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 reason is simple and frequently overlooked: year-to-year weather variation averages out over a long period, and systematic uncertainty does not. A single bad wind year is a real risk to a single year's debt service. Across fifteen years of a debt term it is very largely self-cancelling.
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 | Typical use | |
|---|---|---|
| P50 | The median. Half of outcomes above, half below | The expected case; sponsor base case |
| P75 | Exceeded in 3 years out of 4 | Occasionally used for covenant testing |
| P90 | Exceeded in 9 years out of 10 | Debt sizing |
| P99 | Exceeded in 99 years out of 100 | Extreme downside; rating agency cases |
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 independent components, combined by root-sum-square.
The standard construction separates them into two classes, and the distinction is the key to everything below.
Systematic uncertainty does not diminish with time. It includes the accuracy of the irradiance or wind resource database, measurement uncertainty at the site, the long-term reference period, extrapolation from measurement height to hub height, and the energy conversion model itself. If the resource dataset is biased by two percent, it is biased by two percent for twenty years.
Interannual variability is the genuine year-to-year variation in the weather. It is random, it is well characterised, and crucially it averages out across a long period.
A worked combination from the standard method: satellite-based model uncertainty of ±3.5% and interannual variability of annual irradiance of ±2.6% combine as:
√(3.5² + 2.6²) = 4.36%
And the Pxx values follow from the standard normal:
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 only one of the two uncertainty classes shrinks.
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 — 3.5% systematic, 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 — 6.0% systematic, 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.
The gap is much larger for wind. 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.
Almost all of the convergence happens by year ten. The ten-year and twenty-year columns are nearly identical, because √10 has already reduced the variable component to a small share of the total. Arguing about whether to use a fifteen- or eighteen-year period is not worth the effort; arguing about one year versus ten is.
P99 moves most. Wind's one-year P99 is 80.3% of P50 and its ten-year P99 is 85.4% — a five-point difference on the case most likely to appear in a rating agency analysis or a severe downside test.
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.
The largest component is usually reducible, and reducing it has a computable value. A measurement campaign that cuts resource uncertainty from 4% to 2.5% reduces the total, raises the P90, and increases debt capacity. Whether the campaign is worth its cost is arithmetic: compute the P90 under both uncertainty stacks, run the debt sizing on each, and compare the difference to the campaign cost. This is a calculation almost nobody runs, and on a large project it usually favours measuring.
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.
Degradation Is a Separate Question
A distinction that causes real confusion, because both are expressed as percentages of P50.
An energy yield assessment typically produces a year-one P50, or a long-term average for a new plant. Degradation is then applied on top, as a separate annual reduction — commonly a first-year step followed by a linear annual rate.
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.
Treating degradation uncertainty as part of the resource uncertainty double-counts or omits depending on which way it is done. Degradation rate uncertainty is a genuine additional component — the warranty may guarantee a rate, but a guarantee is a claim against a counterparty, not a certainty about the asset — and it should be stacked explicitly rather than folded into the resource number.
For storage the same structure applies with different content: there is no resource uncertainty, but capacity degradation is larger, faster and driven by the cycling strategy the battery post described. A "P90" for a battery is therefore mostly a degradation and availability statement, and importing the solar convention without saying so describes the wrong distribution.
Which One Belongs Where?
This is the practical question, and the answer follows from what each test is actually asking.
| Test | Question | Use |
|---|---|---|
| Debt sizing | Can the project service debt over the term? | P90 over the debt tenor |
| Annual DSCR covenant | Will it cover this year's debt service? | P90 or P99, one-year |
| Sponsor base case | What do we expect? | P50 |
| Rating agency downside | What if the resource is genuinely poor? | P99, over the relevant period |
| Equity case | What return do we expect? | P50, with a P90 sensitivity |
Two specific errors follow from getting this wrong.
Using a one-year P90 to size a fifteen-year facility is over-conservative. For wind that costs 2.8 points of energy, which on a $17.5m revenue line is roughly $490,000 a year and a meaningful reduction in debt capacity. The lender is protecting against a bad year with a structure that has fifteen of them to average across.
Using a multi-year P90 to set an annual covenant is under-conservative. The covenant tests a single year, and a single year genuinely has 8.49% of uncertainty around it. A lock-up threshold calibrated on a ten-year distribution will be breached more often than the lender expected.
The clean way to express this, and it is rarely done: size the debt on a term P90 and set the covenant headroom against a one-year P90. Those are different numbers derived from the same assessment, and they are the right numbers for their respective jobs.
What P90 Does Not Cover
The point the curtailment post made and which bears repeating here, because it is the most consequential misunderstanding in this area.
P90 is a resource statement. It says the wind will blow, or the sun will shine, at least this much in nine years out of ten. It says nothing about:
- 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 correct treatment combines the distributions, which almost nobody does. The minimum honest treatment is to test the joint case: a P90 resource year and an adverse curtailment year, rather than assuming P90 covers both.
There is a further complication that makes the joint case harder than simply stacking haircuts, and the curtailment post identified it: the distributions are correlated, and in the unhelpful direction. A strong regional resource year is one in which every plant in the pocket generates hard simultaneously, which is exactly when the export constraint binds. So a P90 resource year may well see less curtailment than a P50 one, and a P10 resource year — an unusually good one — may see considerably more.
That correlation means treating resource and curtailment as independent understates the variance of the combination in some ranges and overstates it in others. 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. A two to three percent spread in P50 between reputable assessors is unremarkable, and the uncertainty stacks can differ by more.
That has three consequences worth planning for.
Lenders usually require their own. An independent engineer's assessment, commissioned by the lender, is the number the debt will be sized on — and it will frequently be lower than the sponsor's. 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 equivalently, using the z-values:
P75 → 0.674 P90 → 1.282 P95 → 1.645 P99 → 2.326
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
Resource P90 over the debt term
Curtailment adverse case, node-specific
Basis lender assumption, generation-weighted
Availability contractual guarantee less exclusions
→ Combined downside revenue, NOT a P90 revenue
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?
- Is the debt sized on a term P90 and the covenant set against a one-year P90?
- 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?
A P90 over the debt tenor, not a one-year P90. Using a one-year figure for a fifteen-year facility over-states the risk by about 2.8 points on a wind project, because the lender is protecting a long period against a single-year distribution.
Is degradation part of the P90?
No. An assessment typically produces a year-one P50, and degradation is applied separately on top. The Pxx for year fifteen applies the uncertainty to the degraded P50, and degradation rate uncertainty is its own component in the stack.
Is a measurement campaign worth the cost?
It is a computable question. Resource dataset uncertainty is usually the largest component and on-site measurement is what reduces it. Run the debt sizing under both uncertainty stacks and compare the difference to the campaign cost — on a large project it usually favours measuring.
Does P90 account for curtailment?
No. P90 is a statement about the resource. Curtailment, basis, capture rate and availability each have their own distributions, and a model applying a P90 to generation while using point estimates for those has applied conservatism to one variable out of four.
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, and neither takes any effort. Label every Pxx with its period. And size the debt on the term figure while setting covenant headroom against the one-year figure, because those tests ask genuinely different questions and the same assessment already contains both answers.
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: Solargis — How to Calculate P90 and Other Pxx Energy Yield Estimates · pv magazine — Understanding P50, P90 and P99 in Solar Energy · Edward Bodmer — Solar Uncertainty Analysis (P90, P95 etc.) · Renewables Valuation Institute — How to Model P50, P75, P90 and P99 Energy Yields