Paul Pudaite writes:
I demonstrate that repetition heats players up, while interruption cools players down in NBA free throw shooting. My analysis also suggests that fatigue and stress come into play. If, as seems likely, all four of these effects have comparable impact on field goal shooting, they would justify strategic choices throughout a basketball game that take into account the hot hand. More generally my analysis motivates approaching causal investigation of the variation in the quality of all types of human performance by seeking to operationalize and measure these effects. Viewing the hot hand as a dynamic, causal process motivates an alternative application of the concept of the hot hand: instead of trying to detect which player happens to be hot at the moment, promote that which heats up you and your allies.
Pudaite says his paper is related to this post (and also, of course, this).
If you’re dead, you can’t shoot free throws very well; percentage is very low. Ergo, definitely helps to warm up at least a bit; just be sure to keep body temp below 101F…
Has anyone managed to construct a machine that makes 100% of free throws?
What’s the time-scale?
From Churchland, Afshar and Shenoy (2006):
Seventy isn’t really that impressive, people can make that many in a row in a couple minutes…
http://www.recordholders.org/en/list/freethrows.html
Whoa:
Hi, I’m Ted St. Martin, I’ve held the world record for free throw shooting for over 25 years. The current record is 5,221, this was done on April 28th of 1996, it took 7 hours and 20 minutes, with timeout only to drink some fluids
https://www.youtube.com/watch?v=Z23phgx6y1U
Not quite a Rick Barry granny shot, but it sure is ugly!
Interesting that St Martin (the current record holder) set the record when he was 60 and the previous record holder set it at 72. More years to practice?
Junior year of high school (previous century) I and my gang of fellow delinquents thought it would be cool to build a catapult as an extracurricular project. We had visions of hurling pumpkins into the clouds, but the administration (back then, The Man) let us know that launching anything bigger than a ping pong ball would have serious repercussions on our rear ends (so you know this was long, long ago). But you can’t cultivate interesting amounts of mischief without ingenuity so we countered with a launcher of basketballs, said project woven with appropriate buzzwords from athletics and physics so as to establish sober intent. They bought it, so we slapped together something resembling (if memory serves) some sort of catapult/ballista hybrid (research, we don’t need no stinkin’ research). Coach was curious enough to supply us with the balls and a freshman retriever. It took us two hours of tinkering and fiddling and positioning, but then, from the foul line, we dropped something like fifty in a row. Then we called it a day for two reasons: 1. To get those consecutive fifty we threw over 200 times. It got boring as hell. And 2. setting up the launcher over and over turned out to be hard work. The whole thing excessively challenged both our attention spans and our “work ethic”, and if we were never going to get to fling a VW Beetle over the administration building, then to heck with the whole thing. It never occurred to anybody that this might be pioneering or record setting, and I had forgotten all about it until now.
Interesting approach. Quick comments here.
I see Paul Pudaite is aware of Jeremy Arkes’ free throw paper, that is good. There are some omissions though.
The Pudaite says:
1. On the weak identification point: In the 2014 version of this paper ] this point is made (appendix); weak identification was first discussed on this blog in 2014, point #3 here
2. On players shooting better on the second shot: Bob Wardrop’s 1995 study of free throw data finds evidence of this “heating up” or calibration. Here is the study on Fermat’s library. This was replicated in the by Yaari & Eisenmann in this 2011 paper, whom also replicated Arkes’ work. In Bob Wardrop’s paper he has a nice conjecture how to justify people’s hot hand beliefs: When the average is fan is asked if a player is more likely to hit shot after hitting a few shots in a row, the fan says yes, and is giving a reasonable answer given the way the question was asked. If one were to pool together all the instances in which a shooter hit a few shots in a row, this is a true statement due to the aggregation bias commonly known as Simpson’s paradox. I fan watching the game, might feel the same. [of course this doesn’t explain why fans believe certain players are streaky, but that can be justified in this paper ]
3. There is more evidence on heating up. Across all controlled and semi-controlled studies, we find players shoot worse in their first few shots, even after they have an opportunity to warm-up, this includes the NBA’s Three Point Contest.
4. On free throws there is more somewhat related work. For example players shoot better in the second half of the season this paper (page 10). Goldman and Rao find a home vs. away effect in this paper.
Joshua:
I asked the foll. in comments to an older post, but I don’t think you saw it…
Where exactly in your MS paper are the results for computing the bias when k>1?
I gather there’s no neat formula except when k=1, but you can easily calculate
it for any specific k,n,p. Is that right?
anon:
yeah, didn’t see it. Too bad this wordpress doesn’t send notifications.
In this paper Appendix E (p. 47) we outline the approach. The basic idea is in the first paragraph, and the gory combinatorics follow that (though Lemma 2 is pretty cool and simple).
To answer your question, yes, for k>1 there is a formula, but it’s complicated and slow to calculate when n gets large. We use the formula in the paper, happy to share the matlab code if you email me privately. It’s been cross-validated with simulations for n=100, and both have been cross-validated with direct enumeration for n=10.
Thanks, Joshua!
I’ll add that to my reading todo list and perhaps email you in the (maybe far) future.
Riddle me this. If the hot hand doesn’t exist, why is there something called a heat check?
Whelp, apparently practitioners must be biased.
From How We Know What Isn’t So:
More specifically, on free throws, here is a doozy from 2 weeks ago on Barry Ritholz’s podcast
Premise: a truly random arrangement of hits and misses contains a number of streaks of various lengths
Conclusion: belief in the hot hand should be held most strongly by those closest to the game
I don’t see why???
I guess he means that the practitioner is: (i) pre-disposed to believe in the hot hand, and (ii) paying attention to everything. If this is true then the practitioner will be around when all the streaks happen, and attribute them to the hot hand. A casual observer may miss those rare occasions when the streaks happen. By analogy, if I watch 100 coin flips, it’s unlikely I’ll witness a long streak, but if I watch 10,000 flips, it’s a lot more likely. Those rare events become a part of basketball lore, and contribute to the myth. That’s the story anyway, and it makes sense if you buy the coin flip analogy.
The literature and debate surrounding the hot-hand always has been interesting to me. As a former Junior/University hockey goaltender you would be unable to convince me that confidence doesn’t affect performance; and surely my good/bad play and wins/losses (not necessarily the same thing) both had a significant impact on my confidence. Consequently, I could not have been and can never be convinced a hot-hand effect is not real in sport. It just doesn’t compute at any fundamental level; my prior is strictly 0 for the hot hand not being a real phenomenon. What I always took the original result to mean is that there is probably less of an effect than that perceived by the player because of their closeness to the streaks you describe (slightly different setup in hockey but surely comparable).
Allan:
Your take on the original result was not how the authors took it, or how it was taken by the subsequent literature and popular culture.
Your take seems reasonable based on casual observation, but even this take is not supported by the evidence the original study. In fact, there is no way to know whether people exaggerate the hot hand or not. The lay and professional belief in the hot hand appears to correspond to the subjective probability that a player will make a shot conditional on the player being “hot”/”in rhythm”/”in the zone”; it is impossible to test whether this belief is exaggerated or not due to a form of measurement error we first discussed in this email to Andrew Gelman in 2014, and elaborated upon in our “Surprised” paper in the Appendix titled “Appendix: Size of the bias when the DGP is hot hand/streak shooting”.
The most one can potentially show is that basketball practitioners exaggerate the diagnostic value of streaks; this is likely true as they sort of admit this themselves, without any need of academic researcher telling them that they are doing it wrong, and that they suffer from a cognitive illusion.
Josh:
Ironic that a book called “How We Know What Isn’t So” has something the author thinks he and his colleagues know, but actually isn’t so.
i think applied bayesians call it ‘burn-in’ or the hipper… ‘warm up phase’
http://gelmanstatdev.wpengine.com/2017/12/15/burn-vs-warm-iterative-simulation-algorithms/
The hot hand made it into Game of Zones. Game over!
http://bleacherreport.com/articles/2761164-game-of-zones-special-barack-obama-invades-goz-saves-sam-hinkie
In some (more limited) analysis on a player-by-player basis I also found similar effects – in particular it appears that many players perform markedly worse on their first free throw: https://royalsocietypublishing.org/doi/10.1098/rsos.182174 Some reader(s) of this blog probably reviewed my manuscript at some point so thanks if you did.