P10, P50 and P90 production forecasting

What the three cases mean

The convention is inherited from reserves reporting and it trips people up because the numbering runs the opposite way to intuition. The percentile refers to the probability of exceedance, so a higher number means a lower volume.

P90 — low case

The value the outcome has a 90% probability of exceeding. Conservative, and typically the one closest to a proved-reserves mindset.

P50 — base case

The central estimate, with roughly equal chance of the outcome landing above or below. This is the case an engineering review normally works from.

P10 — high case

The value the outcome has only a 10% probability of exceeding. The optimistic end of the fitted range.

How the cases are produced

All three cases come from the same decline framework. A base decline is fitted to the observed history using the Modified Arps model, producing the P50 case, and the P10 and P90 cases are drawn around it to describe faster and slower decline scenarios for the same well.

The spread is not constant. It is narrow immediately after the forecast cutoff, where the near-term rate is strongly constrained by the last observed months, and it widens with time as the decline shape has more room to diverge. That shape is a property of extrapolation itself: uncertainty about a decline curve compounds forward.

Because the three cases share one fitted model, they move together. Editing Di, the b-factor or the terminal decline changes all three, which is the intended behaviour — the range describes uncertainty about the decline, not three unrelated forecasts.

What P10–P90 is not

PronoHorizon states this on the chart itself, and it is worth restating: P10, P50 and P90 are forecast cases, and no calibrated confidence interval is implied.

A calibrated interval is a claim about long-run frequency — that roughly 80% of outcomes will fall between the P10 and P90 bounds. Making that claim requires demonstrating it on out-of-sample data, repeatedly, across a well population. A scenario band drawn around a decline fit has not demonstrated anything until it has been tested.

Treating an untested band as a probability statement is the specific failure that makes forecast uncertainty look rigorous while being decorative. The honest version is: here are three cases, and here is the measurement that tells you how well the range has held up.

How to check whether the range is realistic

Run a historical holdout. Hide a known period, forecast into it blind from the earlier history, then reveal the actuals and measure P10–P90 coverage: the share of held-out observations that fell inside the envelope.

Read that number in both directions. Coverage well below the range's nominal width means the band was too narrow — the forecast was more confident than it earned. Coverage at or near 100% is not automatically good news either; a band wide enough to contain everything excludes nothing and cannot inform a decision.

Coverage should be read alongside the other three holdout metrics. A band can achieve good coverage while the P50 case inside it is consistently biased high — the range contains the truth, but the number everyone actually uses is wrong.

From cases to EUR

Integrating a forecast case to the end of the well's economic life gives an estimated ultimate recovery for that case, which is how a rate forecast becomes a volume that reserves and economics can consume.

This is where the terminal decline matters most. Because a hyperbolic curve flattens indefinitely, an unconstrained fit integrates to an unbounded volume — the case range would widen without limit at the high end. The Modified Arps terminal decline is what makes each case integrate to a finite EUR.

In PronoHorizon the reviewed forecast case carries its assumptions and any engineer edits with it, so the EUR inputs handed downstream can be traced back to the decline parameters and the review that produced them.