End-to-end pipeline for modelling F1 tyre pace loss from raw timing data. Raw laps → fuel/track-evolution correction → two degradation models → race strategy simulator.
FastF1 API
└─ scripts/build_dataset.py raw lap filtering → data/laps_clean.parquet
└─ scripts/correct_all_races.py fuel + track-evo correction → data/laps_corrected.parquet
├─ model/train_lgbm.py v1 LightGBM + conformal intervals
├─ model/train_lgbm_quantile.py v1b CQR quantile model ← primary
├─ model/train_bayesian.py v2 hierarchical Bayesian (PyMC)
├─ model/eval_temporal.py temporal holdout: 2023-24 → 2025
├─ model/eval_loto.py leave-one-track-out generalisation
└─ model/strategy_sim.py race strategy simulator
| Seasons | 2023, 2024, 2025 |
| Raw laps | 58,970 |
| Races | 62 |
| Races passing quality gate | 53 / 62 |
| Fit-ok laps | 51,437 |
| Tracks | 23 |
| Drivers | 28 |
| Compounds | SOFT, MEDIUM, HARD |
Each race is fit with an OLS model laptime ~ driver + lap_n + lap_n² + age:compound. A race passes if:
- R² ≥ 0.50
- Residual RMSE ≤ 1.0 s
beta_lap_n > −0.10(rules out races where the correction absorbed tyre deg into a physically implausible negative track-trend)
9 races fail, mostly Monaco, Singapore 2023, and Azerbaijan 2025 — SC-heavy races with heavily distorted lap time distributions.
Raw lap time → remove fuel load (0.056 s/lap) → fit quadratic track-evolution curve → subtract per-stint fresh reference (mean of laps 2–4):
deg_s = pace_loss_s − stint_ref_pace
deg_s is zero at fresh tyres and increases as the tyre ages. Mean ≈ 0.40 s, std ≈ 1.1 s.
The target deg_s is the degradation component after removing these confounders. Each is treated explicitly:
| Confounder | Treatment |
|---|---|
| Fuel burn | Fixed correction of 0.056 s/lap (0.035 s/kg × ~1.6 kg/lap burn rate) applied before fitting. Removes the downward slope that would otherwise contaminate deg estimates in early laps. |
| Track evolution | Per-race quadratic OLS fit on lap_n + lap_n² across all drivers. The fitted trend is subtracted from every lap. Races where the fit implies an implausible negative slope are excluded by the quality gate. |
| In/out laps | Excluded during build_dataset.py via PitInTime / PitOutTime flags. |
| Safety car / VSC | Filtered using TrackStatus != '1'. Races with residual SC contamination fail the R²/RMSE quality gate and are excluded. |
| Traffic | No direct signal available in public FastF1 data. Proxied by the lap-time outlier filter (> 110% of driver's stint median) which removes the most egregious traffic laps. Remaining traffic is accepted as noise; it increases variance but does not systematically bias the deg estimate. |
| Driver push/save | Unobservable in public data — drivers deliberately lift without any telemetry flag. Treated as irreducible noise. The per-stint reference normalization (subtracting laps 2–4 mean) absorbs most of the per-driver baseline; lap-to-lap push/save variation remains in the residual. |
| Driver effect | Absorbed partly by the per-stint reference normalization and partly by the team feature in the model. Individual driver intercepts are not modelled separately; the team proxy is sufficient given the small within-team driver variance on tyres. |
| Used sets | Captured by starting_tyre_life (the minimum tyre age at stint start). A tyre starting at age 8 degrades differently from one starting at age 1 even at the same current age. |
Same features as v1. Three LightGBM models per fold: MAE point estimate, lower quantile (α/2), upper quantile (1−α/2). The CQR nonconformity score max(q_lo − y, y − q_hi) calibrates interval width. The resulting intervals are adaptive (heteroskedastic) — narrower early in a stint, wider at high tyre age — with a formal coverage guarantee.
| Metric | Value |
|---|---|
| OOF MAE | 0.630 s |
| Baseline (predict 0) | 0.785 s |
| Improvement | 19.8% |
| 80% coverage | 77.6% |
| Interval width | 1.802 s |
CQR produces adaptive (heteroskedastic) interval widths — narrower early in a stint, wider at high tyre age. This is the model used for the worked example and strategy simulator.
Symmetric split-conformal intervals: [ŷ − q_α, ŷ + q_α]. Simpler than CQR but produces constant-width bands regardless of tyre age.
| Feature | Importance |
|---|---|
| tyre_life | 31.4% |
| event (track) | 23.5% |
| team | 8.9% |
| stint number | 7.2% |
| air_temp | 5.0% |
| starting_tyre_life | 4.5% |
| track_temp | 3.9% |
| evo_swing | 3.7% |
| humidity | 3.2% |
| tyre_life² | 2.8% |
| is_street | 0.9% |
| compound | 0.2% |
compound ranks low because deg_s is stint-referenced. The compound effect lives in the shape of the curve, captured by age_soft/medium/hard interaction features and the track embedding.
| Metric | Value |
|---|---|
| OOF MAE | 0.605 s |
| Baseline (predict 0) | 0.785 s |
| Improvement | 22.9% |
| 80% coverage | 75.7% |
| Interval width | 1.713 s |
By compound:
| Compound | n | MAE | 80% Coverage |
|---|---|---|---|
| SOFT | 3,009 | 0.617 s | 76.2% |
| MEDIUM | 16,405 | 0.544 s | 79.3% |
| HARD | 23,834 | 0.645 s | 73.3% |
Non-centred parametrisation with partial pooling: per-(track, compound) deg slopes share compound-level priors. Handles unseen tracks via prior fallback. Student-T likelihood for robustness to outliers.
beta[track, compound] ~ HalfNormal(mu_beta[compound], sigma_beta[compound])
alpha[track, compound] ~ Normal(0, sigma_alpha)
delta[team] ~ Normal(0, sigma_team)
gamma[compound] ~ Normal(0, 0.02)
mu = alpha[t,c] + (beta[t,c] + delta[team]) * age + gamma[c] * (temp−30) * age/30
y ~ StudentT(nu, mu, sigma_obs)
20k-lap subsampling per fold to keep fit times tractable (~4–6 min/fold, 2 chains).
| Metric | v1b CQR | v2 Bayesian |
|---|---|---|
| OOF MAE | 0.630 s | 0.677 s |
| 80% coverage | 77.6% | 72.2% |
| Interval width | 1.802 s | 1.727 s |
| Total fit time | — | 1,389 s |
LightGBM wins on MAE and coverage. Bayesian undercoverage is partly due to subsampling — the posterior underestimates uncertainty with fewer training laps.
Train on 34 races (2023–24), test on 19 races (2025). The model is fit entirely on pre-2025 data.
| Metric | CV (5-fold) | Temporal 2025 |
|---|---|---|
| MAE | 0.605 s | 0.633 s |
| Baseline | 0.785 s | 0.757 s |
| Improvement | 22.9% | 16.4% |
| 80% coverage | 75.7% | 75.8% |
8% MAE degradation season-to-season. Coverage holds, which means the conformal calibration generalises to a new season.
| Track | n | MAE | Coverage |
|---|---|---|---|
| Emilia Romagna GP | 821 | 0.457 s | 88.9% |
| Abu Dhabi GP | 1,048 | 0.466 s | 85.9% |
| Canadian GP | 1,084 | 0.472 s | 86.4% |
| Qatar GP | 922 | 0.487 s | 82.8% |
| USGP | 707 | 0.533 s | 84.0% |
| … | |||
| Hungarian GP | 1,289 | 0.708 s | 73.9% |
| Japanese GP | 997 | 0.872 s | 57.7% |
| Singapore GP | 1,069 | 1.093 s | 46.9% |
Singapore and Japan are persistent outliers. At Singapore, deg_s has only r=0.49 correlation with tyre age (vs r=0.59 at Austria) — the correction model absorbs real degradation signal into track-evolution noise at street circuits with heavy safety car activity.
model/eval_loto.py trains on all tracks except one, tests on the held-out track, and repeats for every track. This measures how much the model degrades when it has never seen a given circuit.
For the held-out track the event categorical feature falls back to the most common training track — the model can still use tyre age, temperature, team, and is_street to make predictions.
| Metric | Value |
|---|---|
| In-distribution MAE (5-fold CV) | 0.605 s |
| LOTO mean MAE (all tracks) | 0.641 s |
| MAE degradation vs in-distribution | +0.036 s (6%) |
| LOTO mean MAE (permanent circuits) | 0.571 s |
| LOTO mean MAE (street circuits) | 0.895 s |
| Mean 80% coverage (LOTO) | 79.1% |
Street circuits show the largest LOTO penalty: the is_street flag gives some signal but much of what the model learns about Monaco or Singapore is track-specific behaviour that cannot be inferred from other circuits.
Three separate per-compound models vs one joint model:
| Model | OOF MAE |
|---|---|
| Joint LightGBM (v1b CQR) | 0.630 s |
| Per-compound (SOFT/MEDIUM/HARD) | 0.633 s |
The joint model wins by borrowing cross-compound track information. A track that degrades tyres hard in general affects all compounds — the joint model learns this; per-compound models can't.
scripts/worked_example.py picks the richest race from the out-of-fold predictions and plots predicted vs actual deg_s per compound, with the 80% prediction band overlaid on individual lap scatter. The selected race is Dutch Grand Prix 2024 — all three compounds present, 1,337 laps, long hard stints.
| Compound | n | MAE | 80% coverage |
|---|---|---|---|
| SOFT | 87 | 0.435 s | 88.5% |
| MEDIUM | 470 | 0.540 s | 83.8% |
| HARD | 780 | 0.738 s | 83.8% |
| Overall | 1,337 | 0.649 s | 84.1% |
Where the model agrees: coverage is strong across all three compounds (84% overall), and the predicted slope direction is correct for every compound — deg_s rising with tyre age as expected.
Where it struggles: the model systematically under-predicts the degradation rate at Zandvoort. The actual slopes (+0.071 s/lap SOFT, +0.051 s/lap MEDIUM, +0.040 s/lap HARD) are 2–3× steeper than predicted. Zandvoort is an abrasive, high-lateral-load circuit; the model has limited data on it (2023 and 2024 races only) and the corrected deg signal has high variance. The largest single-lap errors reach 3–5 s, driven by a handful of laps where drivers clearly pushed hard on old tyres late in stints — the push/save confounder noted in the dataset caveats.
model/strategy_sim.py compares tyre strategies by predicting cumulative pace loss per stint.
| Strategy | Tyre deg | Pit loss | Total |
|---|---|---|---|
| 1-stop: HARD → MEDIUM | +17.6 s | +22 s | +39.6 s |
| 1-stop: MEDIUM → HARD | +20.5 s | +22 s | +42.5 s |
| 2-stop: MED → HARD → SOFT | +16.5 s | +44 s | +60.5 s |
| 2-stop: SOFT → MED → HARD | +16.7 s | +44 s | +60.7 s |
1-stop strategies dominate once the 44 s double-pit penalty is included. HARD→MEDIUM beats MEDIUM→HARD because the hard compound degrades slowest when fresh — it's more valuable at the start of a stint than at the end.
from model.strategy_sim import load_model, simulate
model, meta = load_model()
laps = simulate(
model, meta,
track="British Grand Prix",
team="Mercedes",
stints=[("HARD", 28), ("MEDIUM", 30)],
)
print(laps.groupby("stint")["pred_deg_s"].agg(["mean", "sum"]))- Street circuits (Monaco, Singapore, Azerbaijan): safety car activity corrupts the track-evolution correction, making deg_s noisy. LOTO and temporal MAE are both ~2× the permanent-circuit average at these venues.
- High tyre age (>30 laps): training data is sparse due to censoring. Uncertainty bands widen appropriately but point estimates are less reliable.
- First 1–2 laps of a stint: tyre warm-up is confounded with driver push; the model sees this as noise and regresses toward zero.
- 2025 regulation changes: if Pirelli compound spec or car performance changes significantly, the model may need retraining. The 8% temporal MAE increase (0.602→0.633 s) suggests limited but non-zero drift year-to-year.
- Out-of-distribution teams: unseen team/track combinations fall back on the average team behaviour. The Bayesian v2 handles this more gracefully via partial pooling.
python -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt
make all # fetch data → train → eval → plots (~30 min + FastF1 cache warm-up)
# Or step by step:
make data # build_dataset.py + correct_all_races.py
make train # v1, v1b, per-compound models
make train-bayesian # v2 Bayesian (~25 min)
make eval # evaluate_model.py, eval_temporal.py, eval_loto.py
make plots # all figures including worked example
make strategy # strategy simulator outputData and model artefacts are gitignored (data/, cache/). Re-running build_dataset.py with a warm FastF1 cache takes ~2 min; the first run fetches ~500 sessions and takes 20–40 min depending on connection speed.