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Concrete MIT Plan: F1 Wet-to-Slick Tyre Strategy

<#>Concrete MIT Plan: F1 Wet-to-Slick Tyre Strategy

<##>Final project title The Crossover Lap: Using Regression and Optimisation to Decide When F1 Drivers Should Switch from Wet Tyres to Slicks

Singapore-facing alternative: Rain at Marina Bay: Modelling the Optimal Tyre-Switch Lap in a Weather-Affected Formula 1 Race

<##>Research question During a mixed-weather Formula 1 race, how can mathematics determine the lap on which switching from intermediate/wet tyres to slick tyres minimises total race time?

<##>Exact H2 Math concept link

<###>Primary H2 concept: 9758 Section 6.6 — Correlation and linear regression This should be the main advertised syllabus link.

Official syllabus items that this project directly uses:

use of a scatter diagram to judge whether there is a plausible linear relationship between two variables;
correlation coefficient as a measure of the fit of a linear model;
interpreting the product moment correlation coefficient;
concepts of linear regression and the method of least squares to find the equation of the regression line;
use of the appropriate regression line to make prediction or estimate a value in practical situations;
explaining how well the situation is modelled by the linear regression model.

Project link:

Variable x: lap number, or time since rain stopped / drying-track proxy.
Variable y: lap time in seconds.
Fit separate regression lines:

- I(x) = a_i + b_i x for intermediate/wet tyres; - S(x) = a_s + b_s x for slick tyres.

Use scatter plots, r-values, and residuals to justify whether the linear model is acceptable.

<###>Supporting H2 concept 1: 9758 Section 2.1 — Sequences and series Official syllabus items used:

concepts of sequence and series for finite cases;
relationship between u_n, the nth term, and S_n, the sum to n terms;
formula for the nth term and sum of a finite arithmetic series.

Project link:

Each lap time is one term of a sequence.
Total race time is a finite sum of lap times.
If lap time is modelled linearly, I(l) = a_i + b_i l and S(l) = a_s + b_s l, then the total time over many laps is a sum of arithmetic sequences.

<###>Supporting H2 concept 2: 9758 Section 5.1 — Differentiation / optimisation Official syllabus items used:

determining local maximum and minimum points;
locating maximum and minimum points using a graphing calculator or graphing software;
local maxima and minima problems.

Project link:

Define T(k) as total predicted race time if the driver switches tyres on lap k.
Find the value of k that minimises T(k).
Since k is an integer lap number, evaluate nearby integer laps after finding the minimum point.

<###>Optional extension: 9758 Section 6.1/6.2 — Probability / expected value Only use this if there is time.

Project link:

If there is probability p of rain returning, compare expected total times:

- Expected time = p(time if rain returns) + (1-p)(time if track keeps drying).

Recommendation: keep the core as Section 6.6 regression + Section 2.1 summation + Section 5.1 optimisation. Do not make probability the main focus.

<##>Mathematical model

Let:

l = lap number;
I(l) = predicted lap time on intermediate/wet tyres on lap l;
S(l) = predicted lap time on slick tyres on lap l;
P = pit-stop time loss in seconds;
N = final lap of the window studied;
k = lap where the driver switches to slicks.

Use regression to fit:

I(l) = a_i + b_i l
S(l) = a_s + b_s l

<###>Basic crossover lap The simplest crossover is where slicks and intermediates are predicted to be equally fast:

I(l) = S(l)

a_i + b_i l = a_s + b_s l

So:

l = (a_s - a_i) / (b_i - b_s)

Interpretation:

before this lap, intermediate/wet tyres are predicted faster;
after this lap, slick tyres are predicted faster.

<###>Better race-strategy model with pit-stop loss The crossover alone is not enough because pitting costs time.

Total predicted time if switching on lap k:

T(k) = sum from l = 1 to k-1 of I(l) + P + sum from l = k to N of S(l)

Using the arithmetic-series formula:

sum from l = m to n of (a + b l) = (n - m + 1)a + b[n(n+1) - (m-1)m]/2

This gives a concrete formula for T(k). Then choose the integer k that gives the smallest T(k).

Decision rule:

Switch when the future time saved by slicks exceeds the pit-stop loss:

sum from l = k to N of [I(l) - S(l)] > P

<##>Data plan

<###>Primary dataset Use FastF1 on a mixed-weather race with both slick and intermediate/wet tyres.

Recommended primary case study:

2023 Dutch Grand Prix Race — strong because it had changing rain conditions and tyre switches.

Backup case studies:

2021 Russian Grand Prix Race — late-race rain strategy.
2022 Singapore Grand Prix Race — strongest local framing, but may be less clean if there are not enough slick/intermediate comparison laps.

<###>Variables to extract From FastF1:

LapNumber
Driver
Team
LapTime
Compound: SOFT, MEDIUM, HARD, INTERMEDIATE, WET
TyreLife
PitInTime / PitOutTime
TrackStatus if available
Weather data: Rainfall, TrackTemp, AirTemp, Humidity

Create a new variable:

TyreCategory = "SLICK" for SOFT/MEDIUM/HARD;
TyreCategory = "WET" for INTERMEDIATE/WET.

<###>Cleaning rules Remove:

pit-in laps;
pit-out laps;
obvious safety car / red flag laps if identifiable;
invalid or missing lap times;
extreme outliers caused by spins/crashes/traffic if they break the model.

Use lap time in seconds.

<##>Analysis plan

<###>Step 1 — Pick the race window Choose a window where the track is drying or changing, e.g. laps where some drivers use intermediates and others switch to slicks.

Output:

a small table of laps, tyre categories, and lap times.

<###>Step 2 — Plot scatter diagrams Make two scatter plots:

lap number vs lap time for wet/intermediate tyres;
lap number vs lap time for slick tyres.

MIT/H2 link:

Section 6.6 scatter diagrams and plausible linear relationship.

<###>Step 3 — Calculate PMCC r-values Calculate r for each tyre category.

Interpretation:

if |r| is close to 1, linear fit is strong;
if r is weak, acknowledge that track evolution, safety cars, and traffic limit the model.

MIT/H2 link:

Section 6.6 product moment correlation coefficient.

<###>Step 4 — Fit regression lines Fit:

I(l) = a_i + b_i l
S(l) = a_s + b_s l

Use least squares regression.

MIT/H2 link:

Section 6.6 least-squares regression line and prediction.

<###>Step 5 — Find the crossover lap Solve:

I(l) = S(l)

Then interpret whether the answer is realistic.

<###>Step 6 — Include pit-stop loss Pick a realistic pit-loss value P, or let the user adjust P in the simulator.

Then compute:

T(k) = sum from l = 1 to k-1 of I(l) + P + sum from l = k to N of S(l)

for each possible switch lap k.

MIT/H2 link:

Section 2.1 finite series;
Section 5.1 optimisation/minimum point.

<###>Step 7 — Choose the optimal switch lap Plot:

switch lap k on the x-axis;
total predicted race time T(k) on the y-axis.

The minimum point gives the recommended switch lap.

Because k is an integer:

if the minimum is at k = 9.6, compare k = 9 and k = 10;
choose whichever gives the smaller T(k).

<###>Step 8 — Validate against the real race Compare the model’s recommended switch lap with actual pit decisions by top drivers.

Discuss why they may differ:

pit-stop traffic;
tyre warm-up;
safety car or red flag;
driver skill;
weather forecast uncertainty;
risk preference.

<##>Final product plan

Best product: Interactive tyre-switch simulator/dashboard

Minimum required screens:

Race and data window selected.
Scatter plot of lap time vs lap number by tyre category.
Regression lines I(l) and S(l).
Crossover lap calculation.
Slider for pit-stop loss P.
Graph of T(k) against switch lap k.
Final recommendation: "Switch on lap __".
Limitations and assumptions.

If there is not enough time for a full app, make a polished notebook or slide deck with the same graphs.

<##>Two-page mathematical report structure

Even if the product is clear, prepare a short report because it protects you during assessment.

<###>Page 1: Model setup and regression

Research question.
Why wet-to-slick strategy is a real-world decision.
Define l, I(l), S(l), P, k, N.
Show scatter plots.
Show regression lines and r-values.
Explain link to Section 6.6.

<###>Page 2: Optimisation and conclusion

Derive T(k).
Show arithmetic-series formula used.
Plot T(k) against k.
State optimal switch lap.
Compare with actual race.
State assumptions and limitations.

<##>Annex checklist Required by MIT guide:

dataset source links;
FastF1 version;
Python/package versions;
all external references with access dates;
group members and roles;
online platforms/tools used;
AI Use Declaration with exact prompts and outputs incorporated.

<##>Suggested group role split

<###>Person 1 — Data lead

Extract FastF1 data.
Clean lap times.
Prepare table and plots.

<###>Person 2 — Maths lead

Calculate r-values and regression lines.
Derive crossover equation and T(k).
Write the mathematical explanation.

<###>Person 3 — Product/presentation lead

Build dashboard/slides/video.
Write assumptions and limitations.
Prepare citations and AI declaration.

If working in a pair, combine data + product for one person and maths + report for the other.

<##>3-day execution timeline

<###>Day 1 — Data and model

Choose primary race: 2023 Dutch GP.
Extract lap data using FastF1.
Clean data and choose a relevant lap window.
Produce first scatter plots.
Fit first regression lines.

<###>Day 2 — Optimisation and product

Calculate crossover lap.
Add pit-stop loss P.
Compute T(k) for all possible switch laps.
Build dashboard/notebook/slides.

<###>Day 3 — Polish and submission

Write two-page report.
Add assumptions and limitations.
Add citations/annex and AI declaration.
Test that every group member can explain the maths.

<##>Teacher pitch We are investigating a real decision in Formula 1 race strategy: when a driver should switch from wet/intermediate tyres to slick tyres as the track dries. We use H2 Math Section 6.6, correlation and linear regression, to model lap-time trends for each tyre type, then use finite series and optimisation to choose the switch lap that minimises total predicted race time. The final product will be an interactive simulator showing the regression model, crossover lap, and optimal pit lap under different pit-stop losses.