P50, P90 and P99: The Number Is Meaningless Without the Period
"The P90 is 89% of P50." That sentence is incomplete, and the missing word is expensive.
A wind project with 6% systematic uncertainty and 6% interannual variability has a one-year P90 of 89.1% of its P50 and a ten-year P90 of 91.9%. Both are correct. They answer different questions, and using the first where the second belongs understates bankable energy by 2.8 percentage points.
The worked example separates a persistent uncertainty component from independent year-to-year variability. Under that simplifying assumption, the year-to-year component declines when averaging multiple years while the persistent component does not. Real energy-yield assessments can use more detailed weather histories, model uncertainty, reliability assumptions and correlations.
This post covers what each Pxx value means, what the uncertainty is actually made of, why the exceedance period matters as much as the percentile, and which combination belongs in which test.
ℹ️ Note: The uncertainty components below are labelled assumptions used to demonstrate the method. Real values come from the energy yield assessment for the specific project and site.
What Do the Numbers Mean?
Each Pxx is the production level expected to be exceeded in xx percent of cases.
| Meaning | Illustrative use / interpretation | |
|---|---|---|
| P50 | Energy level exceeded with 50% probability under the defined distribution | central / median case under that model |
| P75 | Energy level exceeded with 75% probability | more conservative percentile |
| P90 | Energy level exceeded with 90% probability | financing / downside input where the documents or lender methodology use it |
| P99 | Energy level exceeded with 99% probability | severe percentile under the same defined model |
The common error is to read P90 as "a bad year." It is not a scenario; it is a point on a probability distribution, and it depends entirely on how wide that distribution is and over what period it is measured.
What Is the Uncertainty Made Of?
Several uncertainty sources can contribute, and the combination method must match the assessment methodology. The simplified worked example below groups them into a persistent component and an independent interannual component.
Persistent / non-averaging uncertainty in the worked model represents uncertainty that does not disappear merely by averaging more operating years — for example certain resource-estimation, model or parameter uncertainties.
Interannual variability represents weather-driven variation from year to year. If annual variations are treated as independent, the uncertainty of the average over N years declines approximately with 1/√N. Serial correlation or climate trends can weaken that simplification.
A worked illustrative combination of 3.5% persistent uncertainty and 2.6% annual variability, assuming independence and a normal approximation, is:
√(3.5² + 2.6²) = 4.36%
Under the same normal approximation, the worked Pxx values use standard-normal z-scores:
P75 = P50 × (1 − 0.674σ)
P90 = P50 × (1 − 1.282σ)
P95 = P50 × (1 − 1.645σ)
P99 = P50 × (1 − 2.326σ)
Why the Period Changes Everything
Because the worked model assumes only the independent year-to-year component shrinks when averaging multiple years.
Over an N-year period, interannual variability is divided by √N while systematic uncertainty is unchanged:
σ(N years) = √( σ_systematic² + (σ_IAV / √N)² )
The consequence, on the assumptions above:
Solar worked example — 3.5% persistent, 2.6% interannual
| Period | σ | P75 | P90 | P95 | P99 |
|---|---|---|---|---|---|
| 1 year | 4.36% | 97.1% | 94.4% | 92.8% | 89.9% |
| 10 years | 3.60% | 97.6% | 95.4% | 94.1% | 91.6% |
| 20 years | 3.55% | 97.6% | 95.5% | 94.2% | 91.7% |
Wind worked example — 6.0% persistent, 6.0% interannual
| Period | σ | P75 | P90 | P95 | P99 |
|---|---|---|---|---|---|
| 1 year | 8.49% | 94.3% | 89.1% | 86.0% | 80.3% |
| 10 years | 6.29% | 95.8% | 91.9% | 89.6% | 85.4% |
| 20 years | 6.15% | 95.9% | 92.1% | 89.9% | 85.7% |
Three observations within these assumptions.
The gap is larger in the wind example. Solar's one-year and ten-year P90 differ by one point; wind's differ by 2.8. That is because wind's interannual variability is proportionally larger, so more of the total uncertainty is the component that averages away.
Most of the convergence in this numerical example happens by year ten. That result is driven by the assumed split between persistent and interannual uncertainty; another site or methodology can behave differently.
The tail percentile moves more in this example. Wind's one-year P99 is 80.3% of P50 and its ten-year P99 is 85.4% under the simplified model.
Where Do the Components Come From?
Worth going one level down, because the components are not equally solid and not equally negotiable.
Resource dataset uncertainty is the assessor's stated accuracy for the satellite or reanalysis product used. It is the largest single component for a site without on-site measurement, and it is the one that on-site data reduces.
Measurement uncertainty applies where there is a met mast or ground station — the instrument accuracy, calibration, and the representativeness of the measurement location. Good measurement reduces the resource dataset uncertainty substantially and introduces a smaller uncertainty of its own.
Long-term adjustment uncertainty arises from correlating a short on-site record to a long reference period. A one-year measurement campaign correlated to twenty years of reanalysis inherits uncertainty from the correlation quality, and this component is often larger than people expect.
Spatial and vertical extrapolation — from the measurement point to the turbine or array positions, and for wind from measurement height to hub height. Terrain complexity drives it.
Energy conversion uncertainty — the model translating resource into energy, including wake effects for wind and soiling, temperature and inverter behaviour for solar.
Two practical points follow.
Reducing a material uncertainty component can have a computable financing value. A measurement campaign that reduces resource uncertainty can raise the lower-tail energy estimate. Whether that creates enough financing or valuation benefit to justify the campaign is a project-specific calculation: rerun the assessment and financing with and without the improved data.
Root-sum-square assumes independence. Where components are correlated — a resource dataset and a long-term reference drawing on the same underlying reanalysis, for instance — combining them in quadrature understates the total. The assessor should say whether independence has been assumed and on what basis.
Where Does Degradation Sit?
A distinction that causes real confusion, because both are expressed as percentages of P50.
Energy-yield reports can present first-year energy, long-term average energy and/or lifetime profiles. Degradation may be embedded in a lifetime model or applied separately. The financial model must reproduce the assessor's convention rather than assume one universal treatment.
So the energy in year fifteen is:
P50(year 15) = P50(year 1) × (1 − first_year_degradation) × (1 − annual_rate)^14
and the Pxx for that year applies the uncertainty to the degraded P50, not the year-one one.
Two errors follow from conflating them.
Applying P90 to year-one energy across all years ignores degradation entirely and overstates late-life energy — which matters most in exactly the years a merchant tail or a refinancing depends on.
Degradation uncertainty needs an explicit home. If the assessment already includes it, do not add it again. If the report provides only a deterministic degradation path, a separate sensitivity or uncertainty treatment may be appropriate.
For storage, a percentile can describe a different uncertainty problem — availability, degradation, augmentation, dispatch and market exposure rather than solar or wind resource. Do not import a generation P90 convention without defining the distribution being measured.
Which One Belongs Where?
There is no universal mapping of “P90 = debt sizing” or “P99 = covenant case.”
NREL's 2023 work says annual-energy P50 and P90 statistics are used by financing institutions to evaluate repayment risk, but the actual lender methodology is transaction-specific. An older DOE/Navigant offshore-wind analysis, for example, described both P90 cases at lower DSCRs and P50 cases at higher DSCRs as accepted financing approaches.
For the financial model, extract four things from the financing process:
| Question | What to record |
|---|---|
| Energy basis used for debt sizing | P50 / P90 / other defined lender case |
| Period represented by the energy statistic | annual, multi-year average, lifetime or another basis |
| DSCR paired with that energy case | contractual / sizing ratio |
| Separate downside tests | additional resource, price, curtailment, availability or covenant cases |
The percentile and the DSCR are a package. A lender can size on a more conservative energy case with a lower coverage requirement, or a less conservative energy case with a higher coverage requirement. Comparing only the Pxx label is incomplete.
The worked one-year / ten-year table remains useful for showing why period matters when the assessment defines a multi-year average distribution. It should not be turned into a rule that every 15-year loan must be sized on a 15-year P90.
What the Energy-Yield P90 May Not Cover
The point the curtailment post made and which bears repeating here, because it is the most consequential misunderstanding in this area.
A P90 means only what the underlying energy-yield distribution includes. NREL's PV uncertainty work explicitly includes solar-resource variability, performance-model uncertainty and system-reliability considerations. A project's P90 can still exclude or separately model items such as:
- whether the grid will accept the output — curtailment
- what the energy is worth when produced — capture rate and basis
- whether the plant is available to produce it — availability
- whether the offtaker pays for it — counterparty risk
Each of those has its own distribution, and they are not the resource distribution. The hub-settled PPA post worked the arithmetic: a project delivering P50 generation exactly can realise 80.9% of its modelled revenue from location, shape and negative-price effects alone.
So a lender sizing on P90 generation with point estimates for curtailment, basis and availability has applied a probabilistic treatment to one variable and a deterministic one to three others — and believes it has been conservative.
The financial model should identify which risks are already embedded in the energy-yield distribution and which sit outside it. Then test the outside risks separately or jointly as appropriate, rather than assuming the word “P90” covers the entire revenue distribution.
There is a further complication: resource and curtailment can be correlated because both depend on weather and system conditions. In some constrained regions, strong simultaneous generation can increase export congestion; in others the relationship may be weak or different. Use hourly or historical evidence rather than assuming the sign.
Correlation can make simple stacked haircuts misleading. Whether high-resource conditions increase or reduce curtailment risk is location- and system-specific and should be supported by hourly analysis or historical / simulated data. Modelling it properly requires an hourly simulation with both effects, which is genuinely more work than a spreadsheet haircut.
The pragmatic middle ground, and the one worth adopting: run the resource distribution and the curtailment distribution as separate scenarios rather than as a single blended haircut, report both, and explicitly test the combination that hurts — a poor resource year with high curtailment, even though the correlation makes it less likely than independence would suggest. The point of a downside case is not that it is probable.
Two Assessors, Two Answers
A practical reality that the arithmetic above conceals: the same site assessed by two competent firms produces two different P50s and two different uncertainty stacks.
The divergence comes from defensible choices rather than from error. Different resource datasets, different long-term reference periods, different wake or soiling models, different views on how much uncertainty a given correlation quality warrants. Different competent assessments can produce different P50s and uncertainty stacks because they use different data, periods and modelling choices. Quantify the actual difference rather than assuming a generic two-to-three-percent range.
That has three consequences worth planning for.
Lenders may rely on an independent technical adviser or engineer. The financing case can therefore use a technical assessment or assumptions that differ from the sponsor case. Budgeting for that gap at the outset is more useful than arguing it afterwards, because the arguments are about modelling choices that both parties can defend.
Shopping for a favourable assessment is self-defeating. A sponsor that selects the most optimistic of three assessments has not improved its project; it has created a document the independent engineer will disagree with, and the disagreement will be resolved in the lender's favour at a point when the financing timetable makes it expensive.
The uncertainty stack is where the real difference lives. Two assessors agreeing on P50 to within a percent can still produce P90s three points apart, because one has taken a more conservative view of long-term adjustment uncertainty. When comparing assessments, compare the stacks rather than the headline — the headline is the easy part.
The constructive response is to obtain the independent engineer's view early, ideally before the sponsor's case is fixed. It is cheaper to build a model on the number the debt will be sized against than to build one on a different number and reconcile later.
How Do You Build This in Excel?
As an uncertainty stack with an explicit period, and with the period reported alongside every Pxx.
The uncertainty build
Systematic components (do NOT reduce with period):
Resource dataset uncertainty
Measurement uncertainty
Long-term adjustment uncertainty
Extrapolation / modelling uncertainty
Energy conversion uncertainty
σ_systematic = SQRT(SUMSQ(components))
Variable component (DOES reduce with period):
σ_IAV
σ(N) = SQRT( σ_systematic^2 + (σ_IAV / SQRT(N))^2 )
The Pxx calculation
Pxx(N) = P50 × ( 1 + NORM.S.INV(1 − xx/100) × σ(N) )
Or, using positive exceedance z-values explicitly:
P75 = P50 × (1 − 0.674σ)
P90 = P50 × (1 − 1.282σ)
P95 = P50 × (1 − 1.645σ)
P99 = P50 × (1 − 2.326σ)
The two numbers to publish
PF_P90_OneYear (wind example) 89.1%
PF_P90_DebtTerm (15 years) 92.1%
PF_ExceedancePeriodEffect +3.0 pp
Every Pxx in a model should carry its period. A cell labelled "P90" with no period is ambiguous by about three percentage points on a wind project, which is larger than most of the assumptions that get argued over.
The joint test that P90 does not replace
Energy basis financing-case energy statistic as defined
Curtailment separate or embedded, per assessment / lender case
Basis generation-weighted assumption or scenario
Availability modeled assumption / guarantee treatment
→ Combined downside revenue; call it P90 revenue only if it was produced from a revenue distribution
ℹ️ Note: Do not describe a revenue figure as "P90" unless the distribution it came from is a revenue distribution. P90 generation multiplied by a point-estimate price is not a P90 revenue, and calling it one imports a confidence level the calculation does not support.
To build the uncertainty stack, the period-adjusted Pxx table and the joint downside case, prompt Dezzmond with your yield assessment components.
What Do Lenders and Sponsors Actually Check?
- Over what period is each Pxx computed? A P90 without a period is incomplete.
- How is the uncertainty split between systematic and interannual components?
- Which energy percentile and period does the financing actually use, and what DSCR or covenant is paired with it?
- Does the model treat P90 as covering curtailment or availability? It does not.
- Is the "P90 revenue" actually a revenue distribution, or P90 generation times a point price?
- What is the source of the resource dataset, and what uncertainty does the assessor attach to it?
- Has the joint downside been tested — poor resource and adverse curtailment together?
Frequently Asked Questions
What does P90 mean?
The energy production level expected to be exceeded in 90% of cases — so a 10% chance the actual figure falls below it. It is a point on a probability distribution, not a scenario.
Why does the exceedance period matter?
Because interannual variability averages out over time while systematic uncertainty does not. A wind project's one-year P90 is 89.1% of P50 and its ten-year P90 is 91.9%, because the variable component is divided by the square root of the number of years.
How is total uncertainty calculated?
By root-sum-square of the independent components. A worked example combining 3.5% model uncertainty with 2.6% interannual variability gives √(3.5² + 2.6²) = 4.36%.
Which Pxx should size the debt?
Whatever energy basis the lender and finance documents specify. Financing approaches can pair different Pxx cases with different DSCR targets. Do not infer the correct case from tenor alone.
Is degradation part of the P90?
It depends on the assessment. Some lifetime energy models embed degradation; others provide a base energy estimate and a separate degradation path. Reconcile the financial model to the report and avoid double-counting.
Is a measurement campaign worth the cost?
It is a computable question. Estimate how the additional data changes uncertainty and the financing / valuation outputs, then compare that benefit with the campaign cost and schedule impact.
Does P90 account for curtailment?
Only if the energy-yield methodology includes it in the modeled net-energy distribution. Many assessments treat grid curtailment, basis and market-price effects outside the energy-yield percentile. Check the report definition.
Closing: A Percentile Without a Period Is Half a Number
Energy yield assessments are among the most carefully produced documents in project finance. They are written by specialists, peer reviewed, and their uncertainty analysis is genuinely rigorous.
The information loss happens afterwards, when a multi-page uncertainty analysis becomes a single cell in a financial model labelled "P90". At that point the period is gone, the split between systematic and variable uncertainty is gone, and what remains is a percentage that could legitimately be anywhere in a three-point range depending on a question nobody recorded the answer to.
Two habits fix most of it. Label every Pxx with its period and uncertainty scope. Then map the lender’s actual debt-sizing, covenant and downside methodology to the relevant energy statistic rather than assuming one universal P50/P90 convention.
The larger point is the one this series keeps returning to. A P90 is a careful probabilistic answer to one question, surrounded by deterministic point estimates for three others that matter as much — and the confidence the P90 lends to the model is borrowed by the assumptions next to it, which have not earned it.
the next post takes the rate all of this is discounted at: what a project's cost of capital actually consists of, and why the number in most models is a convention rather than a calculation.
Sources: NREL — Quantifying Uncertainty in PV Energy Estimates · NREL — P50/P90 Analysis for Solar Energy Systems Using SAM · U.S. DOE / Navigant — offshore-wind debt sizing examples using different P50/P90 and DSCR combinations · Dezzmond analysis; one-year / multi-year uncertainty examples are illustrative.