Percentiles Explained

What Is P10, P50, and P90? Percentiles Explained

P10, P50, and P90 are percentile values that represent three levels of confidence in a forecast or risk model. The “P” stands for percentile, and the number tells you the probability that the actual outcome will meet or exceed that estimate (probability of exceedance).

Together, these three values provide a complete picture of uncertainty, whether you are forecasting oil production, modeling solar energy output, or estimating construction project budgets.

Quick-Reference Comparison Table

To understand how P-values shift based on context, refer to the comparison table below:

Percentile

Exceedance Probability

Production / Output (e.g., Solar, Oil)

Cost / Budgeting (e.g., Construction)

Confidence & Risk Level

P90

90% chance to equal or exceed

Conservative / Low output

Lower budget (High risk of overrun)

High Confidence / Low Risk

P50

50% chance to equal or exceed

Expected / Median output

Baseline budget (50/50 chance)

Balanced / Flip of a coin

P10

10% chance to equal or exceed

Optimistic / High output

High budget (Includes contingency)

Low Probability / High Upside

What Each Value Means

In fields like energy and engineering, these percentiles are defined using the probability of exceedance ($P(X \ge x)$)—the chance that reality will equal or beat the estimate:

P90 (Conservative Estimate): There is a 90% chance the actual result will equal or exceed this number. It represents the baseline outcome you can bank on with high certainty.

P50 (Median Estimate): There is a 50% chance the result will come in above this number and a 50% chance it will fall below. It represents the most likely expected outcome.

P10 (Optimistic Estimate): There is only a 10% chance the actual result will reach or exceed this number. It reflects best-case scenario conditions.

Example: If a solar project has a P50 of 10,000 kWh/year, there is a 50% likelihood of generating more than 10,000 kWh. A P90 of 8,500 kWh/year means you have 90% confidence the system will generate at least 8,500 kWh.

Why the Numbers Seem Backwards

It can feel counterintuitive that P90 is a smaller number than P10 when forecasting energy or resources.

High Exceedance (90%): You set the threshold low so that reality almost always beats it.

Low Exceedance (10%): You set the threshold high so that only exceptional performance reaches it.

The Road Trip Analogy

Imagine setting mileage targets for a day of driving:

P90: "I am 90% sure I will drive at least 200 miles." (Low, achievable bar)

P50: "There is a 50/50 chance I drive at least 350 miles." (Expected outcome)

P10: "Only if traffic is perfect will I hit 500 miles." (High, optimistic target)

Generating the Data: Monte Carlo Simulations

P-values are calculated through Monte Carlo simulations—computational algorithms that run thousands of iterations using historical data and probability distributions.

+--------------------------+ +---------------------------+ +-------------------------------+
| Input Variables | | Monte Carlo Engine | | Output Exceedance Curve |
| - Weather history | ---> | Runs 10,000+ simulations | ---> | - P90 (Conservative baseline) |
| - Equipment efficiency | | accounting for random | | - P50 (Median expectation) |
| - Degradation rates | | variables and risk factor | | - P10 (Best-case scenario) |
+--------------------------+ +---------------------------+ +-------------------------------+

Two Conventions: Output vs. Cost Estimation

A crucial detail to remember is that different industries use percentiles differently depending on whether they are measuring production or cost:

1. Probability of Exceedance ($P \ge x$) — Energy & Reserves

In oil & gas and renewables, high P-numbers mean lower output values because you are measuring the probability of exceeding that yield.

2. Cumulative Distribution Function ($P \le x$) — Project Costing

In construction and project budgeting, higher P-numbers correspond to higher dollar figures.

P50 Cost: 50% chance project costs will stay at or below this number.

P80 Cost: 80% chance costs will stay at or below this number (includes contingency for risk).

Industry Applications

Oil & Gas Industry (Reserve Classification)

The Society of Petroleum Engineers ties reserves directly to exceedance probabilities:

1P (Proved Reserves = P90): 90% probability of recovering this volume or more.

2P (Proved + Probable = P50): 50% probability of recovery.

3P (Proved + Probable + Possible = P10): 10% probability of recovery under optimal conditions.

Renewable Energy Financing

Banks use P90 output numbers to determine loan eligibility. If a wind or solar project can cover its debt payments during a low-resource P90 year, the project is considered low risk and financeable.

What the Spread Tells You: Risk & Uncertainty

The gap between P10 and P90 indicates the degree of risk in a forecast:

Distribution Spread

P90 Value

P10 Value

Interpretation

Narrow Spread

9,000 kWh

11,000 kWh

Low Uncertainty / High Predictability (e.g., Solar projects in desert climates)

Wide Spread

5,000 kWh

15,000 kWh

High Uncertainty / High Volatility (e.g., Exploratory oil wells or unmapped wind sites)

Skewness: Mean vs. Median

For a symmetrical distribution (bell curve), P50 equals both the median and the mean. However, in highly skewed fields—like oil exploration where a few massive discoveries pull averages up—the mean can be misleadingly high. P50 remains the true median midpoint, ensuring realistic decision-making.