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?

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

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

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

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.

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

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.

Taking it further

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

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).