Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

IA idea · Sport

Where should I aim on a dartboard?

AI SLAI HLAA HL Ambitious Also in: Probability, Games & puzzles

Research question

Given my own measured throwing accuracy, which aiming point on the dartboard maximises my expected score, and at what accuracy does aiming at treble 20 stop being the best strategy?

Make it yours, then agree it with your teacher.

Next step: plan this IA free — the planner opens with this question filled in. For feedback on your own draft, the IA package (€39 once) gives you 5 AI feedback credits and every annotated exemplar in full.

Why it makes a good exploration

Aiming at treble 20 is only best if you are accurate. Measuring your own scatter and computing expected scores over the board is a beautiful mix of probability, geometry and simulation.

The mathematics you'll need

Two-dimensional normal model of throws (explain)
Estimating standard deviation from your throws
Expected value over regions of the board
Simulation to find the best aiming point

The statistics, step by step

Worked with every number shown, with what examiners look for and the common mistakes: Is my data normal? · Descriptive statistics and box plots. Then run the same steps on your own data in Analyse my data, or start from the statistics workflow.

Where the data comes from

Throw 100+ darts aiming at the centre, measure landing coordinates, and use the board's standard dimensions.

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

A possible outline

Measure your scatter and fit a model.
Encode the board's regions.
Simulate expected score at a grid of aiming points.
Find the optimum at your accuracy and others.
Reflect on unequal horizontal and vertical errors.

Pitfalls that cost marks

Assuming circular scatter without checking.
Too few throws.
Incorrect board dimensions.

Showing personal engagement

Use your own throws.
Compare with a friend of different skill.
Produce a “heat map” advice sheet.

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

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Not a natural fit	The core technique sits in the AI course or at HL; an AA SL student could use it only as clearly explained new mathematics.
AA HL	Good fit	Two-dimensional normal model of throws (explain); Estimating standard deviation from your throws
AI SL	Fits — ambitious at SL	Two-dimensional normal model of throws (explain); Estimating standard deviation from your throws
AI HL	Good fit	Two-dimensional normal model of throws (explain); Estimating standard deviation from your throws

Level: Ambitious. Suits confident students; expect to learn some mathematics on your own. 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: assuming circular scatter without checking; and too few throws. Say how each one affects your answer.

Use of mathematics (E)

SL: two-dimensional normal model of throws (explain); estimating standard deviation from your throws; expected value over regions of the board; simulation to find the best aiming point, 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

Allow different horizontal and vertical standard deviations and see how the optimum moves.

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 and AA HL. We rate it Ambitious: it suits confident students, who should expect to learn some mathematics on their own.

What mathematics does this IA use?

Two-dimensional normal model of throws (explain), estimating standard deviation from your throws, expected value over regions of the board and simulation to find the best aiming point.

Where can I get data for this IA?

Throw 100+ darts aiming at the centre, measure landing coordinates, and use the board's standard dimensions. Checked sources and tools: Desmos graphing calculator.

Turn this idea into your IA

The planner opens with “Where should I aim on a dartboard?” filled in: the question, the maths and the data sources.

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