INTERPRET RESULTS
P10, P50 and P90: read the percentile, unit and direction together
In BalanceCheat, P10, P50 and P90 are cumulative sample percentiles: low to high in the output distribution. P50 is the median. Whether the low or high tail is unfavorable depends on the metric. Always confirm the convention before comparing these labels with another report.
| Label | Native interpolated value | Reading |
|---|---|---|
| P10 | 9 EURk | Low cumulative percentile; not automatically the worst case |
| P50 | 45 EURk | Median; not automatically Base or mean |
| P90 | 81 EURk | High cumulative percentile; not automatically favorable |
On this page
Why a percentile need not be an observed value
Use ten synthetic observations, in EURk: 0 → 10 → 20 → 30 → 40 → 50 → 60 → 70 → 80 → 90. These are an illustration for reading statistics, not a financial forecast or a Monte Carlo run. Here 1 EURk means EUR 1,000.
The native statistics routine uses linear interpolation at zero-based position (n − 1) × p. P10 lies at position 0.9, between 0 and 10, and equals 9 EURk. P50 lies at 4.5 and equals 45 EURk; P90 lies at 8.1 and equals 81 EURk.
A small empirical sample and an interpolated quantile need not place exactly the named percentage of observations below the printed value. The empirical CDF is a different calculation: at 20 EURk, three of ten observations are at or below the threshold, so the CDF is 30%.
A P90 exceedance value reverses the direction
Some energy-project reports use P90 to mean an amount expected to be met or exceeded with 90% probability. NREL documents this exceedance convention. For a continuous distribution, that corresponds to the low cumulative P10, not the cumulative P90 used in BalanceCheat.
Ask whether the label means “at or below” or “met or exceeded.” With discrete outcomes or ties, also check the inequality and quantile method. Do not compare two P90 figures solely because their labels match.
| Convention | Meaning of 90 | Position |
|---|---|---|
| Cumulative P90 | About 90% of the distribution is at or below the value | High tail |
| P90 exceedance | The value is met or exceeded with 90% probability | Low tail for a continuous distribution |
Which tail is adverse depends on the financial output
The unit tells you what is being measured; the metric tells you how to interpret direction. The same percentile position can indicate a shortfall in one output and resilience in another.
| Output | Generally adverse direction | What to compare |
|---|---|---|
| Cash / Liquidity Headroom | Lower | The low tail against minimum cash or zero headroom |
| EBITDA / Equity Value | Lower, other assumptions equal | The low tail against the decision threshold |
| Required Funding | Higher | The high tail against available financing |
| A cost or cash outflow | Higher | The high tail against budget or liquidity capacity |
A percentile band is not a confidence interval for the mean
P10–P90 describes spread in modeled outcomes. It does not measure uncertainty in the estimated mean and does not guarantee that 80% of real future outcomes will fall inside the interval. A confidence interval for a mean is a different statistical object requiring its own method and assumptions.
Check the valid denominator. If 100 runs were completed, 90 were valid and 18 valid outcomes crossed a threshold, the reported conditional frequency would be 18 / 90 = 20%, not 18%. Investigate the ten invalid results before using that percentage. This arithmetic example is illustrative and separate from the ten-value percentile sample.
Read the output in its original context
Record the output name, currency and scale, period, scenario, input distributions, valid-run count and percentile convention. Base, median and mean answer different questions and can differ.
Use the Monte Carlo workflow to generate native results. The results reference explains available statistics and stochastic constraints explains conditional denominators. For the method itself, read Monte Carlo in finance.
Sources and conventions
Synthetic examples. Model-based results were reconciled with the current BalanceCheat calculations; assumptions, units and boundaries are specified in each example.