APBRmetrics

Shucks. I think I've left the hard work for you but maybe I will have some further reaction to your expertise that might be of some value.

I am the son of a nuclear chemist but I made the choice / mistake of studying applied social sciences.

Was thinking about the study presented at Sloan last year about "guarded" vs. "unguarded" shots. Tried to google it...ended up finding Beckley Mason quoting Brett Hainline quoting Sandy Weil...

http://hoopspeak.com/2011/03/optical-tr ... 9-offense/

From the breakout box:

The three primary results of Weil’s poring through the data and accounting for things like historical player shooting percentages, distance, and shot type:

•Tight defense (within three feet) drops expected shooting 12 percentage points (a 50 percent shot becomes a 38 percent shot).
•Field goal percentage drops one percentage point for every 1.5 feet from the rim.
•There is something beneficial about the catch and shoot, beyond expectations.

It’s that last one that is most fascinating to me: There is now empirical proof that crisp ball movement can result in a better outcome for the offense. Weil’s data shows that even when accounting for the defender’s proximity, the field goal percentage on catch and shoot plays was higher than expected for the distance of the shot. The new optical data is detailed enough to give the knowledge of how a player got the ball, how long he had it, what the last action was before a shot (dribble, pass, etc), and where the defense was a second before a player received the ball and then as he catches it.

The study in the original post may be lacking some important information regarding "tight defense" and open looks. Don't think anyone would suggest it's better for a poor shooter to quickly shoot a guarded shot, regardless of how much time is left on the clock. I've been trying to watch possessions tonight with an eye on the shot clock. Looks like teams are agressively trying to create open looks for themselves, or at least good opportunities in close that can be kicked out to shooters. I'm not seeing any shooters passing up open looks because it's early in the shot clock (unless they're sitting on a big lead and TRYING to run clock because running clock is the most optimal thing at that moment in terms of the win). It's like the shot clock is irrelevant except when teams have to force something up at the end.

Is it possible that "optimal" team shooting is almost all about the name of the shooter, the spot on the floor, and whether or not he's guarded..that "optimal" really doesn't much involve the shot clock in a meaningful way in terms of the choices offenses are making?

add to our previous exchange, this:

"the royal jelly"

http://espn.go.com/espnradio/play?id=7510545

http://www.dailythunder.com/2012/01/the ... yal-jelly/




On John Wall "potential MVP" though...

in the bottom dozen players in the league who play 25+ minutes per game on FG% from 16-23 feet this season

his eFG% from outside of "close" is 25%

16th worst Offensive Rating amongst players in the league who play 25+ minutes per game

WS / 48 of 0.022

7th worst in the league on non-prior informed RAPM for this season

on prior informed RAPM for this season he is 5th worst

long climb up from there...

Really interesting article.
One thing jumped to mind reading it. Would limiting the domain to exclude fast breaks and offensive rebound put backs on the early end and garbage shots to avoid the shot clock violation (just the last few seconds) be useful? The same article is being discussed on another forum (granted, I think they only read the articles about your article) and it seems to viewed as something already known, mostly because fast breaks are efficient and garbage shots at the end of the clock aren't. If there was a domain where it's reasonable to assume a set half court offense is underway, can the same general conclusion be drawn?

beards, I mentioned that earlier in the discussion. It would make sense to focus on possessions after made field goals.

Whoops. That you did. I think the first time I read that I didn't understand that it would significantly reduce the fast break issue as well, not just the offensive rebounds. I'm sure the shot clock winding down scenario (last few seconds) is small compared with the transition and offensive rebounds, so limiting to after made field goals would be a smart way to do that.

from the article:

"The comparison highlights some limitations of the theoretical model, while also suggesting that NBA teams may be overly reluctant to shoot the ball early in the shot clock."

NBA teams may be overly reluctant to shoot the ball but in a more complex model accounting for some of the things I mentioned (and perhaps other things-such as perhaps the defense sagging inside more early in the shot clock than they are able to later?), I think there is a pretty good chance the finding drifts back to current practice being more rational than in this initial analysis.

I hope the author pursues a more robust model, in the meantime reminds the media of the "may" associated with the finding from this fairly simple model and let us know if the finding of the first study holds up or changes with an even more sophisticiated model.

As per the suggestions made by some of you, I broke down the shooting rate and points per shot a little more based on how the possession began. The results are below. Basically, I found that possessions beginning with a defensive rebound have much higher shooting rates early in the shot clock. In other words, it looks like the offense gets started sooner when the possession begins with a defensive rebound. I guess there's nothing surprising about this.



Strangely, shots that begin with a defensive rebound also have a significantly lower success rate during the law few seconds of the shot clock. This might be because possessions that get started sooner have already exhausted their best options by the time the last few seconds of shot clock roll around, so those last few seconds represent more desperate attempts.

And Crow, I appreciate you making clear that this paper is very speculative, and its methods are very theoretical. The tentative conclusion about NBA players can at best be preceded by "may". I apologize for some of the more misleading media stories that have headlines like "shoot earlier for better success in the NBA". I really did try my best to remind anyone who asked me that this research was still very much in the theoretical stage and should only be compared to data with great caution.

After thinking about the model some more since the time the paper was accepted for publication, I think I'm ready to say that I have very little confidence in the conclusion that NBA players "undershoot". Much of the paper is still useful, I think, but the assumption that shot opportunities arise at some uniform rate in time is not a very good one. If this assumption can be replaced with something a little more intelligent, then I think the paper can be improved significantly.

Does anyone have any good ideas for how this can be done? How can I figure out the probability (density function) that a shot opportunity will arise when there are t seconds left on the shot clock?

I assumed the media was looking for more certainty than you really gave them.

Hope you find the right technique to build upon your mathematical foundation.

gravityandlevity wrote: Basically, I found that possessions beginning with a defensive rebound have much higher shooting rates early in the shot clock. In other words, it looks like the offense gets started sooner when the possession begins with a defensive rebound. I guess there's nothing surprising about this.

Do you mean the shots come earlier in the shot clock AND they are more efficient?

Does anyone have any good ideas for how this can be done? How can I figure out the probability (density function) that a shot opportunity will arise when there are t seconds left on the shot clock?

What is the empirical shot distribution? I assumed it would be normally distributed around 12 seconds, if you just look the shots after a made field goal (oh, and of course, ignoring the handful of shots coming off a missed And1 rebounded by the offensive team!).

I think the issue is that there is no causation in the data why a shot is taken and why not. That a fastbreak is the most efficient scoring opportunity is indeed nothing new. BUT the opportunity for a fastbreak depends not only on the willingness of the players to shoot the ball early, but also on the ability of the transition defense. If all teams would shoot the ball early while ignoring the defense, it will likely even out, you would have more shots and less efficiency earlier in the shot clock.

Well, my rule of thumb would be that a player should take the first really open opportunity to shoot the ball, only passing it up, if a better shooter is also open and easily to reach via passing. That's meant as rule for a real halfcourt set. I think the numbers support that when we look at the 15 sec mark and beyond. The efficiency goes down towards the end of the possession. I would argue that coaches in the NBA are mostly teaching that rule of thumb already. From the 5sec mark on I guess those are shots forced by the opponents defense, meaning, the defense was good enough to prevent an earlier shot attempt.

Excellent synopsis by Mystic.

gravityandlevity--could you also post the number of shots taken (the sample size) at each point in the shotclock?

mystic, great synopsis of the problem. That was exactly the issue I had. How do I infer "shots that were available to take" when the record shows only "shots that were taken"?

Here's the table I used to make the plot above. The data comes from 4720 games during the 2006-2007 through 2009-2010 seasons, taken from Ryan Parker's archive at basketballgeek.com. The first column shows the shot clock time t (rounded up to the nearest second). The first entry of the second column shows the total number of possessions for which the shot clock time could be inferred (no shots immediately following an offensive rebound or a defensive foul, and nothing during end-of-quarter situations, for example). Subsequent entries in the second column show the number of possessions for which the show had not been taken by time t. The third column shows the total number of shots taken during the second t. The fourth column shows the number of points scored by shots taken at time t.

Here is the table first for all shots:
Here is the same table for shots off dead-ball situations only:
And here it is for possessions that begin from defensive rebounds:

Something to think about. The "type" of shot distribution would be interesting as well, particularly whether it was assisted or not. I suspect that distribution would start moderate, trend higher, then drop off at the end of the shot clock.

It's well known that assisted shot attempts have a higher success rate; I suspect a non-assisted shot is available at nearly any point in the shot clock (it only takes an instant to hoist a non-assisted shot), while creating an assisted shot is the objective of the offense (in generality).