SSAC: The Hot hand: A new approach to an old “fallacy.”

So thanks to my wonderful school, I was given another opportunity to attend the MIT / Sloan Sports Analytics Conference.  This year, I am spending most of the first day attending research papers. Whle the panel discussions definitely have some super-star names (I did see Andrew Luck),  the real substance of the conference is in the research sessions.

Here’s my first of a series of posts on the research paper sessions .  After these posts, I will summarize my experience  at the conference, and how it overlaps with my Sports Research course that’s currently going on.

Challenging the  “Myth” of the Hot Hand

Three recent graduates of Harvard University (Andrew Bockocksy, John Ezekowitz, Carolyn Stein) took a new perspective on the long-held belief that the  Hot Hand theory is a myth.  and challenges the previously held assumptions about “shots being taken at random”  in the NBA when a player makes previous shots.  Their paper can be found here.

A rough account of the presentation (with Q/A) is here.

1. Intro: Framing the investigation

A player has made several of his past shots. Is (s)he more likely to make the next shot?   Are shots independent events?

Tversky et al:  No evidence for it,  based on looking at previous shots.  The conditional probability of making a shot did not change based on different prior performances.  They looked at streak lengths, and found it consistent with the assumption of independence.

This became the conventional wisdom for a while in the media (Larry Summers, David Brooks) , an example of “data exposing human biases.

But Here’s the thing:  The  researchers took issue with the key assumption in the paper is questionable: that players randomly select their shots…  Wouldn’t a potentially “hot” player take riskier shots?  So they asked… Do players try harder shots when they have make a series of shots? 

2. Defining Hotness: 

They took data from NBA Roster,  NBA Expanded Play-by-Play,  SportVu optical tracking, and SPoRTVU Play-by-Play optical tracking to create a shot log. For each shot, they recorded the time, shot location, shot type, and location of all 10 players on the short.

With this, they were able crete a linear regression model  to estimate each shot’s difficulty based on game situations, shot situation (including distance from basket), defense, and individual player.

This metric helped them create a metric called “Complex heat.” What’s that? Let’s call simple heat a player’s basic   shooting percentage over their past 4 shots.

From that, we can define  Complex Heat:   (actual shooting percentage) – (expected shooting percentage, based on the  estimated shot difficulty of those shots). A positive value is for complex heat is a  “hot performance.”  Complex heat is a better measure of “hotness,”   because simple heat overvalues easy shots.

3. How does hotness change a player? 

Do players change their behavior, based on a perceived hot hand?  More specifically,

  • Do they take shots from further away?
  • Do defenders defend hot players more closely?
  • Are how players more likely to take their team’s next shot?
  • Does overall shot difficulty increase with heat?

Example:  Ty lawson pulls up for a “heat check”  3 pointer, after making 3 better-percentage shots in a row.  He makes it!  He takes his 5th shot, a “leaner ( a closely contested shot with high difficulty”


  • Shot Distances:  When hot, average shot distance increases by 6.8 inches  (4.5%)
  • Defender Distance: Defenders are, on average, 0.5 in  closer. (1.0%)
  • P(take next shot):  goes up when players are “hot.”   (7.6% increase)

 Bottom line:  “hot” players take harder shots… AND… players who are hot are more likely to make their next shot, when controlling for their next shot’s difficulty.

So there seems to be some evidence that players do indeed get “hot,” but because they take harder shots, the two effects may be “canceling” each other out.

The BIG  takeaway:  There’s probably something legit behind Coaches’ and players’ insistence that players sometimes get into a hot zone. For sure, this analysis came listening to the thoughts and explanations of players  and coaches.   

Unanswered questions:  

  • Should players be going for harder shots?  Is this choice smart decision strategically for their team, or are they missing a chance to pass off to a higher percentage situation?

Audience Questions: 

Q:  Did you differentiate by position?

A:  Not in testing for the hot hand.  A consideration yes may get tricky if you are isolating ju

Q: Complex heat: How do you control for which of the five shots were made ? 

A: If you make a hard shot, your “value added” is higher… It shouldn’t matter:  maikng one really hard shot

Q:  Are FT’s included?

A   No, and that’s a great point.  (BTW,  the male presenter has a habit of interrupting his female colleague – and the reverse is not happening.  This is really evident.) 

Q:  Was your work separated by teams? 

A: Nope. Another thing to look at. Do certain coaches “let players be?”

Q: Did you look at times when players resisted taking harder shots ? 

A:  We’re  controlling for difficulty, so that’s happening:  It’s embedded in the complex heat measurement.

About roughlynormal

I have been a math/statistics teacher for 25 years. I currently teach at an independent school in southern California. I also coach teaching fellows for Math for America - Los Angeles chapter. I love my career, my colleagues, and my friends & family.
This entry was posted in Uncategorized and tagged , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s