Updated 12 October 2026 · By Pete Bromfield, former Head of Maths with IB examining experience

IA idea · Sport

Can a simple rating system predict football results?

AI SLAI HLAA HL Ambitious Also in: Probability, Statistics

Research question

How accurately does an Elo rating system, built from past seasons of [a league], predict match outcomes, and which value of the update constant K gives the best predictions?

Make it yours, then agree it with your teacher.

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Why it makes a good exploration

Elo ratings rank chess players and are used for football and other sports. Building one yourself, then measuring how good its predictions are, is a genuine data-science project with a parameter to optimise.

The mathematics you'll need

The logistic expected-score formula E = 1/(1 + 10^(−Δ/400))
Iterative updating (a recurrence)
Measuring prediction quality (e.g., mean squared error of probabilities)
Optimising a parameter by comparison

Where the data comes from

Use several seasons of results from Football-Data.co.uk (which also include bookmakers' odds for comparison).

Football-Data.co.uk — Match results, shots, cards and bookmaker odds for 25+ seasons of European leagues, CSV.

Real data for this idea

Primary source: Football-Data.co.uk: Results and odds files. Choose a league and season; FTHG, FTAG and FTR give the goals and the result. Licence: No reuse licence found: link to it and cite it, and do not republish the files.

There is no open reuse licence for these figures: copy only the values you analyse into your own table, and cite the page and the date. Links checked October 2026; we link to the data and never copy it. More free data sets.

A possible outline

Explain the Elo formula and its logic.
Build the ratings in a spreadsheet.
Predict each match before updating.
Score predictions and optimise K.
Compare with bookmakers' implied probabilities and reflect on draws and home advantage.

Pitfalls that cost marks

Using results to predict matches that were used to build the ratings.
Ignoring draws.
Not explaining the logistic formula.

Showing personal engagement

Predict next weekend's matches and check.
Add a home-advantage term and justify its size.
Compare your model's accuracy with your own guesses.

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

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Not a natural fit	The core technique sits in the AI course or at HL; an AA SL student could use it only as clearly explained new mathematics.
AA HL	Good fit	The logistic expected-score formula E = 1/(1 + 10^(−Δ/400)); Iterative updating (a recurrence)
AI SL	Fits — ambitious at SL	The logistic expected-score formula E = 1/(1 + 10^(−Δ/400)); Iterative updating (a recurrence)
AI HL	Good fit	The logistic expected-score formula E = 1/(1 + 10^(−Δ/400)); Iterative updating (a recurrence)

Level: Ambitious. Suits confident students; expect to learn some mathematics on your own. See how the IA differs between AA and AI, SL and HL.

How this idea reaches the top bands

Reflection (D)

For this idea, start with the weak points: using results to predict matches that were used to build the ratings; and ignoring draws. Say how each one affects your answer.

Use of mathematics (E)

SL: the logistic expected-score formula E = 1/(1 + 10^(−Δ/400)); iterative updating (a recurrence); measuring prediction quality (e.g., mean squared error of probabilities); optimising a parameter by comparison, each explained in your own words and carried out correctly.

How sport explorations reach the top bands in general: Sport IA ideas. Guides: A · B · C · D · E · self-grade sheet.

Taking it further

Add a margin-of-victory adjustment and test whether it improves predictions.

Extending it for HL

Add an HL technique the question genuinely needs: what an HL sport exploration adds.

See a complete IA, marked

How long does a skydiver take to reach terminal velocity? (AA HL) is a complete sport exploration, marked on every criterion.

Frequently asked questions

Which IB Maths course is this IA idea for?

It works for AI SL, AI HL and AA HL. We rate it Ambitious: it suits confident students, who should expect to learn some mathematics on their own.

What mathematics does this IA use?

The logistic expected-score formula E = 1/(1 + 10^(−Δ/400)), iterative updating (a recurrence), measuring prediction quality (e.g., mean squared error of probabilities) and optimising a parameter by comparison.

Where can I get data for this IA?

Use several seasons of results from Football-Data.co.uk (which also include bookmakers' odds for comparison). Checked sources and tools: Football-Data.co.uk.

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