Is the “hot hand” real? Streaks in my free throws

AI SLAI HLAA SLAA HL Solid Also in: Sport, Statistics

Research question

After making a free throw, is my probability of making the next one significantly higher than after a miss, or are my streaks consistent with independent shots?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Psychologists argued for decades about whether the hot hand exists; a 2018 paper found a subtle bias in the original analysis. Testing your own shots — and understanding that bias — is a fascinating probability IA.

The mathematics you'll need

Conditional probability
Runs and the expected longest streak under independence
Simulation to find the distribution of streaks
Chi-squared test of independence (make/miss × previous shot)

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Shoot and record 300+ free throws in sessions of 50 (or use any repeatable skill: darts, penalty kicks).

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain independence and what a hot hand would mean.
Record sequences carefully.
Compare P(hit | hit) and P(hit | miss).
Simulate independent sequences to judge whether your streaks are unusual.
Reflect on the Miller–Sanjurjo bias in small samples.

Pitfalls that cost marks

Too few shots to detect anything.
Pooling sessions with different conditions.
Not understanding why short sequences bias the conditional estimate.

Showing personal engagement

Use your own sport.
Record how you felt during streaks and compare with the data.
Test a teammate's shots too (with consent).

See Criterion C: personal engagement for what examiners look for.

Taking it further

Reproduce the small-sample bias with a simulation and explain it in your own words.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).