Two curves, not one
The core identity is simple. Expected recovery on day d past due = net resale value(d) × probability of physical custody(d) − recovery costs(d). In buy-here-pay-here the asset is the loan and the collateral is the only real protection, so everything about repossession timing reduces to how those two curves move against each other.
They move at completely different speeds. Used vehicles are depreciating slowly right now, roughly 1% a month in 2026 wholesale data (Black Book and Manheim indices). The odds you ever get the car back are the fast term: they collapse the moment a delinquent borrower stops answering, lets insurance lapse, disables the GPS, and starts hiding the unit. The car is not the bleed. The custody probability is, and it is the term most operators never put a number on.
One denominator discipline matters here. Net resale value is what the unit itself would fetch at sale. It is deliberately not multiplied by an ABS-style loan-balance recovery rate, the 30s,40s percent figures lenders report measure recovery against the loan balance, a different denominator, and folding them in would double-count loss severity.
The slow term: what the car does
At the 2026 wholesale norm of ~1% a month, ninety days of delay costs a unit about 3% of its value from depreciation alone. The model adds a condition drag for wear, miles, and neglect while the car sits with a non-paying borrower, about 0.095% of value per day past due, capped at 14%. Even at a stress case of 1.5% or more a month, the vehicle side of the identity moves single-digit percentages over a full quarter. If that were the whole story, waiting would be cheap.
The fast term: the custody curve
Custody probability is modeled as a logistic slide from a high starting point down to a posture-dependent floor. The parameters below are the actual presets the model runs on, three borrower postures, each with a starting probability, a floor, a midpoint (the day past due at which half the slide has happened), and a steepness scale.
| Borrower posture | Odds at day 0 | Floor | Midpoint of slide | Steepness scale |
|---|---|---|---|---|
| Cooperative | 97% | 66% | day 78 | 15 d |
| Going quiet | 95% | 30% | day 46 | 10 d |
| Hiding it | 90% | 7% | day 28 | 7 d |
Read the "hiding it" row again. Half the slide is done by day 28, and the floor is 7%. On a concealed unit, a month of delay converts a near-certain recovery into a long-shot skip file, while the car itself has lost barely 1% of its value.
The trigger ledger: stage the file vs repo now
The model does not treat days past due as the decision variable. Behavior is. Two tiers of signals govern the file's footing.
| Tier | Signal |
|---|---|
| Hard · repo footing | GPS shows the unit dormant 72h+ or out of the area |
| Hard · repo footing | Starter-interrupt or GPS tampered with or disabled |
| Hard · repo footing | Insurance lapsed, collateral now uninsured |
| Hard · repo footing | Payment reversed / NSF and no contact since |
| Hard · repo footing | Broke a second promise-to-pay |
| Hard · repo footing | No contact for 10+ days (skip behavior) |
| Soft · stage the file | Missed within the first 3 payments (early-payment default) |
| Soft · stage the file | First scheduled payment missed |
| Soft · stage the file | Partial payment only |
| Soft · stage the file | Broke first promise-to-pay |
| Soft · stage the file | Phone disconnected / mail returned |
| Soft · stage the file | Paying later each month (deteriorating pattern) |
The clock that gates all of this is legal, not behavioral. In the model, the cure notice goes out on day 10 past due, and the lawful repo day is that notice day plus the state and contract cure window. Some states allow repossession at default with no notice; others require a cure or notice period, on the order of ~10 days in Rhode Island and Maryland, ~15 in Pennsylvania, ~21 in Illinois. The lawful day is the best day the decay curve will ever offer, which is why the staging logic is built around reaching it pre-positioned rather than starting the process there.
A worked example: the decay table
The table below runs the model end to end on a synthetic default file: an $8,500-net unit, 1.0%/month depreciation, "going quiet" posture with no hard triggers, cure notice served day 10, a 15-day cure window (lawful day 25), $875 in fixed recovery and disposal costs, and $25/day of holding cost from the notice day. Every figure is illustrative.
| Day past due | Unit net value | Custody odds | Costs accrued | Expected net recovery |
|---|---|---|---|---|
| Day 10 · notice served | $8,391 | 93% | $875 | $6,952 |
| Day 25 · lawful day | $8,229 | 88% | $1,250 | $5,984 |
| Day 40 | $8,069 | 72% | $1,625 | $4,182 |
| Day 60 | $7,857 | 43% | $2,125 | $1,242 |
| Day 90 | $7,543 | 31% | $2,875 | −$552 |
| Day 120 | $7,236 | 30% | $3,625 | −$1,451 |
The decomposition is the point. At 30 days past due on this file, the next 30 days of waiting cost the unit about 4% of its value, and cost the custody odds about 49% of theirs. Almost the entire waiting tax is the second term. Early custody also keeps the borrower's redemption and reinstatement options alive: in CFPB data, redemptions run ~22-34% of completed repossessions, and most happen within 30 days of the repo.
Limits
Honesty about what this method cannot see. The custody curves are priors, not measurements. No public source reports a daily custody probability by borrower posture, days past due, GPS status, or broken promises; the posture parameters and trigger penalties are calibrated to the directional CFPB and Fed findings, not fitted to an event-level repossession dataset. The structural claim, custody odds collapse faster than vehicle value, so timing beats auction math, is well supported. The exact coordinates are estimates that should be recalibrated against an operator's own repo history before any dollar figure is trusted. The ~1%/month depreciation figure is a market-wide wholesale index, not any particular lane or segment. The model ignores agent capacity, lot constraints, bankruptcy stays, and the economics of reinstatement. And the legal gate is state- and contract-specific: cure, notice, and self-help rules vary widely, and nothing here substitutes for confirming them in the relevant jurisdiction.