Strategy family: pit-stop and safety-car decision support

Counterfactual, base-rate and stint-ending models built on top of the closed residual and the cliff prediction one already shipped to the app, others built ahead of any consumer.

What this family does

Strategy answers decision-support questions the rest of the pipeline doesn’t: was a pit stop early, late, or undercut-forced; how often does a given circuit see a Safety Car per racing lap; which constructors degrade their tyres faster or hit the cliff later than the field; and why a given stint ended at all. These are counterfactual, base-rate or labelling estimates built on top of earlier families, not new physics terms none of them feeds back into the residual identity.

Upstream spans three families: Pace Baselines (int_compound_cliff_predicted, the cliff model every strategy counterfactual assumes is correct), Residual Decomposition (int_lap_residual_decomposed, for the deg-sensitivity slope), and Staging directly (stg_track_status, stg_results, stg_pits, stg_laps for the two circuit base-rate models, which don’t need any physics decomposition first). Downstream is thin and uneven: only two of the four models are read by anything else in dbt at all.

The sub-DAG

The mismatch this page used to record is now closed. int_pit_loss_circuit’s description said it existed “to replace the largely-imputed constant… used by int_pit_strategy_value”, but for as long as both models existed no ref() connected them and the pit-lane-loss join went straight to circuit_reference.pit_lane_loss_s. int_pit_strategy_value now reads pit_loss_s_shrunk and falls back to the seed only for a circuit that resolves no clean stops — one race in seven seasons, 2018 round 14, whose race_to_track row has a NULL track_id. A pit_loss_source column on every stint records which of the two was used. int_sc_hazard_history remains a genuine leaf: built, tested by its own singular test, read by nothing else in dbt and exported to no app feature.

How it works

The constructor degradation slope is a within-stint fixed-effects regression, expressed in closed form rather than fit with a library a single OLS slope per (constructor, compound, season) cell, computed directly from sums:

slope_raw = SUM((age - mean_age_stint) * (resid - mean_resid_stint))
          / SUM((age - mean_age_stint)^2)

The raw slope is uniformly negative across every constructor (residual fuel under-correction leaking through the decomposition), so the model field-centres each cell against the precision-weighted per-(compound, season) mean before anything downstream consumes it only the centred deviation, not the raw slope, is the production value.

The two circuit base-rate models (SC hazard, pit loss) share one empirical-Bayes shrinkage shape a pseudo-count blend toward a global pooled rate, distinct from the DerSimonian-Laird random-effects shrink the degradation slope uses above:

(c.n_sc_onsets + g.sc_rate * {{ var('sc_hazard_prior_laps', 600) }})
/ (c.racing_laps + {{ var('sc_hazard_prior_laps', 600) }})
    AS sc_hazard_per_lap_shrunk

600 laps of prior weight (roughly a handful of races) keeps a circuit with one or two race-years of history from reading a hazard of exactly 0 or an extreme outlier; int_pit_loss_circuit does the same blend with a 15-stop prior instead of a lap-count prior, since its unit of exposure is pit stops, not laps.

The optimum itself is an argmin, not a rule of thumb. int_pit_strategy_cost_curve prices every candidate pit lap in the horizon and int_pit_strategy_value takes the minimum:

Total_Cost(L) = old_wear_cost_s      -- L laps on the set you are on
              + new_wear_cost_s      -- the rest of the horizon on the next set
              + baseline_cost_s      -- per-lap pace offset between the compounds
              + pit_lane_loss_s * pit_discount_factor

L = H is the no-stop candidate and pays no pit term, which is what makes a stop justify itself. The discount is the part that matters:

pit_discount(L) = 1 - (1 - m) * (1 - (1 - h)^L)

Under a fixed one-stop the pit-lane loss is the same whenever you take it, so it adds a constant to every candidate and drops out of the argmin entirely — a longer pit lane would move nothing. Discounting it by the chance a caution has already appeared (h from int_sc_hazard_history, m the SC cost multiplier) is what makes waiting pay, and it is why a longer pit lane pushes the optimum later. assert_pit_loss_pushes_optimum_later re-minimises the same curve at a pit lane 15 s longer and fails if the answer retreats.

Strategy verdicts on pit timing are then a plain ordered CASE, not a regression a stop within one lap of the modelled optimum is 'optimal'; later is 'overran'; earlier counts as 'undercut_forced' only if the stop landed inside the window where the undercut threat opened, otherwise it’s 'early':

WHEN ABS(r.actual_offset - r.pick_offset) <= 1 THEN 'optimal'
WHEN r.actual_offset > r.pick_offset + 1 THEN 'overran'
WHEN r.first_undercut_threat_lap IS NOT NULL
     AND r.actual_pit_lap BETWEEN r.first_undercut_threat_lap - 2
                              AND r.first_undercut_threat_lap + 3
     THEN 'undercut_forced'

Laps are compared as offsets in valid laps rather than lap numbers, so an invalid lap before the stop cannot skew the comparison.

Design notes

Why this shape

The optimal-pit-lap counterfactual leans entirely on the cliff model (int_compound_cliff_predicted) being correct it isn’t fit independently from race outcomes, it’s a deterministic minimisation over the cliff model’s predicted degradation cost across a fixed window around the modelled onset. That’s a stated assumption in the model’s own header, not hidden: the strategy verdict is only as good as the cliff prediction it’s built on, and a circuit or compound where the cliff model is weak will produce a strategy verdict with the same weakness.

Two different empirical-Bayes shrinkage shapes coexist in this family for a reason, not by accident: the circuit base-rate models (SC hazard, pit loss) shrink a rate toward a global pooled rate with a pseudo-count prior, the natural conjugate form for a count-over-exposure problem. The degradation slope shrinks a deviation (already field-centred, so its prior mean is exactly 0 by construction) using a DerSimonian-Laird between-group variance estimate, the standard random-effects meta-analysis form, appropriate because the thing being pooled across constructors is itself a fitted estimate with its own standard error, not a raw count.

Both circuit base-rate models are now consumed by the optimum itself, not just displayed next to it. int_pit_loss_circuit sets the size of the pit term and int_sc_hazard_history sets how fast that term decays with waiting — the two together are what give the search a pit-loss gradient at all. Until 2026-08-23 neither reached the search: it approximated the argmin as “first lap in the cliff window where expected wear exceeds 0.5 s”, a threshold with no pit-loss term in it, which returned 'optimal' on 8 stints of 7,129 and 'unknown' on 2,231 — more than half of every stint that ended in a stop. The argmin returns 715 and 266.

Two horizons are reported because they answer different questions. The verdict follows the two-stint window — this stint’s first lap through the next stint’s last — which grades the stop inside the strategy the team actually ran. That is the only framing well posed for the 61% of stints belonging to a 2-stop or longer race; a race-remainder one-stop counterfactual scores every 2-stopper’s first stint as 'early' for a reason that has nothing to do with the stint. The race-remainder optimum is carried alongside as optimal_pit_lap_race, asking the harsher unconditional question.

Other approaches

Letting the compound pace offset move the optimum is the open judgement call, exposed as pit_strategy_baseline_delta. baseline_cost_s carries the per-lap difference between the old and new compound, built from compound_grip_peak and the optimal-temperature bounds — and both of those are per-compound constants in compound_cliff_params, one distinct value each across all 403 seed rows, never fitted. As typed, grip_peak prices SOFT (1.03) slower than HARD (0.97). Over a 20-lap arm that is roughly 1.2 s of unmeasured offset pushing against fitted wear effects of the same magnitude. The var is true today; setting it false drops the term and leaves the argmin to fitted wear, cliff onset and severity alone. Fitting a real per-compound pace baseline is the change that would settle it.

A fixed number of stops is the other standing simplification: the cost function prices exactly one stop inside its horizon. Choosing the number of stops needs a different search — over strategies rather than over laps — and is what a full race simulation would add.

A fitted hazard model (logistic or Cox, conditioning on lap number, weather, and grid spread) is the credible alternative to int_sc_hazard_history’s flat per-circuit empirical rate it would let a simulation vary the SC probability within a race instead of treating every lap at a venue as equally hazardous, at the cost of needing more than the circuit-level grain this model currently estimates at.

A stochastic strategy model (Monte Carlo over pit-loss and degradation uncertainty, rather than a single deterministic optimum) is the credible alternative to today’s point-estimate verdict the deterministic minimisation is auditable and matches the rest of the family’s “named assumption, no hidden randomness” style; a stochastic version would need the two currently-unconsumed base-rate models as direct inputs.

Every model in this family

int_constructor_deg_sensitivity

Within-stint FE slope of degradation per (constructor, compound, season), field-centred and EB-shrunk feeds the ghost-car host-identity interaction term.

int_pit_strategy_value

Counterfactual optimal pit lap and opportunity cost per stint, plus an undercut-threat lap and an optimal/overran/undercut_forced/early verdict.

int_sc_hazard_history

Per-circuit Safety Car / VSC hazard rate per racing lap, EB-shrunk toward the global pooled rate. Currently a leaf no dbt or app consumer yet.

int_pit_loss_circuit

Empirical per-circuit pit-lane loss from real green-flag in-lap/out-lap deltas, pooled per physical venue and EB-shrunk. Read by int_pit_strategy_value.

int_stint_end_regime

Why each stint ended, at stint grain: green_pit / sc_pit / vsc_pit / red / race_end / retirement, under a declared precedence. Owns is_censored_stint. 28.8% of the stints the survival target calls completed tyre lives ended under a deployment instead.