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How would you know if there is a hot hand in basketball
Basketball’s ‘hot hand’ phenomenon is real, says this Pitt computer scientist
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This article was co-written by Konstantinos Pelechrinis, associate professor of computing and information in Pitt’s School of Computing and Information, for The Conversation. Faculty members and researchers who want to learn more about publishing in The Conversation can read about the process here.
March Madness is here, and basketball fans are making predictions: Who will be the Cinderella story of the college tournament? Which teams will make a run to the Final Four? And of course, which player is going to get “hot” and carry their team to a championship?
To say a player is “hot” or has “hot hands” means the player is on a streak of making many consecutive shots. A question that has dogged researchers, coaches and fans for years is whether players on these streaks can defy random chance, or if hot hands are just an illusion and fit within statistical norms.
We are two researchers who study information sciences and operations and decision technologies. In our recent study, we examined whether players can indeed get hot in actual live-game situations. Our analysis showed that some players do get consistently “hot” during games and make more shots than expected following two shots made consecutively. However, when we looked at all players together, we found that usually when a player makes more shots than normal after making consecutive shots, they are likely to revert toward the shooting average by missing the next one. Hot hands do exist, but they are rare.
When players get hot, they are a force to be reckoned with on a basketball court.
The science of going on a streak
Fans have always believed in the ability of players to go on a hot streak — as reflected in video games like NBA Jam where the virtual ball would catch fire if a player made multiple shots in a row. But academics have been skeptical of the idea ever since a 1985 study concluded that what people perceive as hot hands is nothing more than the human brain’s tendency to misunderstand chance and averages.
This changed in 2017 when a seminal paper showed that the original study — and the later ones based on it — suffered from small but significant selection bias that threw off the statistical calculations. Basically, the way the team chose which shots to look at when searching for streaks or a hot hand threw the math itself off. When researchers accounted for this bias, the hot hand turned out to be real.
The vast majority of studies on hot streaks in basketball have focused on either free throws, three-point contests or controlled field experiments. We wanted to test the theory in actual competitive games and used data from the 2013-14 and 2014-15 NBA seasons. But in actual game situations, shots are not identical. To control for this, we developed a model that predicts how often a shot will go in based on a number of different factors. These included who the shooter was, the distance from the basket, the type of shot, the distance from the closest defender, who the closest defender was, whether the shot was assisted and other considerations. It is only thanks to the modern, data-driven era of sports that we could even do such an analysis.
Using this model, we were able to simulate any shot by flipping a figurative coin that represents the probability any particular shot will go in. We could then quantify the hot hand effect by comparing the real world field goal percentage of a player after they were on a streak with the expected percentage obtained through simulating the same shots in our model.
For example, imagine that in the real world a player made 55% of shots after making the two shots before. But our model only predicted he would hit 46% of shots after making the two shots before. If this difference between the model prediction and the real world is statistically significant over time, then it is good evidence that the player can get hot and go on streaks.
Who has the hot hand?
Our analysis looked at 153 players who took at least 1,000 shots during the 2013-14 and 2014-15 NBA seasons. We examined shots taken after two, three and four consecutively made shots.
When looking at the shots from all the qualified players, we found that if a person made the two shots prior, their chance of making the next shot was 1.9% percentage lower than the model predicted — their make rate would regress to the mean.
However, when we looked at players individually, the hot hand emerged for a sizable set of players. Specifically, there were 30 players who exhibited a statistically significant higher field goal percentage on a shot following two makes compared to their expected field goal percentage. Of the players who demonstrated the ability to go on hot streaks, the average hot hand effect led to a 2.71% increase in the chance of making a third shot in a row.
For streaks of three and four consecutively made shots, the hot hand effect was even higher — 4. 42% on average and 5.81% on average, respectively.
Why do some people get hot?
It’s important to note that having a hot hand does not mean any player can suddenly make baskets from anywhere on the court. For example, Tim Duncan, Roy Hibbert and Marcin Gortat all showed the ability to go on hot streaks, but these are all centers who do not typically take shots far from the basket. Their hot hands increased their shooting percentages of close-range shots. This led us to the hypothesis that part of the hot hand effect may come from what is called the explore and exploit approach, which refers to a short period of exploring different approaches to solving a problem followed by a period of exploiting the best approach found. For basketball, this would look like a player finding a mismatch during a game — perhaps a shorter player defending them than normal — and exploiting it by taking more of a certain type of shot. Research has also suggested that the explore and exploit approach is connected to streaks of success in artistic and scientific careers.
While this hypothesis is plausible, it may not be the only factor accounting for hot streaks. Could short-term neuroplasticity — the ability of a player’s brain to quickly adapt to conditions in a game — be a cause? What about focus and mental preparation? Whatever the reason, our study provides strong evidence that supports the existence of hot hands. For coaches and players in the NBA or in this year’s NCAA March Madness, it might be a good strategy to follow the old cliche: “Go with the hot hand.”
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Chapter 1. How Would You Know If There is a “Hot Hand” in Basketball?
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You must read each slide, and complete any questions on the slide, in sequence.
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confounding variable
A factor other than the independent variable that might produce an effect in a research study.
By:
C. Nathan DeWall, University of Kentucky
David G. Myers, Hope College
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INTRO
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Note: You will be guided through the Intro, Design, Measure, Interpret, Conclusion, and Quiz sections of this activity. You can see your progress highlighted in the non-clickable, navigational list at the right.
Watch this video from your author, David Myers, for a helpful, very brief overview of the activity.
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DESIGN
So, how would you know if there is a “hot hand” in basketball? Many people believe that a player is more likely to make a basket after having just made one than after missing one—that players who are doing well have a “hot hand.” Is this true? To study this question effectively in your role as researcher, you need to DESIGN an appropriate study that will lead to meaningful results, MEASURE the hot hand in basketball in your participants, and INTERPRET the larger meaning of your results, considering how your findings would apply to the population as a whole.
Click on "Video Hint" below to see brief animations describing Case Studies, Naturalistic Observation, and Experiments.
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Case Studies:
Naturalistic Observation:
Experiments:
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Next, you need to select the participant(s) for your Case Study. With a Case Study design, you will choose one person or a small group of people, such as a specific team or club, and then study them in depth.
What could we learn from these participant choices?
a. One person or a small group of people who regularly play basketball To know whether there is a hot hand in basketball, you would want to observe people who regularly play basketball. You will want to be able to compare apparent “streaks” in shooting performance with participants’ typical shooting performance. HOWEVER, you need to study a larger group, and not one individual or a small group of people, as you would in this Case Study approach, in order to determine if the idea of a hot hand may apply to a larger population.
b. One person or a small group of people who have never watched basketball Just knowing whether people have ever watched basketball does not give us information about whether they would make good candidates for being observed in this study. They might not even know the rules of the game!
c. A talented swimmer who likes to watch basketball This person is not a good candidate because it is unclear whether the individual has ever played basketball. To know if there is a hot hand in basketball, we would need to observe people who regularly play basketball, and we would need information about their basketball shooting history.
d. A basketball fan who believes in the hot hand Just because people believe in the hot hand does not mean that they will be appropriate study participants. We need to know their basketball shooting history.
Trying to choose a participant or small group of participants helps us realize that the CASE STUDY IS NOT THE BEST RESEARCH DESIGN to test this question. We’d get more helpful results by observing large groups of people who regularly play basketball, taking into account their previous shooting performance. This would help us determine whether there is a hot hand in basketball.
Click “Next” to go back and try again to select the most effective research design.
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Nice work! You have correctly chosen a Naturalistic Observation design for testing this question.
You chose People who have never played basketball, but this is NOT CORRECT. You will want to observe those who regularly play basketball, so that they have an average scoring ability that you can use to compare to their rate of scoring after having just made a basket and after having just missed a basket.
Click “Next” to try again to select the best group to observe in your study.
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You chose A group of talented swimmers who like to watch basketball, but this is NOT CORRECT. Knowing whether your participants are fit and athletic is not enough to know whether they would be good candidates for your study. You will want to observe those who regularly play basketball, so that they have an average scoring ability that you can use to compare to their rate of scoring after having just made a basket and after having just missed a basket.
Click “Next” to try again to select the best group to observe in your study.
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You chose A group of basketball fans who believe in the hot hand, but this is NOT CORRECT. Knowing whether people believe in the hot hand does not tell us what we need to know. You will want to observe those who regularly play basketball, so that they have an average scoring ability that you can use to compare to their rate of scoring after having just made a basket and after having just missed a basket.
Click “Next” to try again to select the best group to observe in your study.
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You have chosen an Experimental design for your study. This means you need to set up experimental and control conditions.
This is tricky, isn’t it? In the experimental group, you could ask participants to try to make as many baskets as they can. But setting up a control condition is more difficult. Would you instruct those in the control group to shoot badly? Would their purposely-bad performance really provide an appropriate basis of comparison with those in the experimental group? And what about the effects of a crowd and the reality of playing in an actual game? If this question were tested in a lab, could we generalize the results to shooting behavior in real basketball games?
Click “Next” below to try again to select a research design that would effectively help you to determine if there is a hot hand in basketball.
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MEASURE
Credit: Mike Powell/Allsport Concepts/Getty Images
Good job! You have correctly chosen to use a Naturalistic Observation design, and you’ve selected an appropriate sample of participants—large groups of people who regularly play basketball.
Now you need to determine how best to MEASURE the relevant behavior or mental process, which in this case is a hot hand in basketball shooting—the idea that players are more likely to make their next shot after having just made rather than missed another shot.
You chose Count how many baskets each player makes, but that is NOT CORRECT.
This exercise would tell you something about each participant’s average shooting ability, but it would not give you the information you need about the hot hand. To know whether a prior basketball shooting outcome influences the outcome of the current shot, you need to track players’ performance on consecutive shots, and compare that to the player’s average shooting.
Click “Next” to try again to select the best way to measure the target behavior.
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You chose Have players rate their confidence in making two consecutive baskets, but that is NOT CORRECT.
You need to measure actual basketball shooting in order to determine whether there is a hot hand in basketball. Measuring confidence is not the same thing as measuring actual basketball shooting behavior.
Click “Next” to try again to select the best way to measure the hot hand.
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You chose Observe and carefully track players’ shooting, then determine if the odds of each player’s making a basket after having just made a basket were greater than their team’s average scoring would predict, but that is NOT CORRECT.
To know whether the hot hand exists, you need to compare the probability of your participants’ scoring based on their own average shooting behavior. Comparing a person’s shooting behavior to their team’s average shooting will not tell you if the hot hand exists.
Click “Next” to try again to select the best way to measure the hot hand.
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INTERPRET
Credit: Mike Powell/Allsport Concepts/Getty Images
Good work! You’ve correctly chosen to use a Naturalistic Observation DESIGN, and you’ve selected an appropriate sample—large groups of people who regularly play basketball. You’ve also chosen an effective way to MEASURE the hot hand—you will Observe and carefully track players’ shooting, then determine if the odds of each player’s making a basket after having just made a basket were greater than their own average scoring would predict.
Next you need to consider how you can apply what you’ve learned to the larger population—beyond the people you’ve studied. Consider where you might encounter roadblocks to confidence in your results. What factors might keep you from being able to apply what you’ve learned in a broader context?
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You are interested in knowing whether there is a hot hand in basketball. There are other factors that could affect basketball shooting outcomes in the people you’ve studied. These factors that could potentially interfere with our INTERPRETATION of results are called confounding variables.
Question
Select all of the factors experienced by individual players that could affect your confidence about whether there is a hot hand in basketball shooting.
ZycNTMvpRoSnXPUZl8FiVl5s+iDEL2Bo
Emotional state
3jskoxIwaHnoYr4Fsi2l/v3etGMIufia
Preference for certain types of food
ZycNTMvpRoSnXPUZl8FiVl5s+iDEL2Bo
Current energy level
ZycNTMvpRoSnXPUZl8FiVl5s+iDEL2Bo
Quality of opposing team’s defense
3jskoxIwaHnoYr4Fsi2l/v3etGMIufia
Number of Justin Bieber concerts attended
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Click on "Video Hint" below to see a brief animation describing Confounding Variables.
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Credit: Mike Powell/Allsport Concepts/Getty Images
The confounding variables for your study would include those highlighted below:
Emotional state
Preference for certain types of foods
Current energy level
Quality of opposing team’s defense
Number of Justin Bieber concerts attended
In fact, actual research has shown that ANY GIVEN PLAYER’S ODDS OF MAKING THE NEXT SHOT ARE UNAFFECTED BY THE PRIOR SHOT OUTCOME. The highlighted factors above do indeed affect shooting behavior, so it is important to keep track of how they may affect performance. But immediate prior shooting outcomes give no added clue to the next outcome.
Why do so many players and their fans struggle to come to terms with these ideas? Try a brief demonstration that might help you understand better.
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Imagine that a basketball player, who has a 50 percent shooting average, takes 21 shots in a row. Click a sequence of makes and misses, below, to illustrate what you think a normal random variation would look like for this average player. How many times would he or she make or miss a basket, and what sort of pattern of makes and misses would we see with this average player?
How did you do? Did you correctly portray a typical pattern for a 50 percent shooter? For an average shooter, the next shot outcome would differ from the previous shot (so a miss after a basket, or a basket after a miss) about half the time, so 10 times in this demonstration.
You predicted that the next outcome would differ __ times.
You predicted more alternations, and fewer shooting streaks, than would normally occur in random data. Random sequences are streakier than most people expect.
Having observed streaky play (many shots made in a row, or just the opposite), many players and fans have a hard time not believing in the supposed hot hand phenomenon. They believe that players who are “hot” will make many baskets in a row, and that players who are “not” will miss many in a row.
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CONCLUSION
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You may do better on the Quiz if you take notes while watching this video. Feel free to pause the video or re-watch it as often as you like.
REFERENCES
Blanchard, T. C., Wilke, A., & Hayden, B. Y. (2014). Hot-hand bias in rhesus monkeys. Journal of Experimental Psychology: Animal Learning and Cognition, 40, 280-286.
Gilovich, T. , Vallone, R., & Tversky, A. (1985). The hot hand in basketball: On the misperception of random events. Cognitive Psychology, 17, 295-314.
Malkiel, B. G. (2007). A random walk down Wall Street (9th Ed.). New York: W. W. Norton & Company.
Oskarsson, A. T., van Boven, L., McClelland, G. H., & Hastie, R. (2009). What’s next? Judging sequences of binary events? Psychological Bulletin, 135, 262–285.
ADDITIONAL ACKNOWLEDGMENTS
We are grateful for the assistance of these helpful consultants in the preparation of our prototype for this project:
Pamela Ansburg, Metropolitan State University of Denver
Mackenzie Bayles, Jacksonville State University
Lisamarie Bensman, University of Hawaii, Manoa
Adam Brown, Memorial University
Kristen Doran, Delaware County Community College
Nichelle Gause, Clayton State University
Toni Henderson, Langara College
Darrin Iwamoto, Chaminade University of Honolulu
Rosalyn King, Nova Southeastern University
Claudia Lampman, University of Alaska, Anchorage
Mary Livingston, Louisiana Tech University
Christine Lofgren, University of California, Irvine
Thomas Ludwig, Hope College
Theresa Luhrs, DePaul University
Megan McIlreavy, Coastal Carolina University
Jennifer Poole, Langara College
Lisa Routh, Pikes Peak Community College
Randi Smith, Metropolitan State University of Denver
We are also grateful for the authoring assistance of Jason Spiegelman (The Community College of Baltimore County) in creating the “Video Hint” tutorial animations.
We’ve learned that any given player’s odds of making the next shot are unaffected by prior shot outcomes. We also learned that it is important to expect some shooting “streaks” in any normal variation, and that it’s important to consider a person’s typical basketball shooting performance.
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How does the hot hand phenomenon work? Even Shakespeare, Van Gogh and Einstein had success in courage - and this is scientifically proven in sports - Bank shot - Blogs
mystery and scientific controversy over the series. Below is a brief retelling of its main theses.
The current generation of the NBA grew up on the computer game NBA Jam. Its main feature is the change in the abilities of basketball players as they catch the courage or, in the terminology of the simulator itself, “get hot”. If a player manages to hit several times in a row, then the laws of physics for him change: and now it is more difficult for him to miss, no matter how difficult his attempts are.
The creator of the game, Mark Tarmell, came up with an original mode because he was rooting for the Pistons in the 80s: Vinnie Johnson, nicknamed "microwave", was running on the team, and it seemed that the ball in his hands at times turns into a fireball , which flies into the ring by a homing method.
Thanks to the cult of the NBA Jam, the "hot hand" phenomenon is an axiom for this generation of the NBA. For example, Steph Curry never hid his passion for video games and was convinced that at times exactly the same thing happens to him on the courts as with virtual basketball players: he can smear throughout the entire match, but at some point the ring moves apart and accepts any game. “In all my life, I have never met a person who would not believe in the existence of a “hot hand,” said the Golden State point guard.
The “hot hand” phenomenon goes far beyond the scope of a specific sport.
It can be seen in various areas of human activity.
William Shakespeare produced some of the best tragedies in a short period of time.
Vincent van Gogh caught inspiration, which led to the simultaneous appearance of a number of canvases at once.
Composer Rebecca Clarke wrote all of her major works early in life and then retired from music.
Albert Einstein made the major discoveries of his life in a few fruitful months.
There is even a famous New Yorker article about Nobel laureate Bob Dylan and his "hot hand".
According to Deshan Wong's team, which traversed the careers of 3,000 artists, 20,000 scientists, and 6,000 filmmakers, the pattern is very clear: 91% of financially successful artists, 90% of published scientists, and 82% directors who released films on a wide screen experienced at least one segment in their career during which they caught courage . Their most expensive pictures, most influential studies, and highest-grossing films appeared within a relatively short period.
“If we know your best work, we can assume that around the same time you released those that are in the top 3,” says Deshan Wang himself. - This is the period of the "hot hand" - whatever you do in life, your level suddenly skyrockets. You no longer belong to yourself. And all this is impossible to predict: the “hot hand” phenomenon can visit you at absolutely any moment. ”
Basketball is convenient because the hot hand phenomenon is most obvious in it. It is easy to feel, it is subject to understandable measurements, it can be made the subject of scientific work.
And here's the catch.
The "hot hand" phenomenon has indeed been carefully studied. The work that closed this topic, seemingly forever, appeared in 1985.
And although modern NBA stars live in the realities of NBA Jam, in the scientific world all these years the consensus has been exactly the opposite: there is no "hot hand" , there is only a distorted perception of random events.
“Our brain is a device that is always trying to find patterns. He finds patterns even where there are no patterns.”
In 1971, Israeli psychologists Amos Tversky and Daniel Kanneman formulated the law of small numbers, that is, the tendency to exaggerate the likelihood that a small sample accurately reflects the properties of the general population. People mistakenly assume that a principle that works with a large number of observations will also work with a small sample.
The most famous example of this fallacy is casino roulette: players react to a sequence of colors, although a small sample does not provide any representative information.
In the 1980s, they were contacted by Tom Gilovich, a social psychologist at Cornell, who suggested testing the Law of Small Numbers using basketball as an example. "Basketball fans see a hot hand everywhere, but statistical analysis does not confirm its existence."
In 1981, the trio showed up at an NBA game and asked for help from the legendary stats guru Harvey Pollack, who worked at Philadelphia games for many years and collected all sorts of numbers even before they figured out how to properly process them.
The evidence base for their work was based on three sources.
First, they looked at the Philadelphia players' hitting sequence and calculated the hitting percentage immediately after the player made or missed the shot. If the phenomenon of "hot hand" existed, then after hits - in their opinion - the percentage should be above average.
But that didn't happen.
The players they analyzed were more likely to score from misses than from hits. When it seemed to them that they were catching courage, nothing of the kind - in fact - happened. Even when they laid down three throws in a row, the odds were lower than when they missed multiple times in a row.
Second, they studied how Boston players shoot from the line. All the same observations were repeated here.
Finally, they set the stage for the lab experience by inviting 26 players from Cornell's men's and women's teams to the gym. They were offered to stand at the distance from which they score from open positions with an accuracy of more than 50%, and make 100 shots - while trying to predict before each shot whether the hit will take place or not. And they got paid for it: five cents for a hit, four cents for a miss, or two cents for a hit, one cent for a miss. The more confident they felt, the more they bet. The same was done by people who stood on the rebound and served them balls.
As a result, it turned out that neither the throwers nor the rebounders could predict whether the ball would go into the basket or not. And their belief in the “hot hand” phenomenon also revealed itself during the experiment: after a successful throw, they bet more money on a hit.
In 1985, Tversky, Kanneman and Gilovich published their fundamental work in the journal Cognitive Psychology.
They came to three conclusions:
1. There is no “hot hand phenomenon” in nature, it is a cognitive illusion. After hitting, the percentage of the thrower does not increase. And this can be compared to a coin toss: a series of heads and tails is possible, but this is nothing more than an accident.
2. People tend to exaggerate swagger and trust too small samples.
3. People look at any random data and always try to find patterns in it.
Athletes did not read the study, but always took the opposite view. During an experiment in Philadelphia, scientists spoke to 76ers players Julius Irving and Darrell Dawkins, and both were absolutely sure that a “hot hand” was taking place on the court.
1985 story about a new paper from brilliant psychologists with a bold claim: There’s no such thing as the hot hand.
Jerry West: "I don't believe what they say."
Red Auerbach: “Who is this guy? So he makes a study. I couldn't care less." pic.twitter.com/8vMdZ86DP3
— Ben Cohen (@bzcohen) November 20, 2020
The reaction to the results of the study was even harsher.
“This is complete nonsense. I don't believe what they say there. There are games where you feel different,” said Jerry West.
“There is no doubt that when you hit several times in a row, you feel confident. You ask for more balls and you have no doubts about yourself,” said Dallas assistant coach Bob Weiss.
“Who are these guys anyway? Well, they wrote some scientific nonsense, and then what? Yes, I didn’t give a damn about her,” Red Auerbach closed the discussion.
A few decades later, Peter Ayton and Ilan Fisher repeated similar manipulations on the data of the top scorers in the English Premier League and also confirmed that "believing in a "hot foot" is the same delusion." Ayton also had to answer for the words personally in front of the legendary coach Ron Atkinson live.
“Who are you? he shouted. - You never went into the locker room. And I went into the dressing room. I know what is it".
But what can you take from athletes?
The understanding that the “hot hand” phenomenon exists only in the collective fantasy became dominant in science for many years.
For example, the ethnographer Andreas Wilk conducted experiments on tribes that retained the primitive system: he put forward the theory that the law of small numbers is not just a prejudice programmed in people, but something that has been preserved in the collective memory of society from antiquity, because usually prey or resources in nature occur in a concentrated form.
Moreover, neuroscientist Ben Hayden tested the same theory on monkeys - it turned out that they, too, are victims of delusions associated with the law of small numbers.
Advanced statistics came to the NBA in the 10s. And with it, new technological solutions for collecting information.
Among the most notable is SportVU technology: all the arenas of the league were equipped with cameras that recorded the exact position when making a shot, the degree of difficulty of the shot, the proximity of a defender and other nuances.
New technologies have prompted scientists to return to a question that had been considered solved for thirty years.
In the early 1900s, Phoenix needed someone who could sort through the new data sets and come up with a practical application for them. They brought in John Easyowitz, a Harvard student and blogger whose posts were liked by Mark Cuban.
The first thing he (and his partner, Caronyn Stein) realized was that the evidence base of the 80s study broke down on new material: Tversky, Kanneman, and Gilovich did not distinguish between types of shots and equalized hits from under the shield and a three-pointer and, of course, did not take into account the complexity of the shots.
In their study Isikowitz and Stein asked three questions:
1. Does the behavior of basketball players change when they feel they are gaining momentum?
2. Does the “hot hand” phenomenon appear at this moment?
3. What if everything that has been said about the "hot hand" phenomenon before is not true?
In the end, they learned that not only the throwers, but also the players who defend against them change their behavior - they try to get a few inches closer to them when they think that the opponent is getting hotter. The snipers not only tried to throw more often, but also made more difficult attempts. And it became clear that in the original study they mistakenly took individual throws after hits, it turned out that all the throws are interconnected, which confirms that the players felt courage.
Next Isikowitz and Stein successfully used the concept of "Complicated Courage". It's not just about the number of shots, but also about how difficult attempts the player made. It turned out that the hot hand did show up on the court: it showed up as a 1.2 percent improvement for players who hit one of the last four shots and a 2.4 percent improvement for players who converted two of the last four shots. Thus, if a player hit several times in a row, then he was more likely to hit in the next attempt . At least if you take into account the likelihood of implementing more complex throws. He had a slightly better chance of doing so. He gradually warmed up. And then he took courage.
“In the most extreme case, our findings challenge the general belief that the hot hand phenomenon is a fallacy,” concludes.
Finally, in the late 1990s, Joshua Miller and Adam Sanjurjo became interested in the problem.
At first it seemed to them that the lack of research methodology of Tversky, Kanneman and Gilovich also consisted in a small amount of data.
So they did a similar experiment - they invited players and asked them to shoot from their chosen positions. But not 100 attempts, but 300. And not from a certain distance, but from certain points from which they usually hit at least 50 percent. And without trying to guess the outcome of the next hit: they just threw uninterruptedly.
According to their feelings, which were confirmed by mathematical calculations, the phenomenon of "hot hand" still existed.
But it seemed to them that something was missing.
Then they collected all the records from three-point contests and studied them carefully. It was obvious that when Craig Hodges hit 19 in a row, he could not help but catch the courage. But after checking, it turned out that the mathematical method of Tversky, Kanneman and Gilovich refused to perceive this as a “hot hand” phenomenon.
This has completely stunned them.
Until one day one of them, having nothing to do, started playing with a coin.
As discussed above, in the original 1985 study, scientists were trying to determine whether players would shoot better after a series of hits than after a series of misses. Tversky, Kanneman and Gilovich came to the conclusion that what they saw in the performance of snipers can be compared to a coin toss. That is, that the percentage of heads should be the same for tosses after runs with heads and tosses that follow runs of misses.
Miller and Sanjurjo suddenly - after thirty years of active discussion of the work - saw that the problem lay in the mathematical approach itself. The fact is that if you flip a coin a hundred times and then look at the results of tossing after three eagles in a row, then the percentage of eagles there will not be 50% at all, as one might think.
There are only eight options for tossing a coin three times (in parentheses is the percentage of heads after heads):
РРР (-)
PPO (-)
POP (0%)
OPP (0%)
PPO (100%)
ORO (0%)
OOP (50%)
LLC (1000%) 9002 That is, it turns out that 250% must be divided by six. And this is only 42 percent.
Miller and Sanjurho found that the success rate is less than the probability of success. If you take the order of a coin toss and randomly choose heads, then the chance of it coming up heads again is closer to 40 percent than 50 .
In their experiment, Tversky, Kanneman, and Gilovich divided throws into those that came after three (or more) hits in a row and those that came after three (or more) misses, and compared the percentage of hits between them. Because of this, they did not notice that the fact that the percentage of hit after a precise throw remains above 50, just speaks in favor of the “hot hand” phenomenon - because, according to their data, after a precise throw, the percentage of hits is 11 percent higher than a coin toss would suggest.
An 11 percent increase in accuracy is not just something that can't be overlooked. This is the approximate difference between a mediocre sniper and the best in the NBA . So even the data that Tversky, Kanneman and Gilovich had in the original experiment clearly points to the existence of the “hot hand” phenomenon.
And what's next?
Yes, actually, nothing.
It didn't matter much to science.
Scientists have admitted that now if you believe in a "hot hand", then you can not be considered an idiot (or an athlete). But globally they did not change their attitude towards the experiments of Tversky, Kanneman and Gilovich, because their main task was to illustrate the law of small numbers on practical material and show an erroneous attitude towards chaotic sequences. Outside of this goal, which has nothing to do with sports, but clarifies a lot in the psychology of mankind, in their opinion, everything else is too local. Let the basketball players really take courage and raise the level of the game. What does science care about this?
It didn't really matter to sports either.
Because everyone who closely follows basketball, and without any mathematical confirmations and monographs with references, understands that the “hot hand” phenomenon is quite real. And he was 100% legitimized in the 2016 playoffs, when Golden State rivals demanded a timeout as soon as Steph Curry flunked some incredible contraption. Cooling pause is the best (and only known) way to protect against courage.
Photo: Gettyimages.ru/Jonathan Ferrey / Stringer, William Lovelace / Stringer, Rick Stewart / Stringer, Ronald Martinez, Ezra Shaw; globallookpress.com/Javier Rojas/ZUMAPRESS.com; East News/Associated Press
Hot Hand Really Works: Scientists Confirm Old Basketball Belief
Some people believe that a basketball player during a match can catch the courage, and his hand becomes “hot”: he scores one ball after another in a row. Scientists have found that this is not the case - for most players. However, some basketball players really know how to enter a special state and score with a “hot hand” more than statistical models predict.
American scientists have shown that the phenomenon of "hot hand" in basketball really exists. An article about this was published in the PLOS One magazine.
For a long time, there was a belief among basketball players and fans that a player could turn on the “hot hand” mode, which allows him to make many successful shots in a row. Many coaches, commentators and researchers doubted that this was possible, and the series of successes was explained by mere chance: in the end, the coin can also fall several times in a row on one side. But the "hot hand" has become part of basketball culture, and in the computer game NBA Jam, a virtual ball lights up after several consecutive points scored by the same player. These discussions are renewed with each new impressive series, for example, in 2021 Stephen Curry from Golden State Warriors hit in 105 straight 3-point practice.
Konstantinos Pelecrinis of the University of Pittsburgh and his colleague set out to test this myth statistically to see if players can actually become "hot". Many previous studies have focused on one type of shot—free throw, three-point shot, or special shot. However, in a real game, the rolls are rarely the same.
Therefore, the experts developed a statistical model that analyzes shots based on many factors: who shot, distance to the basket, type of shot, distance to the nearest defender, who was the nearest defender, whether the ball was received after the pass, and much more. Such an analysis became possible only thanks to the developed sports statistics in American basketball, scientists themselves would not have been able to watch such a number of matches.
This model predicts the chance of success of any roll. If we compare the actual percentage of players hitting in a successful streak with the model's predictions for the same game situations, we can find out if there really is a "hot hand". For example, if in reality a player in the same situation will hit 55 percent of shots, although according to forecasts from the same situations he should score only 46 percent, then the phenomenon really exists.
Scientists analyzed the game of 153 basketball players who made at least 1000 shots in the 2013-2014 and 2014-2015 seasons. Throws after one, two, three and four hits in a row were considered. It turned out that if we consider all the players as a whole, then the chances of hitting the third throw after two hits are even 1.9percent lower than the model predicts - that is, the hand becomes not “hot”, but “cold”.
However, when looking at players individually, the picture changes and the hot hand phenomenon begins to show up in some people.
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The 30 players studied had statistically significant streaks in which the percentage of hits was significantly different from the predictions of the model. On average, these players saw their third throw increase by 2.71 percent, and by 4.42 and 5.8 percent on the fourth and fifth, respectively.
Researchers note that having a "hot hand" does not at all guarantee that a player will score from any positions. For example, this phenomenon is often exhibited by players whose position does not involve long-range shots. Scientists have put forward a hypothesis that the “research and use” scheme can work in basketball, when the player first looks for the best ways and options for action, finds and applies them until he gets tired or the opponent adapts. For example, you can find a weak link in the defense - a less skilled defender - and attack in his zone.
“It's important to remember that the phenomenon we've discovered is not necessarily related to what the fans call a 'hot hand'. Maybe it's just about the ability of some players to look for opponents that are convenient for themselves and use them for their series of hits, ”the scientists write.
The authors of the paper do not expect that their article will put an end to the discussions about the "hot hand", but they hope that their methodology will help new research on this problem. In addition, a closer analysis of the behavior of players on a successful series is likely to help coaches stimulate the ability to "hot hand" in their players.
But academics have been skeptical of the idea ever since a 1985 study concluded that what people perceive as hot hands is nothing more than the human brain’s tendency to misunderstand chance and averages.
These included who the shooter was, the distance from the basket, the type of shot, the distance from the closest defender, who the closest defender was, whether the shot was assisted and other considerations. It is only thanks to the modern, data-driven era of sports that we could even do such an analysis.
42% on average and 5.81% on average, respectively.
2 
They might not even know the rules of the game!
You will want to observe those who regularly play basketball, so that they have an average scoring ability that you can use to compare to their rate of scoring after having just made a basket and after having just missed a basket.
12 
Measuring confidence is not the same thing as measuring actual basketball shooting behavior.
You’ve also chosen an effective way to MEASURE the hot hand—you will Observe and carefully track players’ shooting, then determine if the odds of each player’s making a basket after having just made a basket were greater than their own average scoring would predict.
The highlighted factors above do indeed affect shooting behavior, so it is important to keep track of how they may affect performance. But immediate prior shooting outcomes give no added clue to the next outcome.
, Vallone, R., & Tversky, A. (1985). The hot hand in basketball: On the misperception of random events. Cognitive Psychology, 17, 295-314.
We also learned that it is important to expect some shooting “streaks” in any normal variation, and that it’s important to consider a person’s typical basketball shooting performance.
” 
People mistakenly assume that a principle that works with a large number of observations will also work with a small sample. 
If the phenomenon of "hot hand" existed, then after hits - in their opinion - the percentage should be above average. 
The more confident they felt, the more they bet. The same was done by people who stood on the rebound and served them balls. 
It turned out that the hot hand did show up on the court: it showed up as a 1.2 percent improvement for players who hit one of the last four shots and a 2.4 percent improvement for players who converted two of the last four shots. Thus, if a player hit several times in a row, then he was more likely to hit in the next attempt . At least if you take into account the likelihood of implementing more complex throws. He had a slightly better chance of doing so. He gradually warmed up. And then he took courage. 
But not 100 attempts, but 300. And not from a certain distance, but from certain points from which they usually hit at least 50 percent. And without trying to guess the outcome of the next hit: they just threw uninterruptedly. 
And this is only 42 percent. 
So even the data that Tversky, Kanneman and Gilovich had in the original experiment clearly points to the existence of the “hot hand” phenomenon. 
And he was 100% legitimized in the 2016 playoffs, when Golden State rivals demanded a timeout as soon as Steph Curry flunked some incredible contraption. Cooling pause is the best (and only known) way to protect against courage. 
An article about this was published in the PLOS One magazine. 
