P50 vs P90: The Number Your Bank Actually Uses
Your bank doesn’t finance on the P50 in your pitch deck. It finances on the P90. And if you computed it as “the P50 minus 8%,” you may have mis-stated the size of the loan — because that margin isn’t fixed: it depends on the site, the data quality, and the period. This article explains what each number means, why the linear shortcut fails, and how to produce a P90 the independent engineer will sign off on.
TL;DR
- The P50 is the median production (exceeded in 50% of years). It’s your base case, but the bank doesn’t lend against the mean.
- The P90 is the production met or exceeded in 90% of years. It’s the number the debt is sized against.
- Computing P90 as “P50 minus a fixed margin” is wrong: the discount is 1.282 × σ, and σ changes with every project.
- The real distribution has fatter tails than the normal: the modeled P99 is breached ~1 year in 6, not 1 in 100 (kWh Analytics).
- A defensible P90 comes from a Monte Carlo over separated uncertainties (random vs systematic), not from a subtraction.
If you sell, finance, or review solar plants, you live between these two numbers. Confusing them — or eyeballing the second — is the difference between a financial model that survives due diligence and one that doesn’t. Let’s take it in order.
What is the P50, and why isn’t it enough for the bank?
The P50 is the annual energy level the plant meets or exceeds in 50% of years: the median of the production distribution. It’s the central value your simulation returns for a typical weather year, and it’s what you use for your base case and expected return.
The problem is that half the years will fall below it. A developer evaluates the project on the mean; a lender does not — the downside year is what matters, because repayment depends on there being cash even in a weak year. So the P50 is necessary but insufficient: it describes the center of the distribution, not its adverse side. And debt is sized on the adverse side.
What is the P90, and why does the lender finance on it?
The P90 is the production expected to be met or exceeded in 90% of years. Put the other way: only 1 year in 10 should fall below it. That prudence is exactly what a bank wants for sizing debt service.
The mechanism is direct: the lender takes the cash available for debt service (CADS) in the P90 case, applies a target DSCR (typically 1.20–1.35× for contracted solar), and that yields the maximum principal the asset can carry. In our 100 MWdc base case — a P50 of 170 GWh — the P90 of 155.8 GWh cuts the cash ~8% versus the P50, and the debt with it. A higher, well-founded P90 means, literally, more debt at a lower cost.
| Percentile | Exceeded in… | z-factor | Energy (100 MW case, σ = 6.5%) |
|---|---|---|---|
| P50 | 50% of years | 0.000 | 170,000 MWh |
| P75 | 75% of years | 0.675 | 162,541 MWh |
| P90 | 90% of years | 1.282 | 155,833 MWh |
| P95 | 95% of years | 1.645 | 151,823 MWh |
| P99 | 99% of years | 2.326 | 144,298 MWh |
The mistake of computing P90 as “P50 minus a margin”
The discount from P50 to P90 isn’t a fixed number: it’s 1.282 × σ, and σ changes with every project. Treating P90 as “P50 minus 8%” (or minus whatever the last project used) is the most common and most expensive error in a yield study.
The industry formula makes it plain: P90 = P50 · (1 − 1.282 · σ). The entire discount lives in σ, the total uncertainty. And σ is not a constant: it depends on resource-data quality (satellite vs on-site measurement), latitude, climate, and the period you’re assessing. The same P50 produces very different P90s:
| Same P50 (170 GWh) | Total σ | P90 | Real discount |
|---|---|---|---|
| Good data + on-site measurement | 4.0% | 161,282 MWh | −5.1% |
| Typical base case | 6.5% | 155,833 MWh | −8.3% |
| Poor data / high variability | 10.0% | 148,206 MWh | −12.8% |
A fixed 8% margin oversizes the P90 at the bad site and undersizes it at the good one. In the first case, you promise the bank energy the real uncertainty doesn’t support; in the second, you leave cheap debt on the table.
There’s a second, subtler mistake: assuming the distribution is a perfect Gaussian bell curve. It isn’t. Real production has fatter lower tails than the normal — bad years worse than the bell predicts. The fleet evidence is stark: the modeled P99 scenario (which by definition should be breached 1 year in 100) is being breached roughly 1 year in 6 (kWh Analytics, Solar Risk Assessment). The linear subtraction, which assumes normality, is systematically optimistic in the tail.
Monte Carlo: from uncertainty to a defensible percentile
If the linear shortcut fails, the right alternative is to simulate the distribution, not subtract from it. A modern bankable yield study derives the P90 with a Monte Carlo: it samples the uncertainties of each link — resource, transposition, temperature, soiling, degradation, availability — thousands of times and propagates each combination to annual energy, building the full distribution that the P50, P90, and P99 are read from.
This beats the analytical root-sum-square (RSS) combination on three counts:
- It captures the real shape of the distribution, tails included, instead of forcing a normal. NREL documents this in SAM: the analytical (normal) method gives a P90 “a few percent more optimistic” than the empirical method based on real historical years (Dobos, Gilman & Kasberg, 2012).
- It separates random from systematic uncertainty. Interannual weather variability is random: it averages out over the years (as σ/√n). Data and model bias is systematic: it never dilutes (Sandia/Hansen; NREL Prilliman et al., 2023). Distinguishing them is what lets you give a different P90 for one year versus the loan tenor.
- It lets you model correlations. RSS assumes every error source is independent; when they aren’t, it underestimates total uncertainty (Bodini & Optis, NREL, for wind AEP — the same principle applies to PV).
One year, or the loan tenor?
The bank uses two different P90s, and it pays to keep them apart. The one-year P90 governs the annual DSCR (is there cash in this particular year?). The multi-year P90 — over 10 years or the debt tenor — sizes the loan, and it’s higher than the one-year P90 because interannual variability averages out: only the random term is divided by √N; the systematic term stays fixed. Reporting a single one-year P90 for everything is another common error.
What does your lender expect in the report?
A bankable report isn’t a number: it’s a distribution with audited provenance. The independent engineer (IE) who reviews the study for the bank expects, at minimum:
- Explicit P50 and P90, with the P90 given both one-year and over the loan tenor.
- The uncertainty budget broken down by source (resource, transposition, thermal, soiling, degradation, availability) and combined traceably. The industry reference (IEA-PVPS Task 13) puts typical total uncertainty around 6.5%.
- The resource-data provenance: which satellite dataset, its validation, and whether there was site adaptation with ground measurement.
- Degradation and availability assumptions, stated and justified.
- Long-term representativeness: ideally ≥10 years of weather data, not a single favorable year.
- A probabilistic method (Monte Carlo or equivalent), not a single deterministic run with an eyeballed margin.
Above all, it expects coherence: that the P90 derives from the stated σ, and the σ derives from the stated sources. A P90 you can’t reconstruct from the uncertainty breakdown is a P90 the IE will cut — or reject.
Why data precision matters: cutting resource uncertainty from 2.29% to 1.20% adds ≈$175,000/yr of cash for debt service on a 150 MW plant (SolarAnywhere, 2026). Site adaptation, which compresses satellite bias from ±3.5% to ±2–2.5%, doesn’t just raise the P90 — it makes it defensible.
How Heliosolve solves it
Heliosolve produces the P90 the way it should be produced: by probabilistic simulation, not subtraction. The engine builds the energy distribution by sampling each link’s uncertainties and separating the random part (interannual, which averages) from the systematic part (model, which persists). The result is a P50, a one-year P90, and a tenor P90 — all traceable to their sources, exactly what the IE needs to reconstruct.
And there’s a deeper lever: lowering the underlying systematic σ. As we cover in The Real Cost of a PV Simulation Error, model bias is the term that doesn’t dilute over the years. Heliosolve’s high-fidelity physics — advanced irradiance model, optical ray tracing, cell-level computation, and a heat-transfer thermal engine — attacks that bias at every link. Less systematic σ means a P90 that is both higher and more defensible: P90 = P50 · (1 − 1.282 · σ) works in your favor as σ falls.
The point isn’t to report a higher P90 — it’s to report a P90 that survives due diligence. That’s the difference between a study that closes financing and one that delays it.
Frequently asked questions
What’s the difference between P50 and P90 in solar?
The P50 is the median annual production: met or exceeded in 50% of years. The P90 is the production met or exceeded in 90% of years, a prudent scenario. Developers evaluate the project on the P50; banks size debt on the P90, because repayment depends on the bad years.
How is the P90 of a solar plant calculated?
With the formula P90 = P50 · (1 − 1.282 · σ), where σ is total uncertainty — or, better, with a Monte Carlo that samples each source’s uncertainties and builds the full distribution. The 1.282 factor is the 90th percentile of the normal; the Monte Carlo method also captures the real tails.
Why is subtracting a fixed margin from the P50 wrong?
Because the P50-to-P90 discount is 1.282 × σ, and σ changes with the site, data quality, and period. A fixed 8% margin oversizes the P90 at poorly measured sites and undersizes it at well-measured ones. The real distribution also has fatter tails than the normal.
Why is the P99 breached more often than expected?
Because the real production distribution has fatter lower tails than the Gaussian bell. The analytical-normal method is optimistic in the tail: kWh Analytics finds the modeled P99, which should be breached 1 year in 100, is breached roughly 1 in 6. A Monte Carlo over real historical years corrects that bias.
What should a bankable yield report include?
P50 and P90 (one-year and over the debt tenor), the uncertainty budget broken down by source, the resource-data provenance and site adaptation, degradation and availability assumptions, ≥10 years of weather data, and a probabilistic method. Everything must be traceable for the independent engineer.