EvanZ wrote:So, the question I would ask you guys is which play types do you think are influenced by or depend on the shot clock? Could it be that ISO and BALL are plays that are created more towards the end of shot clock and thus contribute to the effect being discussed? Or are all these plays evenly distributed throughout the shot clock. This is similar to schtevie's line of thought, except drilling a bit deeper to get down to the level of individual plays.
It would be interesting to know if there is any correlation between play types and elapsed clock time. I suppose my prior is that there needn't be any such correlation, in the sense that, to a first approximation, each (half court) play type probably takes about the same amount of time, as a realized NBA average. This is surely not to say, however, that the amount of time taken by each type of play is a constant, nor that realized play time isn't related to its productivity (
http://www.82games.com/dribbles.htm).
But let me take a step back and add a few general words of context about plays (and play types) and their general relationship to optimal shot selection theory. Simple stuff. Intuitive stuff. But my guess is not an approach that directly guides much NBA thinking.
Back in the days of yore, when I was pondering and scribbling about these issues, I found plays or "looks", rather than shot clock time remaining, to be the preferred mode for addressing offensive optimization. Though shot clock time, of course, is the ultimate disciplinarian, the relevant framework is how many looks an offense can generate within that allotted period.
According to this general theoretical construct (aside from an independent improvement in the scoring chances at any particular look) there are three ways in which an offense can improve itself. It can:
(1) Increase the number of plays/"looks" within the shot clock. Each additional look affording the offense one more opportunity for an above average scoring opportunity.
(2) For a "set" offense (i.e. a given number of looks) improve shot selection at each look (what has been the primary topic of discussion here, and I think, it is fair to say, the primary point of emphasis of Brian's paper).
(3) Optimize within the offense (defined by a set number of looks) in terms of reshuffling the order of looks.
It is this last point that relates to the concept of "play types". A simple example provides an illustration. Suppose an offense consists of only two looks before the shot clock runs out (and we are abstracting here from fouls, offensive rebounds, etc.). These are a possible alleyoop and a jump shot, each having the exact same expected efficiency, ex ante, of 0.5.
But these play types are not otherwise equal. The jump shot can be attempted regardless of circumstance. The alleyoop however cannot. Either the pass can be made (in which case the passer makes it) which happens 50% of the time (at which point the ball is dunked with a success rate of 100%) or the scorer doesn't get free and the pass isn't made.
So, the question is what is the optimal order of looks for this offense, and the answer is obvious. You run the alleyoop first followed by the jumper and get an offense that overall shoots 75%. The reverse, as an alternative, yields but 50%.
This example, of course, is contrived, but it illustrates an important point. What it says is that you want to organize an offense so as to give early looks to those players that have greater probability mass in the upper tail of the shot distribution (as long as they aren't sinks, of course, who won't move the ball along if the good shot opportunity doesn't obtain, or are more likely to turn the ball over, counteracting the potential scoring gains). All else equal, picking off these "upper tails", in rank order, is the key to optimizing on (3).
Hopefully, in the glorious future, we will begin to see data organized so as to address some of these issues. Until then, I suspect no one will be dislodged from their prior beliefs about how optimal NBA offensive organization/decision-making is.
