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

IA idea · Sport

When should a Formula 1 driver pit? Modelling tyre degradation

AA SLAI SLAA HLAI HL Ambitious Also in: Modelling, Calculus

Research question

Using lap-time data from a real race, can a linear or quadratic model of tyre degradation find the lap on which a one-stop driver should pit to minimise total race time?

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Why it makes a good exploration

Race strategy is mathematics under pressure. Lap times get slower as tyres wear; a pit stop costs about 20 seconds. Modelling the trade-off with real lap data gives an optimisation problem with a clear answer to check against what teams did.

The mathematics you'll need

Regression of lap time against tyre age
Total time as a sum (arithmetic series or integral)
Minimising total time with respect to pit lap
Comparison of one- and two-stop strategies

Where the data comes from

Download lap times and pit-stop data for a race from the Jolpica-F1 API.

Jolpica-F1 API — Free Formula 1 results, lap times and pit stops from 1950 (the successor to the closed Ergast API).

A possible outline

Clean the data (safety cars, traffic).
Fit degradation models for each tyre compound.
Write total race time as a function of the pit lap.
Optimise and compare with the real strategy.
Reflect on fuel load, track position and safety cars.

Pitfalls that cost marks

Including safety-car laps in the fit.
Ignoring that the car gets lighter as fuel burns.
Overlooking undercut/overcut effects.

Showing personal engagement

Choose a race you watched.
Compare your strategy with the winner's.
Explain a surprising team decision using your model.

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

Which course is it for?

Course	Fit	Maths to lean on
AA SL	Fits — ambitious at SL	Regression of lap time against tyre age; Total time as a sum (arithmetic series or integral)
AA HL	Good fit	Regression of lap time against tyre age; Total time as a sum (arithmetic series or integral)
AI SL	Fits — ambitious at SL	Regression of lap time against tyre age; Total time as a sum (arithmetic series or integral)
AI HL	Good fit	Regression of lap time against tyre age; Total time as a sum (arithmetic series or integral)

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: including safety-car laps in the fit; and ignoring that the car gets lighter as fuel burns. Say how each one affects your answer.

Use of mathematics (E)

SL: regression of lap time against tyre age; total time as a sum (arithmetic series or integral); minimising total time with respect to pit lap; comparison of one- and two-stop strategies, 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 fuel-load correction (lap time falls as fuel burns) and re-optimise.

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 AA SL, AI SL, AA HL and AI 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?

Regression of lap time against tyre age, total time as a sum (arithmetic series or integral), minimising total time with respect to pit lap and comparison of one- and two-stop strategies.

Where can I get data for this IA?

Download lap times and pit-stop data for a race from the Jolpica-F1 API. Checked sources and tools: Jolpica-F1 API.

Turn this idea into your IA

The planner opens with “When should a Formula 1 driver pit? Modelling tyre degradation” filled in: the question, the maths and the data sources.

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