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Module 20 · Lesson 20.3

Does the ranking survive?

The factors are uncertain. Test whether the conclusion depends on them — because that is the only result worth acting on.

Why this matters

Everything in the previous lesson rests on carbon factors that are uncertain. A single figure for 'steel' spans a factor of about three depending on recycled content and production route, and the timber figures depend on an accounting choice about sequestration that is genuinely contested.

So the honest question is not what is the number. It is does the conclusion depend on the number — and that is a sensitivity study, which Module 14 already taught.

By the end of this lesson you should be able to

  • Perturb each factor and test whether the ranking changes
  • Distinguish a robust ranking from a fragile one
  • Say what to do in each case
  • State the provenance requirement for any figure leaving the course

The test

Take the base comparison. Perturb each material's factor up and down by some fraction, one at a time, and re-rank. Count how many times the winner changes.

  • No changes — the ranking is robust to that perturbation, and it is worth acting on even though the factors are not verified.
  • Any change — the ranking is fragile, it depends on a number you do not know, and you need verified factors before choosing on carbon alone.

On the four-scheme comparison at a 9 m grid, perturbing every factor by ±30 % produces no change of winner. The CLT hybrid stays first throughout.

That is a genuinely useful result. It says: the factors are unverified, and the conclusion does not depend on them at this level of uncertainty. You can act on the ranking while being honest that the numbers are illustrative.

This is the shape of an honest quantitative argument under uncertainty. Not 'the number is 447'. Rather: 'the ranking is X, and it survives a ±30 % error in any single factor'.

Why ±30 %

Because it is roughly the uncertainty a plausible published dataset carries for a generic material, and because it is large enough to be a real test. If a ranking survives ±30 % it is not resting on the third significant figure.

It would not survive everything. Perturb steel by a factor of three — which is the genuine spread between an electric-arc route with high recycled content and a blast-furnace one — and the steel scheme moves substantially. That is why specifying the material matters, and why a scheme comparison should say which assumption about supply it made.

What to do when it is fragile

Three options, in order of preference:

  1. 1.Get verified factors for the materials the ranking turns on. Usually only one or two of them matter.
  2. 2.Report the ranking as conditional — 'A beats B provided the steel factor is below X′ — which is more useful than it sounds, because it tells the procurement conversation exactly what to secure.
  3. 3.Decide on something else. If carbon cannot separate two schemes reliably, buildability, programme or cost can, and pretending otherwise is worse than saying so.

What must travel with a figure

The course's library enforces this: every carbon result carries a provenance object stating that the factors are illustrative teaching values, not verified against a current published dataset, with a date. No interface can display the number without it.

Outside the course, the equivalent requirement is:

  • The factor set, named, with its version and date.
  • The scope — which life-cycle stages are included.
  • The quantities, and whether they came from a rate or a take-off.
  • The exclusions, particularly foundations and substructure.
  • Whether the ranking was tested for robustness, and to what perturbation.

A figure without those is not checkable, and an unchekable carbon figure is exactly the kind that gets quoted in a document and then repeated.

Worked example

Testing the ranking against its own uncertainty

Given

  • The four-scheme comparison at a 9 m grid: CLT 447, band beam 666, steel 782, flat slab 866 tCO₂e
  • Five material factors: steel, reinforcement, concrete, CLT and glulam
  • Each perturbed by ±30 %, one at a time, and the comparison re-run

Find

Whether the ranking is worth acting on

    Practice

    The lowest-carbon scheme is 447 tCO₂e and the next is 666. By what percentage would the lowest scheme's carbon have to rise before it stopped winning?

    Practice

    Five material factors are each perturbed up and down, one at a time. How many re-rankings does that require?

    Check yourself

    A carbon ranking changes winner when the steel factor is perturbed by 20 %. What should the report say?

    Check yourself

    A scheme ranking survives a ±30 % perturbation of every carbon factor with no flips. What does that justify?

    Summary

    • Perturb each factor, re-rank, and count the changes of winner
    • ±30 % on any single factor changes nothing in this comparison — the ranking is robust
    • A robust ranking can be acted on even with unverified factors; a fragile one cannot
    • State the threshold when a ranking is conditional — it tells procurement what to secure
    • One-at-a-time testing does not cover combinations, and should say so
    • Factor set, scope, quantities, exclusions and robustness all travel with the number
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    This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint