What P50, P80 and P95 mean
P50, P80 and P95 are percentile points on the output distribution of a Monte Carlo simulation of a cost or schedule model. P80 is the value the outcome has an 80% probability of not exceeding. The simulation runs thousands of iterations across the base estimate and the risk register and returns the full range of outcomes.
P50 is the median: half the iterations fall below it and half above. It is not the expected outcome and it is not the most likely outcome. The expected outcome is the mean and the most likely outcome is the mode. Project cost distributions are right-skewed, so the three values separate: the mode sits below the median and the mean sits above it.
The skew has three causes. The lower bound is physical, because cost cannot fall below a floor set by scope and productivity. The upper bound is open, because an overrun has no ceiling. Most risks on a capital project are adverse, so the register pushes outcomes one way. In risk terminology an upside is an opportunity, so this guide calls the long tail adverse exposure.
Read P80 with care. If the model is calibrated, actual cost exceeds P80 about 20% of the time, and on ten independent projects each funded at a calibrated P80 you would expect two overruns. Both conditions are demanding. The Green Book requires an optimism bias adjustment because unadjusted estimates have tended to run low, so do not assume a QRA P80 is calibrated until someone has tested it.
How far apart the percentiles sit
Take a project with a deterministic base estimate of £90m, excluding contingency and optimism bias, and a lognormal cost distribution with a median of £100m and a standard deviation of the logarithm of 0.2. This is an illustration, not a benchmark. The simulation returns a P50 of £100m, a mean of £102m, a P80 of £118m, a P90 of £129m and a P95 of £139m. The mode is about £96m.
P50 to P80 adds £18m across 30 percentile points, about £0.6m a point. P80 to P95 adds £21m across 15 points, about £1.4m a point. Widening the distribution to a logarithmic standard deviation of 0.3 gives a P80 of £129m and a P95 of £164m, so the steps are £29m and £35m.
The P50 to P80 gap is smaller than the P80 to P95 gap only because of the tail, and the reason matters. On a symmetric normal distribution the first step (0.84 standard deviations) is marginally larger than the second (0.80). On a right-skewed distribution the tail is long and thin, so each extra percentile point out there spans a wider range of cost. The absolute difference is modest (£21m against £18m). The difference per point of confidence is large: each point between P80 and P95 costs more than twice as much as each point between P50 and P80.
P95 is not a worst case. Five per cent of outcomes sit above it and the distribution has no stated ceiling.
What the guidance requires
The HM Treasury Green Book, 2026 edition (published 5 February 2026; earlier editions are withdrawn), requires proposals to be adjusted for optimism bias and risk, and points to techniques such as Monte Carlo analysis for high-cost, high-risk proposals. It does not mandate a confidence level. Its percentile illustration is a P90 offered as one way to express uncertainty around a central estimate. That P90 is a reference-class figure, not the output of a Monte Carlo model.
NISTA (formerly the IPA) took over the IPA's functions in April 2025. The IPA Cost Estimating Guidance (2021) remains the extant document and is now owned by NISTA. Step 5 requires the cost estimate to present the Median Scenario, the P50 equivalent. The requirement attaches to projects within the NISTA remit and the Treasury business case process, not to every public project. The guidance expresses confidence by stage as ranges around the Anticipated Final Cost: SOC -20% / +50%, OBC -15% / +30% and FBC -10% / +10%. By exception it allows -50% / +100% at SOC, -30% / +50% at OBC and -10% / +20% at FBC.
Neither source makes P80 a requirement. Where P80 is used, it is because a department's finance function or a sponsor has set it as the risk-appetite point. NEC4 specifies no confidence level for a Target. AACE International 57R-09 Integrated Cost and Schedule Risk Analysis Using Risk Drivers and Monte Carlo Simulation of a CPM Model describes a method, and it should not be quoted as a source for P80 as a standard.
Optimism bias and QRA contingency
Optimism bias is a top-down adjustment set from reference-class evidence and applied to an estimate that has not been risk-analysed in detail. QRA contingency is bottom-up: it comes from the uncertainty on the base estimate and from the risk register. Both cover the same exposure, so applying both in full counts it twice.
As a business case matures and risks are identified and quantified, the QRA should replace the uplift for the risks it covers. The uplift then applies only to the residual the QRA cannot see, and a reviewer will expect you to define that residual. The test we apply is that every risk sits either in the uplift or in the QRA, never both. Agree the treatment with the reviewer before the case goes forward.
Why P80 is common, and how to justify it
P50 as a funding figure accepts a 50% probability of overrun. P95 ties up contingency that other programmes could use. P80 sits between them and has become the convention many departments use for sensitivity testing and contingency-setting. It has no special statistical status: every point in the tail has the rising cost per point shown above.
A defensible position for a UK public-sector case is to present the P50 as the central estimate, as the IPA guidance requires; present the P80 as an upper-bound sensitivity; show the range against the stage bands; and record why the funded position sits where it does. 'P80 because the Green Book says so' is not defensible, because the Green Book does not say so. 'P80 because our finance function has set it as our risk-appetite point' is defensible.
When P50 is the right answer
The first use is performance reporting. Actual cost exceeds P50 about half the time, so a P50 benchmark shows whether the project is running better or worse than the central expectation. A P80 benchmark shows the project on or under benchmark about 80% of the time, so adverse drift stays hidden until it is large. Report against P50 or a current reforecast, and track the headroom to P80 separately.
The second is a target cost. NEC4 ECC Options C and D set a Target from the Contractor's forecast of Defined Cost plus Fee, and NEC4 specifies no confidence level for it. Compensation events then adjust the Target, so risks the Client carries belong outside the Contractor's Target and in the Client's own contingency. If the pain-gain share is symmetric, the Target with zero expected payment sits at the mean, £102m in the example, not the median of £100m. P50 is the common choice and builds in an expected overrun of about £2m before the share is applied. A Target at P80 sits £16m above the mean and pays gain share on outcomes the Contractor would have delivered anyway.
The third is funding that accepts risk explicitly, such as technology demonstrators and early-stage R&D. That is a valid choice if the sponsor makes it knowingly. The failure is funding at P50 while describing the position as P80.
When P95 is the right answer
P95 is justified when an overrun cannot be absorbed, or when a funding shortfall would stop work that cannot easily be paused and resumed. The decision belongs to the sponsor and should rest on those consequences.
The cost is real. At the illustrative shape above, funding at P95 rather than P80 adds about 21% of the P50. On a P50 of £500m that is about £105m held against the last 15 points of probability. Choosing P95 on principle, with no consequence-based reason, ties up public or shareholder capital for those 15 points.
Portfolio percentiles are not the sum of project percentiles. If project risks are largely independent, the portfolio P80 is usually below the sum of the project P80s, because projects rarely overrun together. Shared drivers such as inflation and supply chain keep the portfolio figure closer to the sum. Model the portfolio as a whole with its correlation structure and do not add percentiles.
Schedule confidence levels
The same logic applies to duration. A QSRA produces a distribution of completion dates. The P50 date has an equal chance of being met or beaten, and the P80 date has an 80% chance of being met. Express the gap in time against the baseline finish, and state the programme version and status date the percentiles are measured against.
A cost P80 and a schedule P80 from separate models are not a joint P80. The chance of meeting both is no higher than 80% and is usually lower, because delay drives cost and the two outputs are linked. An integrated model of the kind AACE International 57R-09 describes gives the joint distribution. State which confidence level applies to which output. If a client body such as National Highways requires a particular level for QSRA dates, it will be set in that scheme's own instructions, so confirm it there.
Contingency and who owns the drawdown
Contingency at a chosen confidence level is that P-point minus the base estimate. The base must exclude contingency and any optimism bias uplift, or the figure is counted twice. In the example, contingency is £10m at P50, £28m at P80 and £49m at P95. It splits into estimating uncertainty on the base items and an allowance for discrete risks, and the two should be reported separately.
Who owns it matters as much as how much. Held at project level with project approval, contingency makes teams self-managing. Held at portfolio level with central approval, it is efficient and politically contentious. Two arrangements fail. If every drawdown request is approved, the P80 becomes a ceiling that gets spent. If every request takes a month of governance, the team treats contingency as unavailable and manages to the base estimate under informal pressure. Both stop the QRA output doing its job.
Testing a claim that a programme is funded at P80
A well-run session starts with the sponsor stating in words the tolerable probability of overrun and the consequence if it occurs, then picks the level that fits. That may be P50, P80, P85, P90 or P95. A poorly run session starts at P80, sees the contingency requirement and negotiates it down until the total fits an existing budget. The paperwork still says P80 and the funded position is P60 or P65. That is worse than saying plainly that the programme is funded at P60, because the sponsor keeps an unrealistic view of overrun probability and has no plan for the base estimate proving optimistic.
The defensibility test is whether the reasoning can be written in a paragraph for the board, the NAO or a gateway reviewer. 'We chose P80 because our tolerance for overrun is low given the programme's visibility, and the £25m of contingency above P50 is acceptable against £300m of scope' passes. Reasoning that looks uncomfortable on paper will not hold at the first difficult quarter.
Ask three questions of any 'it's P80' claim. First, P80 of what: which model, which risk register, run when and by whom? A P80 from a model nobody has reviewed is a number, not a confidence level, and the reviewer should be able to see the model, the inputs and the correlation structure.
Second, was it produced before or after the funding envelope was settled? A weak correlation structure, narrow three-point estimates and omitted risks will produce whatever P80 the sponsor wants to see. Independent QRA exists to guard against that.
Third, is it live or stale? After a material risk lands, a scope change is absorbed or the programme enters a new phase, the P80 needs re-running, and the new figure may be higher. A P80 frozen at sanction and used as a performance target is a one-off number, not live QRA.
Putting it together
Present the P50 as the central estimate and show the mean beside it. Choose the funding level from the sponsor's stated tolerance for overrun and the consequence of overrun, not from the default. Show P80 and P95 as sensitivities with the contingency each implies. Record how optimism bias and QRA contingency were separated. Then fund the programme at the level you claim. SOMA's Confidence Level Decision Reference (PDF and XLSX) is the companion to this guide.
On a QSRA or QCRA we report the P50, the mean and the P80 against the baseline, put the model, risk register and correlation structure in front of the reviewer, and re-run when a material risk lands. On Mitsubishi Chemical UK's £400m capital programme, our independent QRA validation, delivered with Bilfinger UK, put the P80 £24m above the contractor's baseline, with 2.2 months of schedule exposure.