Per 36 and rate of attrition

[jagz]

When making player comparisons, the standard rebuttal to those who make per 36 arguments is the fatigue factor. As someone who believes per 36 is enormously important, I concede that the counter-argument is not without merit, and I would like to account for it (my purposes are not limited to casual interest; these considerations are critical to a research-oriented project I am undertaking).

I'm not even sure "rate of attrition" is the exact term I'm seeking or that there is a term for what I'm describing, but I would like to calculate the fatigue factor. Almost everything can be quantified or measured in sports, and I'm wondering if there is a single method or formula that can project the expected decrease in performance level when a player logs a given number of extra minutes (incidentally, it's obvious per 36 is less relevant if you're talking about a player who plays 20 minutes vs one who plays 40 minutes or a role player vs a star; what I'm interested in is, say, a hypothetical case where one star may play 35 minutes or so and another plays like 40 minutes).

If this is too vague, and it will help you answer my question, I can provide example(s) of Player A vs Player B numbers.

[mopper8]

The problem is that its going to be different for different players, and a guy's minutes are going to be a reflection of things other than his stamina - e.g., Lebron played huge minutes in the playoffs last season, probably won't this season, and that's because Miller/Haslem being healthy + addition of Battier means he doesn't have to play 43 mpg. But he obviously can, at least for some stretch of time (he looked gassed in the Finals)

On the flipside, the Heat track this stuff closely and some beat writers said they had hard data that Michael Beasley's production just fell off the planet if he played longer than 9 minute stretches. He basically useless in minutes 10, 11, 12, etc. And they knew how many minutes of rest he needed before he could come back effectively as well. I'm sure they have that info on all their players, at least as best as they can muster. But for some guys, it might not be so clear cut

[giberish]

The problem is that its going to be different for different players, and a guy's minutes are going to be a reflection of things other than his stamina - e.g., Lebron played huge minutes in the playoffs last season, probably won't this season, and that's because Miller/Haslem being healthy + addition of Battier means he doesn't have to play 43 mpg. But he obviously can, at least for some stretch of time (he looked gassed in the Finals)

On the flipside, the Heat track this stuff closely and some beat writers said they had hard data that Michael Beasley's production just fell off the planet if he played longer than 9 minute stretches. He basically useless in minutes 10, 11, 12, etc. And they knew how many minutes of rest he needed before he could come back effectively as well. I'm sure they have that info on all their players, at least as best as they can muster. But for some guys, it might not be so clear cut

There also are differences between big minutes for one game, and minute differences for a season or extended run.

[Nivek]

Per 36 numbers aren't meant to be predictions of what Player X would produce if he actually played 36 minutes. They're a more convenient way of talking about per minute numbers than saying Player X averaged .555 points per minute. No one knows what .555 points per minute means, but even casual fans have a sense for what 20 points per 36 minutes means.

And, just to address a traditional counter-argument before it's made, per 36 minute stats are not extrapolations unless the player in question has fewer than 36 total minutes. Once the player breaks that 36-minute threshold, it's a per 36-minute average. Strictly speaking, we could take Kevin Garnett, for example, and give a per 10,000-minute average. It would be kinda silly, but it would still be an average (not an extrapolation) since he has 45,000+ career minutes.

If you're trying to project what a player might do if he were to have his playing time increased, a straight per minute average probably isn't the best approach. MikeG over at the APBRmetrics board posted some good ideas about how to go about it, though I don't remember his method.