Maths in music, art and sport · Accessible · Dissertation

Predicting race times: a maths EPQ idea

Why it works as an EPQ

A power law widely used by runners, tested on public race results.

Scope and difficulty

Accessible. Accessible. Public, anonymised results only.

The maths

Builds on these A Level topics: Exponentials and logarithms · Sampling and data · Hypothesis testing.

You would learn:

• Power laws
• Log–log regression
• Residual analysis

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

One possible plan

1. Explain the formula usually credited to Peter Riegel.
2. Collect public results for runners who ran several distances.
3. Fit the exponent yourself on a log–log graph.
4. Judge for whom the formula works.

Pitfalls

• Collecting personal data without consent.
• Ignoring survivor bias in who runs marathons.

Where to start reading

• Search for: Riegel formula race time prediction
• Search for: log-log regression power law fit

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.