IA idea · Sport

Are cricket batting scores geometrically distributed?

AI SLAI HLAA HLAA SL Solid Also in: Probability, Statistics

Research question

Do [a batter]'s Test innings scores fit a geometric (or exponential) distribution, as would happen if the chance of getting out were the same on every ball, and what does any misfit reveal?

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

Why it makes a good exploration

If a batter's chance of dismissal were constant, scores would follow a geometric distribution with mean equal to the batting average. Testing that with real innings shows when players are most vulnerable — often early on.

The mathematics you'll need

Geometric and exponential distributions
Chi-squared goodness-of-fit
Survival (probability of reaching n runs) on a log scale
Comparing expected and observed frequencies

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

Download innings-by-innings scores for a batter from ESPNcricinfo Statsguru.

ESPNcricinfo Statsguru — Searchable database of every international cricket match and player.

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 why a constant hazard gives a geometric distribution.
Plot the survival curve on a log scale.
Fit and test the model.
Identify where the fit fails (early innings).
Compare batters of different styles.

Pitfalls that cost marks

Ignoring not-out innings (they are censored).
Grouping scores so expected counts are too small.
Choosing a batter with too few innings.

Showing personal engagement

Choose your favourite batter.
Test your own club scores.
Explain what “getting your eye in” means mathematically.

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

Taking it further

Model a lower chance of getting out after the first 10 runs and compare the fit.

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).