Is the -hot hand- real? - Numberphile
video description
There are days when players are fully in the game; these are days when players are above their average. Days, one might say, that they had a hot hand.
If a player normally makes 60% of their shots then making 40% is a not a hot-hand day. If a player normally makes 30% of their shots (they're on the team for defense) but today makes 40% -- bingo! a hot-hand that day.
Depends on what is meant by -to have a hot hand. -
If a player is having a lucky streak -- not a skill streak -- shouldn't we avoid giving the ball to him? Skill is so much more dependable than luck.
Say a player makes 6 shots out of 10 attempts. When scrambled (1001110011) there a fixed number of each length of streak. In the example one of each length 1, 2 and 3. If a player scores 7 out of 10 the average streak length must be longer. A -streak- -- a -hot hand- -- may well indicate higher than ordinary skill, and not just luck.
Date: 2022-04-08
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Comments and reviews: 9
MachineCake
Like some others have said, I don't think these studies are using the correct definition for -hot hand. - A hot hand means that if you are shooting a higher percentage than you normally do at any point in the game, that the chances of making your next shot remain higher than your normal average. You could look at a player's shooting percentage at halftime, and if it is above average, then see if the percentage remains above average for the rest of the game or regresses to the average. The question is how often can you trust that if a player starts out shooting better than normal, that he will continue to do so. You might also consider that a hot streak could start late in the game, and instead of using full games, look at any set of consecutive shot attempts within a game of at least x attempts, where x is, say, half of the players normal attempts count, and if that set is above average 1/3 of the way in, does it stay above average for the rest of the set.
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Like some others have said, I don't think these studies are using the correct definition for -hot hand. - A hot hand means that if you are shooting a higher percentage than you normally do at any point in the game, that the chances of making your next shot remain higher than your normal average. You could look at a player's shooting percentage at halftime, and if it is above average, then see if the percentage remains above average for the rest of the game or regresses to the average. The question is how often can you trust that if a player starts out shooting better than normal, that he will continue to do so. You might also consider that a hot streak could start late in the game, and instead of using full games, look at any set of consecutive shot attempts within a game of at least x attempts, where x is, say, half of the players normal attempts count, and if that set is above average 1/3 of the way in, does it stay above average for the rest of the set.
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Bobby
Great video as always, but is the common definition of -in the zone- really just 100% accuracy? I have always considered it to be a boost in accuracy. If you use that definition and study the numbers, would you get different results? Obviously that would first require a measure of what a series of shots is considered. For instance, does Steph Curry normally shoot 3 shots within a 5 minute period or 6 shots? Does he shoot more when he thinks he is in the zone? Does his accuracy (shooting percentage in this case) increase from his average? Should a hot streak be capped by two misses in a row or >50% missed shots in a series of shots? If I feel like I'm in the zone, I don't lose the feeling with one miss; i assume that there was a variable that I didn't account for at the time.
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Great video as always, but is the common definition of -in the zone- really just 100% accuracy? I have always considered it to be a boost in accuracy. If you use that definition and study the numbers, would you get different results? Obviously that would first require a measure of what a series of shots is considered. For instance, does Steph Curry normally shoot 3 shots within a 5 minute period or 6 shots? Does he shoot more when he thinks he is in the zone? Does his accuracy (shooting percentage in this case) increase from his average? Should a hot streak be capped by two misses in a row or >50% missed shots in a series of shots? If I feel like I'm in the zone, I don't lose the feeling with one miss; i assume that there was a variable that I didn't account for at the time.
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Dylan
One of my favourite Numberphile videos.
That being said, I think in basketball looking for a hot hand shouldn't just be observed within a game, but it might also be very informative if the same checks for single players in each game were done for many players, but across a whole season.
I think by looking for streakiness not just compared to the rest of the same game (which probably has a Hot hand being carried from earlier streaks, but should be compared to an average game for that player in some way. Or maybe across a season we could compare the number of full games where a player is hot, using a permuted season divided into random games as the Null Hypothesis / baseline.
As a basketball fan I feel llike this bias would yield a much different story.
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One of my favourite Numberphile videos.
That being said, I think in basketball looking for a hot hand shouldn't just be observed within a game, but it might also be very informative if the same checks for single players in each game were done for many players, but across a whole season.
I think by looking for streakiness not just compared to the rest of the same game (which probably has a Hot hand being carried from earlier streaks, but should be compared to an average game for that player in some way. Or maybe across a season we could compare the number of full games where a player is hot, using a permuted season divided into random games as the Null Hypothesis / baseline.
As a basketball fan I feel llike this bias would yield a much different story.
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Bill
I call shenanigans. This (and tons of misguided comments) provide a great example of applying statistics to -prove- a point that is not provable by statistical process. (Actually, that is, -not provable- unless using the exhaustive set of inputs - and this one isn't even on that planet) As a smug sleight of hand artist (which I contend that most statisticians are, I could _statistically, _ _mathematically_ prove, based on samples (let's say, -randomised samples. - Yeah, they always go for that one) of millions of Golden Gate Bridge pedestrians - that you essentially cannot die from jumping off of it. There are lies, damn lies, and statistics. Beware of their pedantic, MSM sanctified and glorified nonsense: ) (You included, Nate -Clinton- Silver: ) )
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I call shenanigans. This (and tons of misguided comments) provide a great example of applying statistics to -prove- a point that is not provable by statistical process. (Actually, that is, -not provable- unless using the exhaustive set of inputs - and this one isn't even on that planet) As a smug sleight of hand artist (which I contend that most statisticians are, I could _statistically, _ _mathematically_ prove, based on samples (let's say, -randomised samples. - Yeah, they always go for that one) of millions of Golden Gate Bridge pedestrians - that you essentially cannot die from jumping off of it. There are lies, damn lies, and statistics. Beware of their pedantic, MSM sanctified and glorified nonsense: ) (You included, Nate -Clinton- Silver: ) )
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Raymak
Klay Thompson scored 37 points including 8/8 from 3, which was the most points and 3's ever scored in a single quarter in nba history. He also didn't even play the 4th quarter of that game. For reference his average is only just over 20 a game. When we say a basketball player has a hot hand it is also in reference to a short period of time within that game. It does not last a whole game. What you should be doing is looking at his most average game, take the string from that and compare that to his string from this game. I can guarantee you'll find the sets to be significantly different. On a side note seeing a numberphile video talking about the NBA literally made my day
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Klay Thompson scored 37 points including 8/8 from 3, which was the most points and 3's ever scored in a single quarter in nba history. He also didn't even play the 4th quarter of that game. For reference his average is only just over 20 a game. When we say a basketball player has a hot hand it is also in reference to a short period of time within that game. It does not last a whole game. What you should be doing is looking at his most average game, take the string from that and compare that to his string from this game. I can guarantee you'll find the sets to be significantly different. On a side note seeing a numberphile video talking about the NBA literally made my day
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ttsgeb
I feel like we're missing something by not comparing the players scoring in each particular game to that player's average. If a player is suddenly making 80% of their shots when their overall average is closer to 50% of shots made, that's a huge difference. Additionally, the timing thing seems incredibly important to me. Are those streaks being broken after a break in the game? Are they being broken when the player hasn't had a chance to make a shot in a while for whatever reason? What are the conditions around the streaks being broken? At what point do the conditions to continue a streak no longer exist?
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I feel like we're missing something by not comparing the players scoring in each particular game to that player's average. If a player is suddenly making 80% of their shots when their overall average is closer to 50% of shots made, that's a huge difference. Additionally, the timing thing seems incredibly important to me. Are those streaks being broken after a break in the game? Are they being broken when the player hasn't had a chance to make a shot in a while for whatever reason? What are the conditions around the streaks being broken? At what point do the conditions to continue a streak no longer exist?
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Matt
This may be me just falling into the same fallacy, but I still don't feel like the shots would be independent. -In the zone- to me means two things: some kind of muscle memory is reinforced by getting something in, and therefore doing the same thing as last time may make it easier to score. The second thing is the positive reinforcement, that maybe the belief of streaks being real improves the player's mood in a way that might make it easier to score, just like the little train that could.
-I am not a basketball player
-I am not a statistician
-I am probably talking out of my rear end
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This may be me just falling into the same fallacy, but I still don't feel like the shots would be independent. -In the zone- to me means two things: some kind of muscle memory is reinforced by getting something in, and therefore doing the same thing as last time may make it easier to score. The second thing is the positive reinforcement, that maybe the belief of streaks being real improves the player's mood in a way that might make it easier to score, just like the little train that could.
-I am not a basketball player
-I am not a statistician
-I am probably talking out of my rear end
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Felix
Interestingly this collides with neurochemical research in the animal kingdom. An animal is more likely to win a fight after it has already won a fight, similarly an animal is less likely to win a fight after it has lost a fight, even when controlling for physical differences. This has been linked to a change in the ratios between neuro-transmitters in the brains of those animals.
I'm now interested if the researchers on this fell into the same mathematical trap than the researchers bested in this video or if there is an error in the way the error-correcting scientists tackled the issue.
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Interestingly this collides with neurochemical research in the animal kingdom. An animal is more likely to win a fight after it has already won a fight, similarly an animal is less likely to win a fight after it has lost a fight, even when controlling for physical differences. This has been linked to a change in the ratios between neuro-transmitters in the brains of those animals.
I'm now interested if the researchers on this fell into the same mathematical trap than the researchers bested in this video or if there is an error in the way the error-correcting scientists tackled the issue.
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AI
Numberphile doesn't understand humans. I noticed this at the coin flip video. Simply, there is no probability as described in these videos, it is always constant relative to the players ability and will. I can choose to lob the ball toward the ceiling if I want, I can practice coin flips until I get heads every time. The only real variables are never factored - wind, atmospheric pressure, greasy hands, human element, etc. This kind of deduction of raw statistics doesn't belong in sports or human activity whatsoever. Meaningless.
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Numberphile doesn't understand humans. I noticed this at the coin flip video. Simply, there is no probability as described in these videos, it is always constant relative to the players ability and will. I can choose to lob the ball toward the ceiling if I want, I can practice coin flips until I get heads every time. The only real variables are never factored - wind, atmospheric pressure, greasy hands, human element, etc. This kind of deduction of raw statistics doesn't belong in sports or human activity whatsoever. Meaningless.
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