P50 / P80 / P95 (Confidence Levels)

When a Monte Carlo simulation produces an S-curve of possible project outcomes, you can read off any percentile. P50 is the median outcome — half of all simulated scenarios finish by that date or within that cost, and half do not. P80 means that 80% of scenarios are at or below that value, giving a much higher level of confidence. P95 is a near-worst-case figure used when the consequences of overrun are severe. The choice of which percentile to use for budgeting or scheduling is a risk-management decision, not a technical one.

What UK guidance actually requires is more nuanced than the convention suggests. The IPA Cost Estimating Guidance specifies that UK government business cases must present the 'Median Scenario / P50 equivalent' as the central estimate at every stage gate, with confidence ranges expressed as percentage bands around the Anticipated Final Cost (SOC ±20–50%, OBC ±15–30%, FBC ±10%). The HM Treasury Green Book 2022 requires explicit risk and optimism-bias adjustment and recommends Monte Carlo for high-cost, high-risk proposals, but does not mandate a specific P-level — its worked example uses P90, not P80. P80 has become a de facto upper-bound sensitivity used by many departments, and is treated as a standard sensitivity alongside P50 in some published departmental guidance (Homes England), but it is a working convention rather than a written HMT/IPA requirement.

A common mistake is confusing the P-value from a risk analysis with a guarantee. A P80 date does not mean the project will definitely finish by then — it means it should do so eight times out of ten, assuming the risk model is well-calibrated. In reality, optimism bias in the inputs means that real-world outturn often exceeds even P80 estimates. Another trap is presenting only the P50 to clients or executives without explaining what it means: many stakeholders hear '50% chance' and assume the project is poorly planned, when in fact a P50 outturn is a well-calibrated central estimate. The worst failure mode is justifying a P80 funding figure by claiming 'the Green Book says so' — the Green Book does not, and IPA reviewers familiar with the source will challenge the justification.