Skill family: de-biasing the car to leave the driver

Seven models, two parallel systems: a teammate-relative rating chain (lap-by-lap gap to the teammate, then Bayesian shrinkage) exported straight to the app, plus one independent pairwise signal that is the family’s only ML feature.

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What this family does

Skill isolates driver performance from car performance using two genuinely different identification strategies that both live in this family. The first is a rating chain: a race-grain equal-car rating, the driver’s median lap-by-lap gap to his teammate in the same car (LORO: leave-one-driver-out, so a driver is never in his own baseline), then per-cell Bayesian shrinkage at season and circuit grain. A de-biased constructor×race fixed effect read from an external pyfixest fit feeds a parallel field-anchored signal used only by the era-affinity model. No era offset is applied: a teammate-relative rating cancels a car-era shift inside each pair. The second is int_synthetic_teammate, a single self-contained pairwise comparison with no shrinkage and no fixed-effects fit.

These signals are not the additive identity’s closure-defined driver_skill. That term (pace_delta minus the four physics components, see The Additive Identity) is computed entirely inside Residual Decomposition, from a different baseline. No model in this family ref()s anything in Residual Decomposition, and no residual model reads anything here verified directly against manifest.json, not assumed (see the correction note on this tab’s overview). This family’s outputs are an independently-estimated, complementary rating system, built for ranking and leaderboards rather than for closing a per-lap identity.

Upstream is mostly Pace Baselines (int_field_pace_curve, int_track_evolution) and Physics (int_lap_fuel_state, int_stint_geometry), plus one external source the constructor car-pace fit lives outside dbt run entirely, in data/fits/constructor_car_fe.parquet. Downstream is asymmetric: of the seven models, only int_synthetic_teammate is read by any other dbt model (fct_driver_skill_features, the one ML feature mart this family touches). The other six are leaves in the model DAG, reachable only by their own CI tests and four of those six are exported straight to the app by scripts/export_app_data.py, each powering a named feature directly with no marts model in between.

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The sub-DAG

The four directly-exported models power, by name: int_era_normalized_driver_rating → Era Ratings Timeline, Era Translator, Hidden Performance; int_driver_circuit_affinity → Driver Circuit Affinity; int_driver_circuit_era_affinity → Ghost Race Standings, Hidden Performance; int_synthetic_teammate → Synthetic Teammate (in addition to its fct_driver_skill_features edge above) verified against the app’s own query files, not inferred from the export script alone. int_constructor_car_fe, int_driver_race_skill_loro, and int_driver_season_ratings are pure pipeline stages: nothing reads them except the next stage and their own tests.

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How it works

The LORO baseline is the family’s representative move: a driver’s car baseline is the mean of his other same-car teammates’ median pace delta, built by subtracting his own contribution out of the car’s summed total rather than computing two separate baselines per car:

CASE
    WHEN ca.n_car_drivers > 1
        THEN (ca.sum_driver_median_s - dra.driver_median_pace_delta_s)
             / (ca.n_car_drivers - 1)
END AS loro_car_baseline_s

Three of the seven models pull an observed cell mean toward a wider prior via the same conjugate posterior, the bayesian_shrinkage macro:

$\hat\mu_{\text{post}} = \frac{n \cdot \bar x_{\text{obs}} + k \cdot \mu_{\text{prior}}}{n + k}$

where $k$ is the prior weight, expressed as virtual observations ($k=5$ everywhere in this family five virtual races or circuit-visits’ worth of pull toward the prior mean).

1. Car FE

   int_constructor_car_fe reads a two-way fixed-effects fit (pace_delta_s ~ 1 | driver_id + constructor_race) from an external pyfixest artifact: car pace net of who drove it, anchored globally so one weak driver’s slowness can’t leak back in as car pace.

2. LORO baseline

   int_driver_race_skill_loro computes two parallel signals per driver-race: driver_skill_loro_s, the median of the driver’s lap-by-lap gap to his teammate on laps both ran clean (paired on lap number), feeding the rating chain; and a field-anchored signal, median pace delta minus the car FE, used only by the era-affinity model below.

3. Per-cell shrink

   int_driver_season_ratings (season grain) and int_driver_circuit_affinity / int_driver_circuit_era_affinity (circuit and circuit×era grain) each shrink their observed cell mean toward a wider prior mean with the same conjugate macro.

4. Publish, no era offset

   int_era_normalized_driver_rating publishes the season rating as era_adjusted_rating with no offset. It still measures the average shift of drivers with ≥8 races on both sides of the 2022 boundary, as a diagnostic only.

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Design notes

Why this shape

The car-pace fixed effect lives outside dbt run because a two-way HDFE with high-cardinality terms (driver × constructor-race) is a real linear-algebra problem, not something a window function expresses the offline fit-and-promote shape mirrors Reference’s seed-and-promote cycle for the compound-cliff coefficients.

LORO exists because a same-car median baseline is contaminated by both drivers, including a weak one subtracting it hands the weak driver’s slowness back to his teammate as “skill.” LORO removes the focal driver from his own baseline; the field-anchored variant goes further, replacing the single-teammate baseline with the FE’s global driver anchor specifically for the era-affinity model, which otherwise inflates a driver paired with a persistently slower teammate.

driver_skill_loro_s compares like with like, lap by lap. Until WI-14b (2026-09-28, audit finding F40) it was the driver’s 20th-percentile (ceiling) lap delta minus the teammate’s median, meant to discount a dominant-car leader’s cruising. A ceiling against a typical lap mixes lap-time scatter into the level: scatter read as speed, and in 79% of two-driver cars both teammates were rated faster than each other. Pairing the two drivers’ clean laps on the same lap number and taking the median gap is antisymmetric by construction (a pair’s ratings sum to 0) and did best on split-half reliability and qualifying agreement in the design round that chose it.

int_driver_circuit_era_affinity and int_driver_circuit_affinity read the circuit_reference seed directly rather than going through Reference’s dim_circuits, because they need circuit_id_from_name’s physical-venue resolution so a renamed event or a double-header pools into one track record. int_driver_circuit_affinity shrinks each circuit’s gap to the teammate toward the driver’s own mean and publishes the difference, affinity_vs_driver_mean_s, as the affinity (F44: drawing the shrunk level itself painted every cell one colour).

There is no era offset because a teammate-relative rating has no era level to remove: a change of car era moves both teammates alike. The bridge-driver offset this model used to apply (t = −1.5, no significance gate) inverted the between-era field-mean gap it was meant to remove (F45). assert_era_offset_shrinks_gap fails if an offset comes back with |t| < 2, or widens or inverts that gap.

Other approaches

A full hierarchical or mixed-effects model is the credible alternative to closed-form conjugate shrinkage at every shrink point in this family. The conjugate form is auditable in pure SQL and adequate for a Normal-Normal problem with a roughly stable within-cell variance; a mixed-effects fit would need to leave dbt run the way the car FE already does, for a precision gain this family’s CI tolerances don’t currently need.

LORO/FE de-biasing and int_synthetic_teammate’s pairwise comparison are not competing designs here both shipped, deliberately, for different jobs. The pairwise comparison needs no shrinkage or fitted car term and is the one signal stable enough at single-race grain to feed an ML model; the LORO/shrinkage chain is tuned for a season- or career-length rating, not a per-race feature.

An era adjustment of any shape (a bridge-driver step at 2022, or a continuous era covariate) is only needed for a rating measured against the field. The chain measures against the teammate instead, so the car and its era cancel; the price is that a rating says as much about the teammate as about the driver.

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Every model in this family

int_constructor_car_fe

Thin reader over an external two-way fixed-effects fit (driver × constructor-race): car pace net of who drove it.

int_driver_race_skill_loro

Two skill signals per driver-race: the median lap-by-lap gap to the teammate for the rating chain, and a field-anchored car-FE baseline for era affinity.

int_driver_season_ratings

Race-grain skill shrunk to season grain via Bayesian conjugate shrinkage toward the season mean.

int_era_normalized_driver_rating

The published season rating, on one scale across eras because it is teammate-relative; no era offset applied.

int_driver_circuit_affinity

Per-(driver, circuit) affinity: how much better or worse a driver does against his teammate at one circuit than his own average.

int_driver_circuit_era_affinity

The same affinity, era-split and car-removed via the FE baseline the “equal-car track record” leaderboard signal.

int_synthetic_teammate

Lap-by-lap synthetic teammate comparison, tyre-state-adjusted no shrinkage, no FE, the family’s only ML feature mart input.