Maths in music, art and sport · Solid · Dissertation

Why tennis scoring rewards the better player: a maths EPQ idea

Why it works as an EPQ

Games, sets and matches stack probabilities; recurrence and binomial arguments make the effect exact.

Scope and difficulty

Solid. Solid. One player's point-win probability, worked up to a match.

The maths

Builds on these A Level topics: Probability · Statistical distributions · Sequences and series.

You would learn:

• Recurrences for deuce
• Markov chains
• Simulation

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

One possible plan

1. Find the probability of winning a game from the point probability, including deuce.
2. Extend to sets and matches.
3. Check with simulation.
4. Judge whether the scoring is fair or simply decisive.

Pitfalls

• Assuming points are independent without discussion.
• Tie-breaks ignored.

Where to start reading

• Search for: probability of winning a tennis game deuce formula
• Search for: Markov chain tennis model

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.