Selecting only shots that follow a run of successes changes the finite sample being analyzed. The preceding successes are consumed by the selection condition, while a miss ends the eligible sequence, creating a systematic downward bias in the measured post-streak percentage even when every shot is independent.

Retrospective conditioning uses information from adjacent outcomes
Completed streaks remove successes from the remaining finite sample
A miss acts as a stopping event
Equal post-hit and post-miss percentages can indicate improved performance

“Not in reality, their probability is always the same. But we don't observe the probability. We calculate the percentage, and that's where the biases come…”
Joshua Miller · 25:58

“But the mistake is understanding the benchmark.”
Joshua Miller · 26:18

#selection bias#probability#hot hand#streaks

Myth Buster55:08

Why Accurate Hot-Hand Detection May Look Uncorrelated With Results

A person can correctly identify when a shooter is hot without every prediction matching the next shot. The shooter's underlying probability may rise substantially, but one binary outcome remains noisy, so simple prediction-outcome correlation can understate the observer's skill.

Latent performance states differ from observed outcomes
One shot provides a weak signal about the underlying probability
A skilled observer can appear inaccurate over noisy individual trials
Players in the study shot better when peers predicted success

“while she's perfect at detecting his state, the outcome of the state is noisy.”
Joshua Miller · 56:24

“Bob shoots seven around seven percentage points better when and predicts that he's gonna make it”
Joshua Miller · 57:01

#measurement error#prediction#latent states#basketball

Hot Take· 1

Hot Take34:38

The Hot Hand Exists, but Its Mechanism Is Still Unsettled

Miller expresses confidence that recent success predicts elevated subsequent performance, but cautions that this statistical signature does not identify one unique cause. Calibration, confidence, physiological state, strategic responses, and other mechanisms can all create similar patterns.

Evidence supports a hot-hand effect
The label can cover multiple mechanisms
Statistical detection does not establish causation
Live-game strategy complicates interpretation

“I don't have any doubt that the hot hand exists.”
Joshua Miller · 34:43

“What you mean by the hot hand is where the doubts come in, because there's many different mechanisms”
Joshua Miller · 34:47

#hot hand#causality#behavioral economics#sports science

Explainer· 3

Explainer09:28

Why Success Can Create a Real Hot-Hand Mechanism

Miller distinguishes games of skill from independent games of chance and identifies plausible mechanisms behind streaky performance. Early successes can increase confidence, reduce conscious interference, and help an athlete trust practiced movements, while misses may trigger disruptive adjustments.

Athletic performance requires calibration
Success can reinforce confidence in training
Overthinking can disrupt automatic movement
Repeated adjustments can reduce consistency

“Sometimes you get a few successes in a row and it gives you more confidence in your training.”
Joshua Miller · 12:14

“You don't overthink it, and you return and trust your training.”
Joshua Miller · 12:16

#hot hand#confidence#sports psychology#performance

Explainer14:36

How Defensive Adjustments Can Hide a Hot Shooter

A hot player's raw shooting percentage may remain flat because defenders respond by applying more pressure and forcing harder attempts. The player's heightened threat can still benefit the team by drawing defenders and opening opportunities for teammates.

Modern optical tracking estimates player and defender locations
Hot shooters may face more difficult attempts
Flat raw accuracy can conceal improved underlying performance
A hot hand can create value through spacing and teammate opportunities

“the important thing isn't so much as the player doing better in the context of the game, but as it helped the teammates if they're…”
Joshua Miller · 15:49

“what looks like it's random is you're shooting the same percentage but with a whole lot more defensive activity on you.”
Barry Ritholtz · 16:21

#basketball#defense#optical tracking#team effects

Explainer21:18

What the Hot-Hand Bias Shares With Monty Hall

Miller connects the coin-flip result to the bridge principle of restricted choice and the Monty Hall problem. When an observation is selected using information about neighboring outcomes, the selector's available choices reveal information and alter conditional probabilities even though the underlying flips remain independent.

Selection procedures can carry information
A constrained choice is more informative than an unconstrained one
Independence of events does not erase selection effects
Monty Hall offers an intuitive model of conditional probability

“the stable restricted choice, which is essentially the intuition of Bay's rule”
Joshua Miller · 21:56

“the host looking at door one and two used information about both doors to determine which door to open up to you.”
Joshua Miller · 23:11

#monty hall#conditional probability#bayes rule#restricted choice

Story· 3

Story38:46

Craig Hodges's 19-Shot Run Exposed a Statistical Problem

Miller and Sanjurjo became suspicious when the original hot-hand test found nothing unusual in Craig Hodges's shooting-contest data. Hodges had made 19 consecutive shots despite being roughly a 50% shooter, prompting them to ask what the test would report if his shots were generated like coin flips.

The original method contradicted an extreme observed streak
Hodges made 19 consecutive shots
The anomaly motivated a controlled comparison
The eventual discovery began partly through luck

“he hit nineteen in a row at one point, never missed more than five, and he was around fifty percent shooter”
Joshua Miller · 40:08

“What if Craig Hodges was a coin?”
Joshua Miller · 40:20

#craig hodges#discovery#basketball#research

Story47:43

Andrew Gelman's Independent Check Confirmed the Result

After the paper went online, statistician Andrew Gelman independently examined the result in public. His analysis agreed with Miller and Sanjurjo, providing influential external validation before attention spread through academic, financial, and sports media.

Public scrutiny created both opportunity and risk
Gelman independently repeated the work
His result agreed with the authors
External validation accelerated broader attention

“Gelman went and did the work himself, and he found what he found agreed with what we found”
Joshua Miller · 48:53

“There is a hot hand that was his post”
Joshua Miller · 49:02

#peer review#andrew gelman#statistics#validation

Story1:17:56

The Risk Their Peer-Lending Model Failed to Price

Miller and a graduate-school friend built an automated peer-to-peer lending strategy that survived the financial crisis and earned a positive return. The venture ended because regulatory changes altered the legal and counterparty structure, exposing a risk their quantitative borrower model had never included.

The lending algorithm produced positive returns
The model focused on borrower risk
SEC-driven rule changes altered the business structure
Counterparty and regulatory risk made the strategy impractical

“We had a real confidence in our model. We had our automated bidding algorithm.”
Joshua Miller · 1:18:27

“the thing we didn't anticipate was, you know, the legal uncertainty of the of the enterprise.”
Joshua Miller · 1:18:18

#peer lending#regulation#model risk#entrepreneurship

Takeaway· 2

Takeaway33:19

Some Players Appear More Capable of Sustaining Streaks

Research on Spanish semiprofessional players suggests meaningful differences in streakiness across individuals. Players who handle and shoot the ball less often may have fewer opportunities to establish and sustain a rhythm, while individual NBA estimates remain difficult because shooting-contest samples are small.

Player-level hot-hand effects are heterogeneous
Touch and shot frequency may affect rhythm
Individual estimates require large samples
Aggregate evidence can be strong even when player identification is uncertain

“there seemed to be a clear difference with players.”
Joshua Miller · 33:30

“there's some players that can and some players that seem like they can't.”
Joshua Miller · 33:50

#basketball#player performance#sample size#heterogeneity

Takeaway1:19:24

It Is Never Too Late to Get Serious About a Technical Career

Miller advises aspiring economists and statisticians not to believe that an unfocused school record permanently closes the field. Motivated adults can return to school, begin at a less prestigious institution, secure funding, transfer, and build competence over several patient years.

Do not expect to have life figured out immediately
Adults can return to education in their twenties or thirties
A lower-ranked starting point does not determine the destination
Patience and sustained motivation can close educational gaps

“Don't be in too impatient to have life figured out.”
Joshua Miller · 1:19:34

“It's never too late to get serious.”
Barry Ritholtz · 1:20:14

#career change#education#statistics careers#patience

Frameworks in this episode

Ground-Truth Simulation Benchmark

Payoff-Weighted Performance Test

Preregister-and-Replicate Research Protocol

Insights & moments

⚡Myth Buster· 2

Why Post-Streak Percentages Are Not Neutral Benchmarks