Maths in music, art and sport · Solid · Dissertation

Game theory and penalty kicks: a maths EPQ idea

Why it works as an EPQ

Penalties are a two-player game with a mixed equilibrium you can compute and test.

Scope and difficulty

Solid. Solid. Simple 2 × 2 and 3 × 3 games and published data.

The maths

Builds on these A Level topics: Probability · Algebra and functions.

You would learn:

• Mixed strategies
• Equilibrium in zero-sum games
• Testing predictions with data

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Model kicker and keeper choices as a game.
2. Find the mixed-strategy equilibrium.
3. Compare with published penalty data.
4. Judge how far players behave as the theory predicts.

Pitfalls

• Small samples from one team.
• Payoffs with no data behind them.

Where to start reading

• Search for: Palacios-Huerta professionals play minimax penalty kicks
• Game Theory: A Very Short Introduction (Ken Binmore)

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths in music, art and sport ideas · all 93 ideas

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.