Hot Hand in Basketball: when science takes its time to catch up to reality
Welcome to the premier issue of Hoops and Beans! We're tipping off with the 'hot hand' phenomenon in basketball. We explore the research that's finally catching up to what players knew all along!
Let's delve into the great feeling of possessing the "hot hand" or being "on fire” while playing basketball. Imagine the basket appearing wider, and as a player, each shot you take feels just right. It's a moment where your hands, eyes, body, and mind align with the rim and backboard, giving you the confidence that your shot will find its mark even before it leaves your fingertips. On the rare occasions when you miss, it feels like an anomaly.
Longtime basketball enthusiasts and players alike are familiar with this phenomenon. Those who have spent years on the court have not only experienced this incredible feeling themselves but have also observed their teammates caught in this unstoppable zone.
Starting from the top
Let’s explore some examples to understand truly what’s happening. We commence with LeBron James, who is widely considered to be among the top two players of all time, sharing the top with none other than Michael Jordan.
Lebron James feeling good
On February 28, 2024 Lebron James and LA Lakers faced off against the LA Clippers1. During the first episode of his new podcast with JJ Redick “Mind the Game”, he said that at some point while running with the ball he was feeling that if he made the next shot it would be “like NBA JAM on fire”.
He said that usually he is not shooting dribbling going to his right, yet he felt in rhythm. Just watch and listen to him describing perfectly how he “felt good at that moment”.
Michael Jordan feeling good too
Jordan had being hot a lot of times, and one of the most famous ones is him torching the Clyde Drexler and the Portland Trail Blazers with six 3 pointers in the first half of Game 1 of 1992 NBA Finals2, giving us the famous “shrug”. The game and the sequence has been part of the history of basketball, and the shrug of his shoulders one of the most famous celebrations.
The greatest shooter ever? Steph Curry?
Steph Curry changed the game of basketball. He has the most 3 pointers ever, and is known renowned for his incredible shooting ability, particularly from the three-point line. He is an all-time great, and shifted how teams across the league approach the game, making the three-point shot a more central element of offensive strategy.
Famous example of him feeling good and having the “hot hand” is his game winner against OKC on Feb 27, 2016. This is an amazing shot and a pure example of Curry’s ability and confidence to shoot from that deep3.
How about the other Splash Brother? Klay Thompson
Klay Thompson has one of the most fundamentally sound shooting technique; his shot is textbook, shoulders and feet are squared with the basket and his release point is perfect. Most famous example of Thompson getting hot is scoring 13/13 field goals in less than 10 minutes of basketball, getting 37 points against Sacramento Kings on January 23, 2015. Just enjoy Klay not being able to miss :-)
JR Smith - The definitive streaky player
JR is one of the most streaky players that we have seen. He really helped the Cleveland Cavaliers win a championship in 2016, he was always looking to shoot and is a joy to watch him make consecutive 3s. Just watch him being “hot” after making 6 threes and on his way to set the new record of 3s for Cavaliers 8 :-)
Luka Doncic
Luka Doncic possesses a rare combination of size, skill, and court vision. His ball-handling skills are elite, and he uses a variety of dribble moves — crossovers, behind-the-back, step-backs — to create space from defenders. His step-back three-pointer is extremely hard to defend, he plays the game with such a nice pace and he gets on fire very often. Just enjoy him torching (once more) the Clippers.
What does research say?
Let’s now deep dive on research and how it took the long route to conclude that the “hot hand” exists.
“Hot hand” is a fallacy
Back in 80s, Gilovich (Cornell University), Vallone (Stanford), Tversky (Stanford) published a paper entitled “The Hot Hand in Basketball: On the Misperception of Random Sequences”.
In the paper the authors, for short reference GVT, performed analyses using the observational shooting records of Philadelphia 76ers from 1980-81 NBA season, and data from a controlled shooting experiment with the varsity teams of Cornell. They performed a variety of analyses and experiments and they all led them to claiming that hot hand does not exist.
Their major findings which solidified the belief that hot hand does not exists are*:
P (making the next shot after make) is lower than P(making next shot after a miss)
P(making the next shot after made 3/4 or 4/4 last shots) is lower than P(making shot | made 0/4 or 1/4 last 4 shots)
*P stands for probability in the statements above.
Analysis of runs
They also analyzed sequences of consecutive made (or missed) shots; called them “runs”. Their hypothesis is that the more players made shots cluster together (being “hot” or “cold”) in sequence, the less the runs.
They used Wald–Wolfowitz runs test and used every sequence of consecutive makes or misses as a run. They found only one player (Darryl Dawkins) with less runs (more clustering of shots) than expected, solidifying more their view that “hot hand” does not exist.
Solidifying the fallacy
The main conclusion of their paper is that people “see” a positive serial correlation in independent sequences, and they fail to detect a negative serial correlation in alternating sequences.
Gilovich in 2017 in Freakonomics podcast again re-iterated:
The “feeling exists when you make several shots in a row — you will feel hot. That feeling very surprisingly doesn’t predict how you’re going to do in the next shot or the next several shots — the distribution of hits and misses in the game of basketball looks just like the distribution of heads and tails when you’re flipping a coin. Although of course, not every player shoots 50%. Very few of them do”.
All 3 authors are well-known scientists on the field of psychology and have really deep dived in humans and biases. Tversky had worked previously with Kahneman and you can clearly see the background of their thought process through a couple of early published papers about biases4 5. Gilovich also has published with Kahneman a really important book on “Heuristics and Biases”.
Kahneman, nobel memorial prize winner in economic sciences for his work with Tversky, wrote that “the hot hand is a massive and widespread cognitive illusion” in his popular book “Thinking, Fast and Slow” published in 2011.
Modern Sports Analytics Experts
Analytics over the years has entered basketball. One the of most prominent early people is John Hollinger, former VP of Basketball Operations for Memphis Grizzles in NBA.
Back in 2009 he was quoted:
“Until we're offered some kind of evidence as to how or why the Hot Hand might exist, the default, conventional-wisdom position now should be that it doesn't”6
For reference, John Hollinger has also made the PER rating that is widely used in the analytics world of basketball, and has been prominent in the MIT Sloan Sports Conference7; arguably the top conference in sports and data.
Back in 2011 MIT Sloan Sports Conference, Sandy Weil, currently Director of Sport Analytics at Swish Analytics, gave a talk entitled “Debunked: The Myth of the Hot Hand”. Furthermore, in similar tone expressed his view in an email conversation presented in an ESPN article as following:
“What we found is that, contrary to the existence of the hot hand, the 49 prolific shooters in our sample are less likely to make a shot after a made basket than after a miss.”
So not only does the hot hand not exist, but also being “hot” makes you likely to miss the next shot! And we are talking about professional "prolific shooters in the NBA.
Of course such statements make former NBA greats like Charles Barkley say “analytics was crap”.
Bias in analysis?
In 2018, Miller and Sanjurjo (University of Alicante) claimed that they realized an error in the analysis of Gilovich et al. They used the same data and published their results in a paper entitled “Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers”. 8
Their perspective is that the mistake starts from how Gilovich et al. used proportions to calculate conditional probabilities.
Let’s use the following example to display how they calculated them; we assume an unbiased coin and we throw the coin three times, observe the results and calculate the proportion of “Heads” following one or more “Heads” and the proportion of “Heads” after one or more Tail as displayed in the table.
If there is a player with a probability of making a shot of 50%, this seems like it shows that the success rate increases after a miss and decreases after a made shot. This is the basis of the calculation of the original authors, and Miller and Sanjuro analyzed the reason that in their perspective this introduces a bias.
They quantified this bias by calculating the expected proportions of made shots for different values of k sequential made shots, various probabilities of made shots (y-axis, dotted line), and n total shots (x-axis).
Miller and Sanjuro, adjusted for this bias (mean correction) and re-analyzed the raw data for the players of Cornell.
They published that they found that the average difference in the shooting percentage of players after making 3 shots VS the shooting percentage of players after missing 3 shots is 13%9 with a SE = 4.7 percentage points and not 3% as published by GVT.
The Hot Hand: A New Approach to an Old “Fallacy”
Bocskocky, Ezekowitz and Stein from Harvard in 2013 used a dataset of 83k shots with optical tracking data of both the players and the ball. They emphasized an important point; players could be taking more difficult shots after past makes and this may mask the Hot Hand 10.
Therefore, they attempted to create a model for the shot probability P of player i taking shot s controlling for a variety of factors:
Game Condition Controls takes into account signals such as:
time remaining
score difference
Shot Controls takes into account signals such as:
shot distance
shot type (e.g. fade away shot)
Defensive Controls takes into account signals such as:
distance between the player shooting and closest defender
angle with the basket
heigh difference between shooter and defender
Player fixed effects capture the historical observations per player in terms of shot making.
They trained a regression on a random set of 50% of the data using Ordinary Least Squares, because they claimed using Login or Profit they had convergence issues. They capped the predictions to not go above 0.99 and below 0.01, and they did not report the coefficients of this regression.
They displayed the calibration curve in the test set (see Figure 2). The x-axis has the predicted scores and y the observed frequency of made shots for each bin of predicted scores.
The curve displayed is seemingly of a well calibrated model.
Unfortunately, they did not display the distribution of scores in the test set, and they did not report any other measure of evaluation.
Research catches up to reality
The authors defined the probability of making a shot as following where P-hat comes from the previous model they developed11:
They defined as Heat:
Heat = % over past 4 shots - Expected % over past 4 shots
They claimed that if the hot hand does not exist, and each shot is truly independent they would expect α = 0 , β = 0, γ = 1, while if it exists they would expect β > 0.
They trained then a new OLS on the above defined equation, and they reported the following for this model12:
Following these results, having Heat with a positive weight, they wrote:
”At the very least, our findings cast doubt on the overwhelming consensus that the Hot Hand is a fallacy. Perhaps the next time a professor addresses the Harvard Men’s basketball team, the Hot Hand will not be so quickly dismissed”131415.
For many years, influenced by GVT's work, researchers dismissed the 'hot hand' as a myth. However, recent studies challenge this view, suggesting the 'hot hand' does indeed exist. As we continue to gather extensive tracking data, we can develop more sophisticated models to better understand and identify the factors contributing to the 'hot hand' phenomenon.
Fun fact: long time and multi-champion coach of Boston Celtics (9 championships during 1950-1966 as coach, 7 championships during 1966-2006 as executive), Red Auerbach when asked about the GVT study he replied: “Who is this guy? So, he makes a study. I couldn’t care less.”
P.S. If you want to deep dive even more on the research on hot hand, go ahead and read my extra notes.
Footnotes
Full Lebron VS Clippers Feb 28, 2024 highlights from that game in youtube
Full Jordan VS Blazers Game 1 1992 NBA Finals highlights from that game in youtube
Various angles of the same game winner shot of Curry against OKC in overtime.
Take into account that the difference between the top three point shooter in 2015-16 NBA season and the median three point shooter was 12%
It’s unclear what is the reason they did not just develop one model for estimating the probability of making a shot given all the controls and heat.
When they defined Heat just as the absolute % of makes over the last 4 shots, and tried to learn the regression with OLS, the coefficient of Heat was negative (-0.0237).
Causality is not proven with just observing co-efficients / weights
They also published an updated paper with minor changes in the coefficients/weights reported
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