Week 7: The safety car

Price one lap of waiting for a possible Safety Car, reject unavailable tyre sets before scoring, and state the hazard that would reverse the call

19 April 2027

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Until now, a stop has had one measured cost. This week an interruption may change that cost before the next lap ends. A deployed Safety Car neutralises the race: cars reduce speed and form a queue. On-track running slows while the pit lane remains a separate, speed-limited path, so a tyre stop may lose less race time relative to cars that stay out. The mechanism is real. Every cost and probability in our fixture is synthetic.

We describe the uncertainty with a next-lap hazard: h_l = P(SC starts on lap l | no SC before lap l). The condition matters. This is not the chance that a Safety Car appears somewhere in the race, and it is not a probability estimated from Formula 1 history. The scenario supplies it. Survival across several laps multiplies the chances of no arrival, but our call stays bounded to one lap: stop now or wait one lap.

Before we price either action, we check that it can be carried out. A returned tyre set is unavailable. A used set that has not been returned may be refitted under the allocation boundary from Week 3. A cheap projected stop that names a set outside the remaining ledger is not a candidate, however attractive its expected cost looks.

For feasible actions that retain the same projected finishing position, we score waiting analytically: the supplied hazard times the Safety Car cost, plus the chance of no Safety Car times the normal-running cost. We compare that expectation with stopping now and solve the break-even hazard. We do not draw a random event to approximate two terms we can calculate exactly. Finishing position remains first; expected adjusted time only breaks a position tie.

The output is a call with its projected position, expected adjusted cost, required physical set, supplied hazard and break-even hazard. It also says that the hazard is a synthetic scenario input. The final instrument must carry the same assumptions beside its recommendation, where a reader can inspect them.