Cost Model

Assumptions

Everything the model believes, stated before the math. If you do not buy one of these, do not buy the output.

1. The sponsor's announced CAPEX is a claim, not a fact. It enters as OBSERVED only with a primary document.
2. Overruns are a reference-class phenomenon: the right prior is what happened to comparable projects, conditioned on class and stage at announcement.
3. Evidence-backed change orders adjust the estimate; a larger fixed-price contract share narrows the distribution but never lowers the reference-class mean.
4. Below 8 resolved class cost outcomes, the reference class is thin and the model runs on a labeled wide prior (mean ratio 1.25, sd 0.35).

Derivation

The base distribution is the empirical final-to-announced CAPEX ratio over resolved outcomes in the project's class:

The project estimate multiplies announced CAPEX by that ratio distribution, adjusted only for evidence-backed change orders. Bands are read off a normal approximation (Abramowitz-Stegun 7.1.26 CDF):

Contingency requirement is the P90 less the announced figure - the capital that must exist for the project to absorb a reference-class overrun:

A fixed-price contract share compresses sigma toward the contracted fraction but the mean stays at the reference-class mean: a contract transfers risk to the counterparty, it does not repeal the base rate.

Identification strategy

Why the estimate supports the claimed meaning - and where the model refuses to claim more than the data carries.

• Reference-class forecasting is the identification strategy: the estimate is anchored on the realized overrun distribution of comparable finished projects, which is immune to the optimism inside any single project's own plan (the inside view).
• Conditioning on class and stage at announcement is what makes the reference class comparable - a transmission upgrade announced at permit stage overruns differently from one announced at concept.
• The fixed-price rule identifies contract value correctly: it changes who bears the tail, not the size of the tail. Letting it lower the mean would dress a risk transfer up as a cost saving.

Inputs and outputs

Calibration and gate evidence

Validation design

• Backtested on outcomes' original-vs-final CAPEX pairs; coverage of the P10-P90 band must hold on resolved projects before the band is shown narrow.

Evidence on record

• Band-coverage results are not yet published in the sealed source. The thin-class wide prior is coded and labeled; coverage testing begins as the outcomes collection accrues cost pairs.

Failure modes

The ways this model declines, degrades or goes UNKNOWN - and what it prints when it does.

• Thin reference class (n < 8): wide prior ratio (1.25 +/- 0.35), labeled in the notes.
• No announced CAPEX with primary evidence: the estimate has no anchor and the outputs degrade to the class ratio alone, badged accordingly.
• Change orders without evidence backing do not move the estimate.

Sensitivity

• The reference-class mean ratio is the dominant driver: every point of historical overrun moves expected CAPEX one-for-one.
• Sigma (the overrun spread) drives the contingency line: on a wide prior the P90 sits far above announced, which is the honest price of thin history.
• Fixed-price share moves the band width only - verify on any project that the mean does not move when contract terms change.