APBRmetrics

It's a little more directly interpretable in your first regression. In the last chunk of regulation (coded 0 by your description), there's about an 7.97% chance of Duncan being mentioned if the game is tied (i.e., that's just the intercept). If the Spurs were up 10, there's still a 7.91ish %chance. That doesn't strike me as 'big', but maybe others disagree.

xkonk wrote:It's a little more directly interpretable in your first regression. In the last chunk of regulation (coded 0 by your description), there's about an 7.97% chance of Duncan being mentioned if the game is tied (i.e., that's just the intercept). If the Spurs were up 10, there's still a 7.91ish %chance. That doesn't strike me as 'big', but maybe others disagree.

The idea was to use the regression, some of Duncan's other stats, and the hypothesis that usage is driven by the team lead to produce an inferred usage curve, and then compare that to the usage curve that we actually see for Duncan.

With quick and dirty assumptions...
Duncan plays about 34.5 minutes per game, so let's assume that the ~ 0.11 average rate of mention that I have for him corresponds to that rate floor time.
That corresponds to a 0.71 duty. So let's say the duty rate is roughly 6.5 times the mention rate.

Duncan takes a shot about .435 times per minute (or .080 times per chunk)

Let's say, for example, that Duncan misses a shot in the first 'chunk' - so the spurs are - roughly speaking - 1 point behind.

when the spurs are 1 point behind he's .00025 times more likely to be mentioned,
so 6.5*.00025 times more likely to be on the floor,
so he spends 239*6.5*.00025 extra chunks on the floor
so he takes 239*6.5*.080*.00025 (about .03) extra shots over the course of the game.

That kind of calculation can be extended to produce a usage curve prediction, which can then (hopefully) be compared to published data.

So if Duncan stats the game with a missed shot - so the lead is -1, then, from the regression we'd expect him to take .03 extra shots (as calculated above). Let's assume that an average miss adds 0.015 to his shots per game on average, and a make subtracts -0.015. Duncan typically uses around 17.7 possessions shooting per game (15 FGA, 6.3 FTA).

Let's suppose Default make rate is 0.5. So, if Duncan is '-1' on a game, we'd naively expect him to take 17.715 shots and and make 8.33575 - a rate of 0.471, and when he breaks even we expect 17.7 shots with 8.35 made - a rate of 0.5. That corresponds to a slope of 1.88, which is way too big. I guess things need to be done in a more sophisticated fashion.

Using the same logic as Eli did in his original study, I think we could find more accurate and reliable skill curve numbers if we separated players into groups depending on what role they played on offense. a spot up three type player is going to have a completely different trajectory than a big man who only gets put backs.

If role is considered, I'd suggest that age be considered as well.