Week 10: Whose Race Is It?

One outcome set, two interests

The turn

Week 9 gave us distributions: where each strategy finished across repeated, shared scenarios.

A distribution does not prefer a strategy.

This week asks:

When the same joint race outcomes serve two cars, what changes when we rank them for the team rather than one named driver?

We change the rule for ranking. We do not change the evidence.

Objective and stakeholder

An objective is the explicit rule used to rank candidate decisions.

A stakeholder is the named interest that rule represents.

Our two objectives use the same points scale:

team: maximise expected constructors’ points across car 14 and car 22
car 14: maximise car 14’s expected race points

The quantity and stakeholder belong in the same sentence. Maximise points does not say enough.

Joint plan and expected points

A joint plan is one candidate strategy containing outcomes for two distinct cars under every supplied path.

Expected points is a probability-weighted mean:

for each path:
    score the finish or finishes named by the objective
    multiply that score by the path weight
add the weighted scores

It is a ranking over possible outcomes, not a promise about the result of one race.

The real rule, and where it stops

For one ordinary race whose leader completes at least 75% of scheduled distance:

Finish	P1	P2	P3	P4	P5
Points	25	18	15	12	10

Finish	P6	P7	P8	P9	P10
Points	8	6	4	2	1

FIA 2026 Section A, Issue 03, Articles A2.1.4(b) and A2.2.1: constructors’ points use both cars’ results. Expected points is our synthetic decision model, not an FIA method or recommendation.

Validate before ranking

For every plan/path pair, require:

exactly one record for car 14 and one for car 22
each finish inside P1–P10
distinct finishing positions for the two cars

Across paths, require:

each path has one non-negative weight
the weights sum to 1.00
every plan has outcomes on the same path set

Invalid input produces no ranking. A plausible winner from malformed evidence is still malformed.

Four failures to stop at the door

Input	Failure
weights `0.25, 0.25, 0.25`	probability mass is `0.75`
car 14 appears twice	car 22 is missing
car 22 finishes P11	finish is outside the lookup
car 14 P3, car 22 P3	two cars occupy one position

One more check protects comparability: a plan missing Path 4 cannot be ranked against plans that include it.

Stop. Report the invalid record. Do not calculate around it.

The synthetic fixture (1 of 2)

Each cell is car 14 / car 22. Every path has weight 0.25.

Joint plan	Path 1	Path 2
protect 14	P1 / P8	P2 / P7
balance	P2 / P3	P3 / P4
split risk	P1 / P8	P2 / P7

These are supplied counterfactual outcomes, not predictions from the FIA and not measured Formula 1 data.

The synthetic fixture (2 of 2)

Same plans, same car order, same 0.25 path weights.

Joint plan	Path 3	Path 4
protect 14	P3 / P6	P5 / P4
balance	P4 / P5	P6 / P2
split risk	P7 / P2	P8 / P1

All three plans now have four complete joint outcomes. We have not chosen an objective yet, so we have not chosen a winner.

Derive `balance` path by path (1 of 2)

Under the team objective, score both cars and add them.

Path	Joint finish	Points	Team total	Weighted
1	P2 / P3	18 + 15	33	8.25
2	P3 / P4	15 + 12	27	6.75

The path total comes before the weighting. Adding only car 14 would answer the driver question while labelling it as the team question.

Derive `balance` path by path (2 of 2)

Path	Joint finish	Points	Team total	Weighted
3	P4 / P5	12 + 10	22	5.50
4	P6 / P2	8 + 18	26	6.50

E[team points | balance]
= 0.25(33) + 0.25(27) + 0.25(22) + 0.25(26)
= 27.00

Every figure above is synthetic. The arithmetic is still checkable.

Rank for the team

Apply the same both-car calculation to all three plans.

Joint plan	Team totals by path	Expected team points
protect 14	29, 24, 23, 22	24.50
balance	33, 27, 22, 26	27.00
split risk	29, 24, 24, 29	26.50

Team selection: balance. It ranks first under the declared objective: maximise expected constructors’ points across both cars.

Expected does not mean certain. Another supplied path could still favour another plan.

Change stakeholder, not evidence

Now maximise car 14’s expected points.

Keep fixed:

the three joint plans
all four paths and their 0.25 weights
both cars’ finishes on every path
the P1–P10 points lookup

Change one operation: score only car 14’s finish before weighting.

No resimulation. No new draw. The stakeholder changes; the evidence does not.

Rank for car 14

Joint plan	Car 14 points by path	Expected car 14 points
protect 14	25, 18, 15, 10	17.00
balance	18, 15, 12, 8	13.25
split risk	25, 18, 6, 4	13.25

Car-14 selection: protect 14. The two alternatives tie below it at 13.25.

The fixture did not change. The ranking changed because the named interest did.

Account for the trade

Compare the team selection, balance, with the car-14 selection, protect 14.

Interest measured	Balance	Protect 14	Change
team	27.00	24.50	-2.50
car 14	13.25	17.00	+3.75
car 22	13.75	7.50	-6.25

The objective change benefits car 14 and costs car 22 enough that the team’s expected total also falls. That is an account of named interests, not a claim that one objective is neutral, selfish or correct.

Four outputs, four questions

Output	Question answered
expected team points	Which plan ranks highest for both cars’ points?
expected driver points	Which plan ranks highest for one named car?
finish distribution	Where might one strategy finish?
head-to-head probability	How often does one option beat another?

A plan can win more often and still lose on expected points when the losses cost more than the wins gain. Week 11 must keep the objective ranking distinct from the probability and from each distribution.

Two assertions protect the meaning

Catch a one-car team total:

assert team_points(path) == points(car14) + points(car22)

Catch changed evidence between objectives:

before = fingerprint(plans, paths, weights, outcomes)
rank_for_team()
rank_for_car14()
assert fingerprint(plans, paths, weights, outcomes) == before

The first protects the stakeholder. The second proves the new ranking came from a new objective rather than a new race.

What leaves this week

The objective-change report records:

FIA 2026 Section A, Issue 03 and the at-least-75% race assumption
the synthetic boundary and candidate set
both objectives, with each stakeholder named
both complete rankings and selected plans
team, car-14 and car-22 deltas
limitations of the supplied paths

Week 11 consumes the expected constructors’-points ranking as given. Its wall may also show a distribution or head-to-head probability, but it must name the objective because those quantities do not replace it.

Week 10: Whose Race Is It?#

The turn#

Objective and stakeholder#

Joint plan and expected points#

The real rule, and where it stops#

Validate before ranking#

Four failures to stop at the door#

The synthetic fixture (1 of 2)#

The synthetic fixture (2 of 2)#

Derive balance path by path (1 of 2)#

Derive balance path by path (2 of 2)#

Rank for the team#

Change stakeholder, not evidence#

Rank for car 14#

Account for the trade#

Four outputs, four questions#

Two assertions protect the meaning#

What leaves this week#