Streaks, confidence and the hot hand debate 

Four consecutive baskets can transform the atmosphere of a basketball game. Spectators anticipate another successful shot, defenders pay closer attention, and teammates direct more possessions toward the same player. Whether accuracy has improved remains uncertain.

The hot-hand effect concerns temporary changes in an athlete’s probability of success, rather than consecutive positive results alone. Its investigation produced an unusual scientific dispute: an influential finding about human judgment was itself challenged on statistical grounds.

The 1985 Study That Questioned the Hot Hand

In 1985, psychologists Thomas Gilovich, Robert Vallone and Amos Tversky examined whether recent basketball successes predicted subsequent accuracy.

Their investigation combined professional game statistics, free-throw records and controlled shooting experiments. In their Philadelphia 76ers analysis, the reported weighted average shooting percentage was 51% following a successful attempt and 54% following a miss.

These results appeared inconsistent with the belief that players enter periods of unusually high accuracy. The researchers argued that spectators and athletes were interpreting ordinary statistical variation as evidence of changing form.

Random sequences can contain surprisingly long runs. People frequently expect chance events to alternate more regularly than probability theory predicts, making clusters appear more meaningful than they are.

Sports betting brings perceptions of form and momentum into markets for sporting outcomes. Market prices express expectations about uncertain events. They do not establish that a player’s recent streak will continue.

The study’s interpretation of basketball streaks depended partly on statistical comparisons that would come under scrutiny.

How a Statistical Correction Changed the Debate

Joshua Miller and Adam Sanjurjo revisited the question in research published in 2018. They identified a finite-sample selection bias affecting a common measure of shooting accuracy after consecutive successes.

A four-flip coin example illustrates the problem. For each possible sequence, calculate the proportion of heads among flips immediately following heads. Two sequences contain no qualifying flip, so exclude them. Giving each of the remaining 14 sequences equal weight produces an average of approximately 40.5%.

Each individual flip still has a 50% chance of heads. The lower figure arises from averaging percentages within short sequences, rather than pooling all qualifying flips across the possible sequences.

Correcting for this bias, Miller and Sanjurjo found statistically significant evidence of hot-hand shooting in the original controlled experiment with college players. This concerned the experimental data, rather than a direct reversal of the Philadelphia 76ers percentages.

Their analysis did not establish that every streak represents improved form. It showed that evidence previously interpreted as an absence of persistence could support a different conclusion.

Their later research, published in 2024, examined four controlled shooting experiments and reported further evidence of hot-hand performance, including patterns within individual players across multiple sessions.

Confidence and the Direction of Causality

Confidence offers a possible explanation for changes in performance, but its contribution is difficult to separate from the effects of previous success.

A 2022 meta-analysis involving 3,711 athletes across 41 studies estimated a correlation of approximately 0.25 between sport-confidence and performance. This small positive association was stronger in individual sports than in team sports.

That relationship leaves a question unresolved: does confidence improve execution, or does effective execution produce confidence?

Both processes may occur. Successful attempts can reinforce an athlete’s sense of competence, affecting concentration, hesitation and tactical choices. Yet the same psychological response may encourage unnecessarily difficult decisions.

Confidence also differs from psychological momentum. An athlete can experience heightened motivation or control without demonstrating improved accuracy.

The meta-analysis supports a relationship between confidence and performance across sporting settings. It does not establish that rising confidence causes a particular shooting streak or explain changes in accuracy between attempts.

Why Competitive Conditions Complicate the Evidence

Shooting experiments offer relatively consistent conditions. Competitive basketball introduces defensive and tactical adjustments that can conceal changes in individual performance.

In research presented at the 2014 MIT Sloan Sports Analytics Conference, Andrew Bocskocsky, John Ezekowitz and Carolyn Stein analyzed more than 83,000 NBA shots alongside optical tracking data. Players who had recently exceeded their expected shooting performance subsequently attempted harder shots, faced tighter defense and were more likely to take their team’s next shot.

A player whose execution has temporarily improved might therefore maintain an unchanged shooting percentage against more difficult opposition. Equally, favorable opportunities can produce consecutive successes without any improvement in underlying ability.

After accounting for shot difficulty, the researchers estimated an increase of approximately 1.2 to 2.4 percentage points in the probability of making a shot. Raw shooting percentages can therefore miss changes that emerge when circumstances are considered.

Controlled experiments examine standardized attempts, while game statistics reflect ability, opposition, tactical decisions and opportunity together. Detecting persistence experimentally does not tell a coach precisely when a player has become more accurate, how long the change will last or how defenders will respond.

What Streaks Reveal About Human Judgment

The statistical reassessment challenged the dismissal of hot-hand belief as an illusion. It did not make every apparent run evidence of improved shooting ability.

For spectators and coaches, observing consecutive successes is easier than explaining them. Four baskets are visible; the contributions of confidence, shot difficulty and temporary changes in execution are harder to separate.

The useful question is what changed during the run: the player’s execution, available opportunities or defensive responses. Results alone cannot resolve those possibilities.