IA idea · Sport
Are cricket batting scores geometrically distributed?
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?
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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
Modelling the data, step by step
This idea usually needs an exponential model. See it worked step by step, with a criterion tip at every step: Exponential y = a e^(kx) + c and y = a·bˣ.
Model your own data Paste it from Desmos, GeoGebra or a spreadsheet and get the same play-by-play with your numbers. New to modelling? Start with the modelling workflow. Writing it up? The IA modelling planner comments on each paragraph as you draft — it never writes it for you.
The statistics, step by step
Worked with every number shown, with what examiners look for and the common mistakes: Chi-squared goodness of fit. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.
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.
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.
Which course is it for?
| Course | Fit | Maths to lean on |
|---|---|---|
| AA SL | Good fit | Geometric and exponential distributions; Chi-squared goodness-of-fit |
| AA HL | Good fit | Geometric and exponential distributions; Chi-squared goodness-of-fit |
| AI SL | Good fit | Geometric and exponential distributions; Chi-squared goodness-of-fit |
| AI HL | Good fit | Geometric and exponential distributions; Chi-squared goodness-of-fit |
Level: Solid. Needs some independent work beyond class examples. See how the IA differs between AA and AI, SL and HL.
How this idea reaches the top bands
Reflection (D)
For this idea, start with the weak points: ignoring not-out innings (they are censored); and grouping scores so expected counts are too small. Say how each one affects your answer.
Use of mathematics (E)
SL: geometric and exponential distributions; chi-squared goodness-of-fit; survival (probability of reaching n runs) on a log scale; comparing expected and observed frequencies, each explained in your own words and carried out correctly.
How sport explorations reach the top bands in general: Sport IA ideas. Guides: A · B · C · D · E · self-grade sheet.
Taking it further
Model a lower chance of getting out after the first 10 runs and compare the fit.
Extending it for HL
Add an HL technique the question genuinely needs: what an HL sport exploration adds.
See a complete IA, marked
How long does a skydiver take to reach terminal velocity? (AA HL) is a complete sport exploration, marked on every criterion.
Frequently asked questions
Which IB Maths course is this IA idea for?
It works for AI SL, AI HL, AA HL and AA SL. We rate it Solid: it needs some independent work beyond class examples.
What mathematics does this IA use?
Geometric and exponential distributions, chi-squared goodness-of-fit, survival (probability of reaching n runs) on a log scale and comparing expected and observed frequencies.
Where can I get data for this IA?
Download innings-by-innings scores for a batter from ESPNcricinfo Statsguru. Checked sources and tools: ESPNcricinfo Statsguru.
Turn this idea into your IA
The planner opens with “Are cricket batting scores geometrically distributed?” filled in: the question, the maths and the data sources.
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