We move to J.J. Cale and his smooth guitar playing in a song that ends too soon.

We move to Little Willies, and the warm voice of Norah Jones.

In a different tune, much less known, we find Dawn Brothers and their most known song “Vampire” and its playful lyrics.

We move to Mexicali Blues by Bob Weir, better known from Grateful Dead, in a fast and uplifting song.

We move to more modern tune by Stereophonics and their definitely catchy tune.

Definitely adding one of the most chill blues players; John Lee Hooker in a song with Carlos Santana!

We move with Soulshine by Gov’t Mule with a memorable intro, great lyrics coupled with the voice of Warren Haynes, and keyboard and guitar playing off each other.

Moving to Van Morrison, whose voice was meant to sing acoustic tunes, in one of his most famous songs.

Last but not least, we close with another song by J.J. Cale with such nice drum tune and guitar playing that is meant to move you.

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Starting with Bobby “Blue” Bland with drums and bass driving the whole song!

Moving to Albert King and “Playing on Me”; one of the most groovy songs from his famous “I wanna get funky” album.

Changing pace and style to the chill and cool J.J. Cale and Cajun Moon!

Moving back to one legendary groovy blues voice; Muddy Waters in “I’m A King Bee”.

Of course, John Lee Hooker and One Bourbon, One Scotch, One Beer can’t be missed; voice and guitar grooving together!

Moving to Buddy Guy and Joss Stone in a groovy duet!

Of course, Taj Mahal and Keb’ Mo’ definitely an unbeatable pairing singing and playing together: “Don’t Leave Me Here”

A groovy playlist must have Eric Clapton and B.B. King in it; even better together in one song: “Hold On I’m Coming”.

Let’s not forget the other blues royalty; Freddie King!

And we close the same way we started; Albert King in a funky vibe!

So, turn it up and get ready to move—this playlist is all about the groove :-)

A version of it that has been gaining popularity is actually manual small batch (1-3 cups) pour-over.

There are different parameters the people have tried to optimize over the years:

• the grind size

• the dripper shape/size

• the water characteristics

• the method of pouring water

• steering of coffee

Bloom; where magic happens

The first phase of extracting filter coffee is called blooming. Blooming is the first pour of water over the bed of coffee.

The coffee bubbles and it's essentially degassing with the release of carbon dioxide.

Blooming is where major part of the taste is captured.

Water temperature

One noticeably consistent though parameter has been the water temperature. Most recipes have been following is ~90-95 degrees Celcius

You can check the recipes of World Brewer’s cup competitors in 2017 for example.

You can also see the technique of Lance Hendrick where he uses 89-95 degrees Celsius.

Colder blooming

One of the other famous coffee experts is James Hoffmann. I wanted to check his technique and learn how to pour over better.

As I was watching the video, I noticed something interesting. The temperature of the first 1 minutes is actually in the range of 50-70 celcius.

So there is some lower temperature during blooming in his technique.

Then searching a bit more about it I found out that there has been different people trying lower temperature of 60-70 celsius to capture more taste with the earliest being Rubens Gardelli using 62 degrees back in 2014 World Brewers Cup. His goal was to capture the aromas and tastes.

Actually, Lance Hendrick also made a video about it and even named Samo Bloom after Samo Smrke, who is researching on coffees, compounds and aromas.

Again, same goal: influencing the blooming phase where a large part of the aromas of the coffee are captured.

Over the last year I have been using lower temperature for the blooming, even trying with room temperature water and I have to say that the coffee is sweeter, less bitter and has a better overall taste.

Try it yourselves, and enjoy your cup of coffee while reading Hoops & Beans!

In just 15 years, basketball's DNA has mutated. It's all about raining threes, thunderous dunks, and acrobatic layups and the mid-range is made from lava.

The “Three-point revolution” is full-blown with its own wikipedia page. Its roots; Steve Nash and Mike D'Antoni's Phoenix Suns.

And the revolution happened with the best shooter of all time as its leader; Steph Curry.

Crunch time eye test

Watching tons of games over all these years, still my eye-test says that top teams when the clock's ticking and the scoreboard's tight, they rely on the mid-range; Steph and Lillard led-teams aside.

Time to dive into the data and check whether my gut-feeling is true or is just me growing up watching basketball in the 90s and 2000s.

Enter Data

I use the following data:

• NBA Seasons 2020-21, 2021-22, 2022-23, 2023-24

• All the playoff games of these seasons

• Random 15% sample of the regular season games of these seasons

Crunch time

• Less than 5 minutes left in the game

• Point difference less than 10 points

• We keep only the playoffs teams. Playoff teams are the best half of the league essentially. We keep the regular season and playoff games of the teams that every year went to the playoffs.

• We keep only made shots.

Crunch time shots - Regular Season

Let’s plot the regular season crunch time shots from the playoff teams!

We see that:

• Close to the basket shots (0-4 feet) are the majority: 40% of the total shots

• Mid-range (10-16 feet) shots are there too: 9% of the total shots

Crunch time shots - Playoffs

• Close to the basket shots are the majority yet in a lower percentage of 36%

• Mid-range is increased to 13%

Let’s test

We can actually test whether the distance of crunch time Playoff shots is generally closer than the Regular Season crunch time shots.

I use the Mann-Whitney U one sided test to compare the two distributions of shots. The alternative hypothesis is that the shots of the playoffs are closer in distance than the regular season.

Running the test gives us

• effect size: 0.034

• p value: 0.04

The effect size for the problem at hand is important and the p-value gives us good confidence.

Yes, the 3 point revolution is here to stay. Yet, in crunch time good teams are shooting from closer during playoff games, and this difference comes mostly from mid-range shots.

It seems the data match the eye-test after all :-)

Top mid-range playoff team

Closing, let’s check what happens on team level. The team with the most made and attempted mid-range shots in tight game situations in playoffs are the New York Knicks with 32/68 shots!

Definitely their top two players the last years, Jalen Brunson and Julius Randle, are mid-range specialists.

Knicks also thought they were relying too much on mid-range. They had the biggest trade of the summer. Now that they got the Karl Anthony Towns “(self-proclaimed) best shooting big ever” and traded Julius Randle, let’s see how their shot selection goes when it truly matters.

2024-25 NBA Season is starting! Let the games begin!

PS. With all due respect to Karl Anthony Towns, I think Dirk and KD are the best shooting bigs ever.

The Rides - I’ve Got To Use My Imagination

One of the greatest openings of blues songs. Bobby “Blue” Bland sung this back in 1973. The Rides covered it perfectly. The Rides is a supergroup consisting of legendary Stills from Crosby, Stills & Nash, one of the best modern blues artists Kenny Wayne Shepherd, and Barry Goldberg, who played keyboards with tons of famous blues artists.

Kenny Wayne Shepherd & Warren Haynes - Breaking up somebody's home

Albert King’s iconic song, covered by Kenny Wayne Shepherd and Warren Haynes. Albert King is one of the most famous and all-time best blues guitarists, known for his perfect pace riffs and rhythmic playing style. Warren Haynes is one of the best living guitarists, known from his work being part of one of the best jam rock bands Gov’t Mule, and of course Allman Brothers.

Gov’t Mule - Going Down

One the well-known rock blues tunes. Going Down is a song that became popular by Freddie King. Gov’t Mule do a great live cover with the iconic bass line played by Roger Glover of Deep Purple.Just enjoy.

Fan fact: it’s originally created and played by Moloch.

Joe Bonamassa - Never make your move too soon

Joe Bonamassa has been established as one of the best blues guitarists of all time. He really makes a great cover of the songs played by the one and only B.B. King.

Herbie Hancock, Derek Trucks & Susan Tedeschi - Space Captain

Originally sung by Joe Cocker, one of the most dynamic bluesy singers. Covered by legend of jazz Herbie Hancock, Derek Trucks amazing guitar playing and & Susan Tedeschi’s great voice from Tedeschi Trucks Band.

Eric Clapton & Tom Petty - I Got the Same Old Blues

You know you are great when Eric Clapton makes a whole album for you; in this case J.J. Cale. Clapton collaborates with amazingly chill Tom Petty to honor this song.

Eric Clapton - Born under a bad sign

Another Albert King legendary blues songs, and again a superb cover by Clapton. Pure slowhand magic.

Kenny Wayne Shepherd - The Thrill Is Gone

Kenny Wayne Shepherd covers along with B.B. King one the best songs of B.B. King sung and played. Original by Roy Hawkins in 1951!

Stevie Ray Vaughan - The Sky is crying

Another iconic, and covered by many, blues song. Original by Elmore James in 1959, made famous by Albert King.

Joe Bonamassa - Tiger in your tank

Last but not least, Joe Bonamassa, covers this great tune live by Muddy Waters known by his gritty style, originator of Chicago style Blues.

That’s it! This is the first playlist of Hoops & Beans. Thanks for reading, and enjoy listening to it.

Bonus 1: For the ones that read the whole issue, here is an extra; just enjoy Haynes and Bonamassa making an amazing live performance of Breaking Somebody’s Home.

Bonus 2: Enjoy this great video of Kenny Wayne Shepherd with B.B. King playing this song. Not available in Youtube, but in Dailymotion: https://www.dailymotion.com/video/x2yjilq

Espresso Fundamentals

To grasp the innovation behind “turbo shots”, it's essential to know the basics of espresso preparation. Simply put, espresso is made by violently pushing water through a compressed puck of finely ground coffee. Baristas rely on visual cues to understand if the extraction of coffee in espresso is good. They search for uniformity of the extraction and absence of obvious channeling. These days the rule of thumb is “18 grams of coffee, ratio of 2:1 coffee out/coffee in, in 25-35 seconds, around 9 bars, 88-96 celsius”1

The rise of Specialty coffee

Over the last 15 years, the coffee industry has pivoted towards “specialty coffee”. Its premise has been great, and it has really opened up the opportunities to diverse flavors. “Specialty coffee” has influenced the coffee world end-to-end, introducing multiple positive changes:

• the use of higher quality coffee cherries

• a variety of processing methods to extract the coffee bean from the berry, enhancing flavor profiles

• a preference for lighter roasts, allowing for the emergence of more nuanced flavors, offering a departure from the traditional, more bitter coffee profiles, with an increased opportunity to experience fruity undertones

However, this shift hasn't come without its challenges:

• the process of extracting coffee has become more complex, raising the bar for precision and skill

• higher risk to produce a cup of coffee that might lean too much towards sourness or, at times, a mix of sour and bitter flavors, diverging from the intended taste profile

Turbo shots to the rescue?

“Turbo shots” claim to be an answer to the problem of extraction and the sour and bitter taste. First of all, the name is great, just great😁. Second, it's not all in the name—the concept goes beyond merely speeding up the process Let’s deep dive.

Modeling the magic of espresso

Back in early 2020, Cameron et al. made waves in the coffee community with their publication in Matter titled “Systematically Improving Espresso: Insights from Mathematical Modeling and Experiment”. They questioned the magic numbers of the rule of thumb and attempted to model the extraction of coffee in espresso, and in specific to model Extraction Yield (EY). This measure quantifies the solubles dissolved during brewing of coffee and is calculated using the following (simplified2) formula:

• Coffee brewed and grounds are expressed in grams.

• Total Dissolved Solids (TDS) is the percentage of the dissolved coffee in the liquid of brewed coffee.

EY is measured with a refractometer using a few drops of coffee.

Crucially, each coffee (blend or single origin) has its own sweet spot in terms of taste relative to EY. Typically this falls in the range 17%-23% EY, and deviating from this range results in:

• Over-extracting if we have higher EY than the sweet spot

• Under-extracting if we have lower EY than the sweet spot

Finding the sweet spot requires trial and error for each coffee, and it’s a process referred as “dial-in espresso”3.

Model and expectations

The authors developed a model that describes the extraction of espresso. The model has a lot of details and its mathematical equations can be found in the section “Development of a Rational Model for Espresso Extraction” of their paper. The model relied on the distribution of particles of ground coffee, and given some assumptions and techniques taken by modeling lithium ions and battery electrodes4, they formulated an equation (number 24 in the paper) which they tried to validate.

Their model predicted that Extraction Yield increases with finer grind size, lower pressure water and using lower ratio (less coffee for fixed beverage weight).

While fixing the pressure to 6 bars5, they displayed, see Figure 1, the expected relation of extraction yield (EY) and grind setting for various dosages, and various ratios always expecting 40g espresso.

They also fixed the dosage and ratio 1:2 20g coffee beans resulting in 40g espresso, and displayed, see Figure 2, the relation of the expected EY and grind setting for various pressures.

Volcano Effect

The authors used EK43 which is a really popular and good grinder, PUQ automatic tamper, 20 gram ridge-less baskets6 and San Remo Opera - three group head machine for espresso extraction set at 92 celcius.

They observed clogging in their experiments with fine grind settings with the pressure set to 9 bars; thus they used 6 bars of pressure.

Their observations were partially contradictory to their model, and in specific the expected monotonic relation of the Extraction Yield to the grind setting. In specific let’s explain with Figure 3:

• Green area: A “standard” flow where the increase in grind size results in decreased Extraction Yield as expected by the model.

• Pink area: A “partially clogged” flow where the increase in grind size results in increased Extraction Yield, and this is where their model was way-off. The hypothesis on why this occurs is that parts of the coffee puck that are not accessible by water and are entirely dry when grinding finer.

This whole flow is not particularly really new knowledge. Baristas, including home ones, know that if you start from a “coarser” grind setting and you gradually grind finer, you find the setting where your extraction seems uniform and tastes good. This is the “standard” flow.

Baristas also know that after some point if you grind even more fine, the shot starts to gradually clog and create channelling, and it falls apart easily after some time. These are indications you are in the “partially clogged” flow.

One thing to note is that the authors claim the the turning point was on 1.7 setting in EK43 and that baristas use below 1.7 setting for espresso. Seven Miles Coffee Roasters recommend 1.5-2.5 setting8, and James Hoffman when tested in Square Mile found their turning point to be at 1.859.

It is important to clarify that this “turning point” is not necessarily the “sweet spot” for a given coffee.

• Turning point = max EY

• Sweet spot = best taste

The most important lesson in my view is that using EY as the measurement of taste is flawed. It hides information since the same EY can be achieved with different grind settings.

Moreover, EY is measured using some drops from the coffee, thus expressing the average EY in a cup and not characterizing the uniformity of extraction. For example, 22% EY can be extracted by having uniform extraction from the whole coffee puck or half of the regions of the coffee puck over extracted (e.g. 25%) and the other half under extracted (e.g. 19%).

Turbo shot strategies

Out of all these lessons, the authors propose a process for baristas to “optimize” their extraction. Here are the two strategies:

Strategy A

1. find the “tasty point” / “sweet spot” and note the EY, we call this EY_tasty

2. start grinding coarser and find the maximum value of EY, we call this EY_max

3. use the grind setting of the EY_max and stop the extraction earlier/decrease the ratio, aiming to get EY_tasty

Strategy B

1. find the “tasty point” / “sweet spot” and note the EY, we call this EY_tasty

2. reduce the coffee used, increase the ratio, start grinding much coarser until you find the EY_tasty

Please note that both strategies start from finding your “sweet spot” or “tasty point” as the authors name it for a given coffee.

Making it commercially saves cost, time and helps the environment since you achieve the same Extraction Yield with less coffee; again caveat that taste and Extraction Yield are not the same thing.

Turbo shot recipe

In summary, (a) turbo shot recipe extracted from the paper can be:

• 15 grams of coffee in (less coffee)

• 1:2.6 ratio, 40 grams of coffee out (more water)

• 7-15 seconds (faster shots)

• 6 bars of pressure (less pressure)*

This should result in faster shots, with less channelling and a more even extraction resulting in a more clean taste of these lighter roasted coffees.

The shot are supposed to be more easily reproducible, the nice/expected flavors and notes of the coffee are captured and the bitterness can be avoided.

Making it at home

Playing with the grind size, amount of coffee, and different ratios you can actually achieve a turbo shot at home without changing the pressure of the valve. Yes, you can get more “clarity”, “aromatics” in the shots. You also get much thinner coffee and have a higher chance to get sour coffee in my observations so far.

Moreover, there is a catch that in most of the home used semi automatic machines, e.g. Lelit Anna which is what I use10, you cannot easily change the pressure of your valve. Opening the espresso machine and finding the valve and changing the pressure is work that cannot be part of the daily routine. Some of the espresso machines allow you to control the pressure e.g. Lelit Bianca allows you to control the water flow, Decent exposes software of full pressure profiling, yet these are not your standard at home machines and they come with considerate price tags.

Turbo-shots origin

Visiting the blog post by Cameron about Turbo-shots, unveils that the real story is a bit different than the paper published, and arguably more cohesive.

First, the whole thing started by Cameron lowering the pressure and enjoying the taste of a coffee. This discovery a series of trials of pulling espresso and observing the “Volcano” effect. Following that the connection with the mathematicians of the list of authors (W. Lee, J. Foster) occurred. They had a mathematical model for coffee extraction and comparing it to the observations they were not matching the empirical observation of the “Volcano” effect.

The sequence of the rest of the story, is about discussing the choice of using Extraction Yield, the limitations of the refractometer, the focus on faster shots and how to achieve the “turbo-shots”.

This is one more point suggesting that the 6 bars of pressure used by the authors seem to be accidental and not by design. As Scott Rao mentions “the choice of six-bar pressure was merely a hack to decrease the severity of channeling”11.

Final Thoughts

In my view, the flavor profile and taste of turbo shots are much different. I find it interesting to try it occasionally, yes the “clarity” can be there, yet I usually prefer more sweet and full-bodied coffee and turbo shots diminish the thickness of the espresso. Keep in mind that other experts like La Marzocco advocate to use 6 bars, finer grind, and longer shots considering that lower pressure causes less agitation12.

Ultimately, turbo shots have not replaced my usual espresso routine, they inspired me to think about the “rule of thumb” parameters and being more flexible about them.

Footnotes

GVT Deeper Dive

Aside from what was discussed before, Gilovich (Cornell University), Vallone (Stanford), Tversky (Stanford), for reference GVT, as part of their paper The Hot Hand in Basketball: On the Misperception of Random Sequences”, they also performed more analyses on their data and performed a controlled experiment.1

Introducing Partitions

They partitioned the records of shots of players into non-overlapping sets of four consecutive shots. They created partitions starting from the 1st, 2nd, 3rd, 4th shot of each player.

They grouped the partitions to 3 groups:

• high performance (4/4 or 3/4 made shots)

• moderate (2/4 shots)

• low performance (1/4 or 0/4 made shots)

They compared the number of high, moderate, low sets for each of the nine players of 76ers to the values expected by chance, assuming independent shots with the average shot-making field goal percentage as probability(making a shot | shooting a shot).

They found no evidence to support that some players have more high performance shots than expected.

Hot VS cold nights

They also compared the variability of shooting percentages of players across games. They used the Lexis ratio of the standard errors (SE) of their shooting percentage:

SE observed in a game / SE expected using the average observed shooting percentage.

They found no player that the Lexis ratio was “significantly” greater than 1, concluding that the shooting percentages across games do not deviate from their overall shooting percentage more than expected.

Controlled shooting experiment

They also designed an experiment in a controlled setting. For each player of the 26 players of the varsity teams of Cornell, 14 males and 12 females, they found the distance that each player was shooting 50%.

They drew two 4.5 meter in length arcs on the floor from which each player would take their shots with an angle of 60 degree from the left and right sides of the basket. The players shot 100 shots, 50 moving on each arc designed individually for them.

They analyzed also there the runs (consecutive makes or misses) similar to the 76ers and again found only one player with less runs (more clustering of shots) than expected.

Miller & Sanjuro Deeper Dive

Miller and Sanjuro challenged the findings by GVT in their paper “Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers”.2 Following their general bias correction, in their paper they also had two more interesting sections.

Player Analysis

They applied the bias correction and calculated for each player of the Cornell team of the GVT study the effect of each player getting on-fire as following:

Bias-Corrected Difference = P(shot made | 3 made shots) - P(shot made | 3 missed shots)

Then they displayed the results for each player in y-axis of Figure 1 sorted in increasing difference value.

You can see that for 5 out of the 25 players the lower bound of the 95% Confidence interval is above 0, which indicates that these players could be getting the “hot hand”.

Streaky shooting

Every calculation of Miller and Sanjuro assumed that the player has a fixed probability of making a shot which does not take into account the actual “hot hand” / streaky shooting.

In the Appendix B of their paper they estimated the size of the bias given that the process of shooting is not characterized by a fixed probability of success. They hypothesized that being “hot” is characterized by an increase in your probability of making a shot. They used a hidden markov chain over the player’s ability to make a shot.

In summary, they displayed that if being “hot” increases your probability of making a shot by 10%, then the bias is around 2x than the baseline bias.

Essentially, the results they computed were an underestimate of the actual difference, thus the effect of being hot is even larger in the shooting of players.

More interesting reads

For the ones that are interested to read even more, here are some more links to follow and deep dive on your own. I read about them and they were all really interesting from different angles and perspectives.

• Fun discussion about betting between Miller VS a person from a hedge fund

• Paper about “Hot hand” and three point contest3

• Similar analysis to Bocskocky et al. was done by Pelechrinis & Winston in the paper “The hot hand in the wild”.

• Baseball has hot hand paper publication too

• Detailed paper with explanations by Miller and Sanjuro

• Paper claiming Warriors’ players in 2016-17 were not “hot”, and a video with the explanation from one of the authors too. Just noting that the Warriors that season are arguably one of best teams ever (so far).

  Go ahead and enjoy the top plays of this amazing team :-)

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 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.

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:

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:

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

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