A prototype-to-production multiple compares the cost of reaching a declared production or transfer boundary against the cost of the investigation that came before it. Two ratios share the name and answer different questions, and the difference between them is exactly one.
Two ratios
Fix three event boundaries first: the start of the investigation, its decision or closure, and acceptance of a specified operational service. Name whose acceptance counts and what service scope it covers.
Let P be the scoped investigation cost and A the additional cost after that boundary to operational acceptance. Then the additional-cost multiple is A divided by P, and the cumulative multiple is P plus A, divided by P. The second is always the first plus one.
Take P of 10,000 and A of 30,000 on the same cost basis. The additional-cost ratio is 3 and the cumulative ratio is 4. Both are correct. An unattributed “3×” or “4×” conceals which question was answered, and the two are quoted interchangeably.
Why a bigger multiple can be a cheaper project
Hold A at 30,000 and set P to 5,000 instead of 10,000. The cumulative ratio rises from 4 to 7, and total scoped cost falls from 40,000 to 35,000.
The ratio got worse and the project got cheaper. This is not a paradox: the multiple measures a relationship between two quantities, and shrinking the denominator moves it without touching the money. A small, subsidised, or partially recorded prototype cost produces an alarming multiple and tells you nothing about whether the programme was well run.
The corollary is that the multiple cannot be a target. Managing it downward is achieved most easily by spending more on the prototype, which is the opposite of the behaviour it appears to encourage.
Making the numbers comparable
P and A must use the same cost perspective, the same currency, the same price basis, and must contain disjoint items. A ratio built from a vendor invoice as the denominator and full internal-plus-external cost as the numerator compares two scopes.
Report both underlying amounts alongside the ratio, state the formula used, and mark each amount observed or forecast. Where P is zero, unknown, or an inappropriate denominator, no finite multiple should be published.
The cost items themselves extend well past code. Software cost guidance includes testing, infrastructure, purchased services, and post-deployment sustainment, and identifies purpose, integration, size, and complexity as the drivers of development effort. Rebuilding is one line among many, and it is the one people estimate.
Reuse is not the default path. Prototype guidance warns that the same code can fail to be reusable and cautions against copying it into a live service, which means A can legitimately contain a rebuild of the thing P paid for.
The survivorship problem
Multiples get computed from projects that finished. That population excludes the ones that stopped.
Register the admitted cohort, the entry period, and the observation cutoff. Record which cases reached the endpoint, which are still running, which were stopped, and which have no identifiable production successor. A stopped investigation does not acquire a zero-cost completed transition: its cost stays in the cohort record while its transition ratio is simply not applicable.
Publish the number eligible for each reported ratio alongside the number excluded or unfinished. A multiple reported over completed transitions is conditional on completion, and saying so is the difference between a statistic and a claim.
One further arithmetic trap: a ratio of aggregated costs and an unweighted average of individual case ratios are different quantities. State which was computed.
The rule
What stays fixed is the requirement that both amounts share a boundary, a basis, and a population. What changes is the boundary itself, which is a decision about what “production” means for the specific service — and the multiple is uninterpretable until someone has made it.
Where the number misleads
The boundary moves mid-comparison. Including continuing operation in A for one case and excluding it for another produces two incompatible numbers presented as a range.
The portfolio question gets answered with the project statistic. The cost of all investigations plus their subsequent services is a different question from the conditional cost of transitioning one that succeeded. The first includes stopped work the second omits by construction, and one number cannot serve both.
Not to be confused with
A forecast. The multiple describes what happened, or what is projected under stated assumptions. The next decision compares the alternatives still available, and the historical ratio is an input to that comparison rather than the comparison itself.
Manufacturing scale-up. Production here means an agreed service-readiness boundary. Nothing is being copied.