 28.

If you divide by the actual number of players, you get 24.21 minutes at 24, and 44 minutes at 28. It looks like playing time increased, even though every one of the 100 players got less time at 28 than at 24.

At Wednesday, April 07, 2010 5:28:00 PM,  Don Coffin said...

The problem I have with using aggregate playing time as a means of identifying the effects of *aging* is that it conflates age with player quality. In your example, the reason those 99 guys are no longer around is not because they got older--it's because they were lousy to begin with. They didn't *lose* playing time because they got older, they lost playing time because they were bad to begin with.

So the issue is pretty complicated, I think. And I think the only way to approachit is by looking at (and maybe aggregating, on the basis of some measures of player quality) individual player age-playing time profiles. If you do that, I think you're right that exceptional players (e.g., Jordan) will show little "aging" effect. Here's Jordan's M/G for his career:

Age..........MPG
21............38
22............25...(Injured)
23............40
24............40
25............40
26............39
27............37
28............39
29............39
31............39
32............38
33............38
34............39
38............35
39............37

On the other hand, here's above-average, but not great, forward Bobby Jones:

Age...........MPG
23............32
24............34
25............30
26............33
27............29
28............26
29............25
30............29
31............24
32............23
33............20
34............22

And here's Walter Russell, a guard out of Western Michigan, drafted by the Pistons, who also played for the Pacers (career 1982-88)

Age..........MPG
22............11
23............7
24............18
25............2
26............11
27............1

Three different patterns, with Jordan playing essentially arund 40 MPG throughout his career, Jones' playing time falling off fairly steadily once he passed 26, and Russell almost never playing. Jordan was great, Jones was good, and Russell was bad.

Why aggregate those three very disparate players to try to look at aging? Don't we want to look at aging conditional on (initial) player quality? Isn't it reasonable to conclude that superstars (Chamberlain played about 40 MPG throughout his career; Wes Unseld about 30; and so on) age differently than arevage players, and that schlubs should maybe be ignored altogether?

I do not see a particularly compelling justification for counting what happened to Walter Russell's playing time as a consequence of aging. I do see a justification for looking at Bobby Jones and Michael Jordan type players separately. (Incidentally, Shaq's career looks very much as one might expect--roughly stable--37-40 MPG from age 20 through age 31, with a slow decline since, to 30 MPG in 2008/09. So not even all superstars are equal.)

At Wednesday, April 07, 2010 8:54:00 PM,  Phil Birnbaum said...

>"I do not see a particularly compelling justification for counting what happened to Walter Russell's playing time as a consequence of aging."

Well, Russell was good enough to play in the NBA when he was around 24, but not good enough when he was 29. That tells you a lot about aging, doesn't it? I bet if you checked, you'd find a lot of NBA players with short careers centered around 24, but very few with short careers centered around 29.

>"Isn't it reasonable to conclude that superstars age differently than arevage players, and that schlubs should maybe be ignored altogether?"

Sure, if you like ... the problem is that you don't know if a player is a superstar or not until you've seen him age. If you look only after the fact, you're selectively sampling players who aged well, regardless of how good their careers were.

But I agree with you that superstars might be different ... you could check a bunch of players who are great between 22-23, and see how they age after that. But if you wait until they're 30 to see how they age, you're going to come to the conclusion that players in general age well, rather than the (justified) conclusion that players who manage to stay in the league until 30 have retrospectively aged well.

If that makes sense.

At Thursday, April 08, 2010 10:50:00 PM,  Unknown said...

Phil: Of course you have more people with short careers centered around age 24 than 29. NOBODY comes into the league at age 27 or 28!

There are many players as doc says who come into the league and are given a chance to play for a year or two before the coaches realize that their college talent didn't translate to NBA ability. Don't you understand all these college kids coming out, have the POTENTIAL to be good in the NBA, but the teams need to find out if they will realize that potential. This involves playing them...

So the study probably conditions on the players being "good" as doc guesses. Or more likely the players having an NBA career of say 5 years + (so aging will actually be a factor in their playing time). And if, even for merely a subset of all NBA players (but one could argue a very important subset) playing time peaks well after effectiveness peaks one could make the argument the authors do that NBA coaches underestimate the effects of aging. One could also argue the NBA coaches aren't playing such players enough when they are younger. Or one could argue that there is a natural gap between performance diminishing and minutes diminishing (ie you have to earn your way off the team just like you earned your way on it) although a 4 year gap seems like a long time to earn your way off the team...

Anyways, I'm just a grad student who stumbled his way onto this site and will stumble my way outta here now=)

At Friday, April 09, 2010 12:25:00 AM,  Phil Birnbaum said...

Hi, Robert,

That's a good point you raise -- since the peak is close to the entry age into the NBA, you don't really know if the player aged his way out of being in the NBA, or if he was never good enough in the first place.

But:

1. There are a lot of minutes for 21 to 23 year olds. You'd think a lot of the bad ones would get weeded out early, no? Your theory would explain a lot of minutes for 21-year-olds, but not so much a lot of minutes for 24-year-olds.

2. If it's true, as Berri and Schmidt say, that basketball players peak at 24, then that's perfectly consistent with Walter Russell's record. If you refuse to consider that confirmatory evidence, then you're *guaranteeing* that it'll look like players peak later. That is: you're considering only evidence on one side of the hypothesis. That can't be right.

At Friday, April 09, 2010 1:16:00 AM,  Unknown said...

I dunno about your first point. I would think actually that there are many NBA careers that consist of garbage minutes in the first year, an opportunity or two given in the second or third year, and then out of the league by the fourth or fifth. This profile would correspond to getting most of your playing time as a 23/24 year old, as also these players who are given a shot and don't succeed aren't likely to be the players coming in at the youngest ages of 19/20.

I agree there is bias in looking at only players with long careers, which lets define to be over five years. Namely, if your career lasts at least 5 years, that means it is quite likely your performance in your early years was at least decent, biasing you to an early peak in performance. I think you also raised an excellent point that I missed earlier about the upper bound on minutes per game. If, once we restrict ourselves to "good" players we note their performance goes down from age 24 to 28, but not their minutes, the coaches might not be doing anything wrong! Player X might be a worse player at 28 than 24 but if he is still the best player in the league, lets hope the coach is still playing him 40+min a game.

Those points aside, I still think such a four year gap is interesting to note! I also think such a low age for peak of performance is interesting in its own right, and is a good argument against the ridiculous age discrimination (the one and done rule and such) that I don't understand how the NBA gets away with.