Maths in music, art and sport · Solid · Dissertation or artefact

How Elo ratings work: a maths EPQ idea

Why it works as an EPQ

A logistic formula and an update rule you can implement, test on results and tune.

Scope and difficulty

Solid. Solid. Implement on one season of public results.

The maths

Builds on these A Level topics: Exponentials and logarithms · Probability · Sequences and series.

You would learn:

• Logistic curves
• Update rules and the K-factor
• Testing predictions

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

One possible plan

1. Derive the expected score formula and the update rule.
2. Run Elo on a season of results.
3. Test its predictions and tune K.
4. Judge it against league tables.

Pitfalls

• Tuning on the same data you test on.
• Draws and home advantage ignored.

Where to start reading

• Search for: Elo rating system expected score formula
• Search for: Elo football home advantage

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

Making something? Read the artefact guide first: an artefact still needs a research-based written report.

Similar ideas

• Why tennis scoring rewards the better playerWhy does tennis scoring turn a small edge on each point into a big edge in matches?Music, art and sportSolidDissertation
• Why a piano cannot be perfectly in tuneWhy can't a piano be perfectly in tune? Equal temperament versus just intonationMusic, art and sportSolidDissertation or artefact
• Why instruments sound differentWhy do a violin and a flute playing the same note sound different? Fourier analysis and timbreMusic, art and sportAmbitiousDissertation or artefact
• Perspective in Renaissance artHow did Renaissance artists use geometry to create perspective, and how accurate were they?Music, art and sportAccessibleDissertation or artefact

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.