While I know that there's no great love for basketball in these parts, I can't let Jonah Lehrer's post on the "Hot Hand" go without comment. It's about a paper analyzing the statistics of jump shooting, which finds that contrary to popular belief among basketball players, they don't really get "hot" in a statistically significant way. In fact, in some cases, they found the opposite:
The 76ers were shocked by the evidence. Andrew Toney, the shooting guard, was particularly hard to convince: he was sure that he was a streaky shooter, and went through distinct "hot" and "cold" periods. But the numbers told a different story. During the regular season, Tooney made 46 percent of all of his shots. After hitting three shots in a row--a sure sign that he was now "in the zone"--Tooney's field goal percentage dropped to 34 percent. (Ironically, when Tooney thought he was "hot" he was actually more likely to miss a shot.) The opposite phenomenon was also true: after missing three shots in a row, Tooney made 52 percent of his shots, which was significantly higher than his normal average.
Of course, this should make perfect sense to anyone who plays the game. When you get "hot," you feel like anything you throw up will go in, and you start taking shots that you wouldn't otherwise. I had a stretch earlier this fall where I was shooting about 75% while drifting out of bounds on the right-side baseline. Once I noticed that, I threw up some awful crap from that area, and quickly beat that percentage down...
On the other hand, when you get "cold," you're less likely to shoot anything other than a wide open lay-up. It's one of my standard rules for pick-up games-- if the first few shots don't drop, just rebound and play defense, and let somebody else shoot.
I haven't looked at the actual paper yet, but I may check it out, because I'm curious to see what if anything they did about the influence of defense. After all, shooting in a basketball game isn't actually a random process-- the players on the other team are actively trying to stop you from scoring, and you might reasonably expect the defense to have a significant influence on the shooting percentage.
Oh, wait. Their data were from the 1985 NBA season. Never mind.
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problem with the whole statistics thing is that each shot is NOT an identical sample!!!! Ya got layups, jumpers, jumpers where no ones on you, jumpers where theres two dudes in your face.......
And besides streaks and hot hands, what about clutch? Why DID Bird usually manage to make those real important shots. Do great players shooting percentage go up in clutch situations?
Basketball players and shots are not identically weighted coins. Course you have to start there probably but........
The real key is CORRELATIONS. What is the probability you make the shot given you made the one before? What is th probability you made the shot given you didn't make the one before??? So Toney's percentage goes back down after a 3 shot run. Well it has to go down at SOME POINT or the average would go up. The very nature of what an average IS means the streak has to end!!!! But what is the correlation length/time???? FOr TOney, evidentally it was 3 shots. So make one, take 3, wait awhile....Is that a winning strategy????
As Chad said - there are not similar conditions either - if the defense sees somebody starting to make shots - well they'll adjust, and start to cover closer or try to force to positions they know the guy doen't like. In fact looking at the article I had always understood it wrong. The data there do show a correlation to past shots, which is opposite what I had always heard. It is fairly meaningless because of the non-independent nature of things, obviously there will be regression to the mean. A streak could just be the defense letting you get to your favorite location on the floor and then stopping. I would think that the free throw example should be more independent. They are each similar so there should be a more non-correlated probability. Although people do get tired, start making some physical mistake, etc.
I posted this on Jonah's site so I will repeat it here.
I'm sorry but there is a big difference between calculating the odds of a coin coming up heads and calculating the odds of a basketball player making a shot.
The difference is inert vs living. People have emotions. People have days when they haven't had enough sleep, or too much sugar or carb. People react to stress by producing adrenelin which affects coordination and concentration.
If you have ever played a sport under competitive conditions or even ever listened to interviews with pro, or college, athletes, you know that "nerves" are a big factor. So, an athlete, during the course of a game can go up and down in terms of energy, concentration, coordination and confidence. That is why some people are the ones that can make the crucial shot while others can't. And that is also why athletes will get "in the zone" sometimes. It is more than statistical. Pennies do not have phyiological or emotional responses.
Sorry, it is a real phenomenon.
Ahhh... This was a frequent Biz School Stats class discussion topic. When they re-analyzed the 1985 study to consider only shots taken in close temporal proximity, there was only one man who truly had the "hot hand": Vinnie "the Microwave" Johnson. He heated up fast.
...Or maybe not. Vinnie's "hot hand" was mainly due to a 7 for 7 streak that, upon review of game videos, turns out not to have happened. He missed once in the middle of the streak.
Regardless, as a Dr. J and Sixer fan (and Celtic hater) as a kid, Andrew Toney was the man.
Yes Karl, you posted it on Jonah's site and I'l just repeat the fisking you got there. Discussion of mechanisms is irrelevant when the purported phenomenon is shown to not occur, and that's what the study shows.
If "the zone" theory were true, we would see an increase in shooting percentages, or whatever the performance measure is, after some number of successes (whatever indicates being "in the zone"). Those doing the study did not, and in fact found the opposite, which makes a lot more sense for reasons others have posted - particularly the behavior of the opposition.
Human beings are notorious for seeing patterns where there are none, and assuming erroneously that any series of successes is nonrandom when it is very random. The fact that it may apply to their own performance is irrelevant. Perceptions and instincts, which drive the thinking of most people on these issues, tend to be very inaccurate, which is why we need to do studies and get actual data in the first place.