APBRmetrics

This new study claims to have identified "hot hand" patterns in NBA 3-point competitions: http://papers.ssrn.com/sol3/papers.cfm? ... id=2611987.

And the kool kidz seem to think the hot hand is now a non-fallacy: http://www.vox.com/2015/6/3/8719731/hot-hand-fallacy.

Thoughts?

For those interested, I published an article on the existence of hot hands in the 3-point competition (and home run derby) a couple years ago.

http://onlinelibrary.wiley.com/doi/10.1 ... 9/abstract

Another shocking revelation: The Earth revolves around the Sun!

Actually, it is pretty shocking. Years of research have shown little or no hot hand effect, across multiple sports.

And I'm not sure I buy this finding.....

There's been a lot of studies showing that hot hand may in fact exist... not that shocking.

http://www.sloansportsconference.com/wp ... proach.pdf

The Vox article has a mention at the end of a lack of a 'cold hand'. It's hard for me to think of a mechanism that would (convincingly) create a hot hand but not a cold hand. Any ideas?

There's been a lot of studies showing that hot hand may in fact exist.

I think a more accurate summary would be that there have been a handful of recent studies purporting to discover a hot hand study. Usually, they involve very sophisticated statistical techniques that unearth what are, at most, small hot hand patterns (and could well be something else). The linked study is interesting, but the finding rests entirely on accepting the idea they are able to perfectly measure and control for the true level of shot difficulty, which may or may not be true.

The three-point study only shows that shooters' true talent varies, within and/or between different annual contests. At least two possible explanations immediately present themselves: 1) at least some players shoot better from certain spots on the floor than from other locations; and 2) some players were better 3-point shooters one year they participated than in the other(s). Both seem quite possible, if not likely. The big spreads in FG% we see for some players based on floor location could be chance, I suppose, but it certainly seems players often have "sweet spots."

Alex: that's a really good question. One answer is that because these guys shoot 54%, hot streaks are almost twice as likely to occur as cold streaks, increasing statistical power for the former if I'm thinking about this correctly. And if I'm right that some players have a sweet spot they shoot well from, that could help explain the pattern too -- but only if they don't have an offsetting "cold spot".

Guy wrote:

And if I'm right that some players have a sweet spot they shoot well from, that could help explain the pattern too -- but only if they don't have an offsetting "cold spot".

A sweet spot is an interesting idea. The ones that always leap to mind for me probably fall into the category of what you describe as 'not completely controlled for' shot difficulty. Something like the guy has a favorable match-up, for whatever reason. Or the micro level of what you describe for the 3 point study, some nights a player just feels good and is actually shooting better than other nights.

The counter to those, of course, is that sometimes a player should have a bad match-up, or feel bad and have a bad shooting night. If those 'cold hand' nights don't show up in the data, it makes me wonder if maybe cold nights get selected out: players who are going to have a cold night don't get the opportunity to shoot (due to their own actions, teammates, coaches, whatever). If there's a selection bias like this going on, you would have an artificial, but practical, hot hand effect.

Seems the "hot hand" as it is traditionally used is a completely different animal than in the context of a three-point competition or home run derby. I'd be surprised if anyone debates that you can get dialed in to a repetitive task. Snowballing recent success when you are taking shots from different spots on the floor after bouts of playing defense and navigating screens in between seems much more difficult.

Has anyone studied whether players do vary in their success rate on 3s from different points around the arc? Obviously, in any given year a player will often have much more success from one location (say, a specific corner), but that could be random variation and/or differential defensive pressure. Do people think it's plausible that some players just shoot better from specific spots, in a context where defensive pressure isn't a factor? If so, that alone could explain the results of the recent study.

I went back and looked at the Sloan paper linked above. The results are really quite underwhelming. Their finding is that a player who makes four consecutive shots increases his expected FG% on his next shot by about one point (if he's a 50% shooter, we now expect him to shoot 51%). And that's if you believe they have controlled fully for shot difficulty! That is very hard to do, despite their impressive effort. One obvious explanation for their result is that players sometimes match up well against a specific defender, beyond what the two players' heights and other controlled factors can capture. In that case, the player will be more likely to be hot, and also more likely to make the next shot, creating the illusion of a relationship. Playing at home could have the same impact, and as best I can tell HFA is not controlled for. Honestly, it's shocking they don't find a larger effect than they do, given that any uncontrolled factor that improves the player's efficiency in a given game will tend to create a positive coefficient for their "heat" variable. I would say the paper is very strong evidence that the hot hand effect is either non-existent or very small, and therefore confirms the long-held finding that the perception of a hot hand (by both players and fans) is a kind of cognitive failure.

I wonder if from a Bayesian perspective (which few, if any, of these articles seem to embrace) we would see "hot handedness" simply as another intrinsic parameter of "shooter quality". It makes perfect sense to me that some individuals have more tendency to go on runs while others do not. The effect may not be very large, and it may easily be missed given the "experiments" that have been done previously.

Guy wrote: Thoughts?

Well, I just created 100 random samples of 33 players taking 166 shots at the respective hit rates reported in table 1. Guess what? In all of those 100 samples I found an increased performance level after hitting 3+ shots in a row ranging between +0.001 and +0.074 with an average of +0.037. Just to be on the safe side I ran that experiment again, this time the performance level increased over base rate from +0.002 to +0.078 with an average of +0.043. Well, third time's a charm? +0.000 to +0.081 with an average of +0.039. I might be biased, but I would argue that my computer has a hot hand ...

Do you mean that you pooled all 33 players together into a single sample (and then did that 100 times)? If so, that would certainly account for your result. Otherwise, you obviously aren't generating truly random samples...

I mean that I created a random sample of 33 different shooting sequences based on the reported hit rates where each sequence has 166 shots. Then I applied the method described in the paper to those sequences and got those average values. Overall I now have 300 of such 33-player-sample and each showed a higher performance level after 3+ makes than the base rate ranging from +0.000 to +0.081. The results are also significant at the p<0.05 level, which is obvisiouly a result of the experiment's design.

One shooting sequence looks like this:
Where 1 is a make while 0 is a miss. This example is based on Craig Hodges 56% hit rate. One sample contains 33 such sequences each based on those individual hit rates from table 1.

I can't pinpoint the reason, but it seems that the results are rather based on the experiment's design than truly showing an effect. Because I thought it might be explained by the higher than 50% rate of the shooters, I tried a sample with a decreased hit rate of in average 0.5 instead of 0.543, but a similar result showed up: +0.000 to +0.087 with an average of +0.047.

Are you comparing the hit rate after 3 makes to each "player's" expectation, or to the overall average of 54%? If it's the latter, that would explain your result: the better shooters will generate a disproportionate share of the streaks of 3 makes, and their expectation on the next shot will be higher than average. But if you are comparing the post-streak hit rate within each 166-shot sample to that player's specific hit rate, then your result doesn't make sense (your randomization process must have some non-random element).