IA idea · Sport

Where should a winger shoot from? Maximising the angle to goal

AA SLAA HLAI SLAI HL Solid Also in: Calculus, Geometry & Voronoi

Research question

Running parallel to the touchline at a given distance from the goal line's centre, at what point is the angle subtended by the goal largest, and does shot data support shooting from there?

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

Why it makes a good exploration

The goal looks biggest from a particular spot on a winger's run — the same mathematics as the best cinema seat and the rugby conversion problem. Linking the geometry with real shooting data makes it a sports-analytics IA.

The mathematics you'll need

Inverse trigonometric functions for the subtended angle
Differentiation to find the maximum
Showing the optimum is where a circle through the posts touches the line
Comparing with shot data

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

Use pitch dimensions from the laws of the game; film or chart shots in your own matches.

GeoGebra — Free geometry and graphing software — Voronoi diagrams, loci and regression built in.

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

Set up coordinates on the pitch.
Write the angle as a function of distance run.
Maximise it.
Prove the tangent-circle property.
Compare with where goals are scored in your matches.

Pitfalls that cost marks

Treating a larger angle as the only factor in scoring.
Wrong pitch dimensions.
No link to real play.

Showing personal engagement

Chart your own team's shots.
Compare with rugby conversion kicks.
Advise a winger in your team.

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

Taking it further

Add the goalkeeper's position and find the angle of the open goal instead.

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).