Engineers in oil and gas, especially reservoir engineers, are no strangers to uncertainty. Whether we’re estimating reserves, forecasting production, or evaluating project economics, we often compress a complex, continuous distribution into just three numbers: P10, P50, and P90.
But what do these percentiles actually mean? And more importantly, are we using them the right way?
🔢 The Percentiles
P10, P50, and P90 represent quantiles of a continuous probability distribution:
- P10: There’s a 10% chance the outcome will be higher (a.k.a. High Case).
- P50: The median, 50% chance the outcome is higher (sometimes mistakenly called Most Likely).
- P90: A 90% chance the outcome will be higher (a.k.a. Low Case, and often considered conservative).
These values are often assigned weights, like 30%, 40% and 30%, to estimate an expected value, such as NPV.
But hold on: if you remember your Statistics 101, you’ll know that the probability of any single exact value in a continuous distribution is essentially zero. So what’s going on?
🔍 Discretisation: What You’re Actually Doing
What we’re really doing here is discretising a continuous distribution, which is converting it into a set of discrete points with assigned probabilities. The P10/P50/P90 approach is a form of quantile discretisation (a.k.a. equal-frequency binning).
Its goal? To preserve a balanced representation of outcomes, like the expected NPV, while simplifying the model enough to use in decision trees, economic spreadsheets, or reserves reporting.
This practice is entrenched in oil and gas workflows. In fact, regulatory standards like SEC and PRMS explicitly require these percentiles.
While we won’t go into depth on quantile techniques here, it’s worth noting that more advanced methods also exist—such as fuzzy logic approximators, decision-tree-based ML models, or orthogonal polynomial approximations. These are used in more computational or data-rich environments where fidelity matters.
🎲 Monte Carlo vs. Discretisation: Why Not Just Simulate?
Let’s simplify. Suppose you’re throwing two fair dice, die A and die B. You have 6 × 6 = 36 possible outcomes. Now imagine A and B are continuous variables instead. That means the possible outcomes are infinite.
To handle that, we use Monte Carlo simulation, which samples thousands of possible outcomes to estimate a distribution. You get a much more realistic view of the tails, skewness, and expected value of your model.
So… why not always use Monte Carlo?
🤔 Why Engineers Still Discretise
Despite the power of Monte Carlo, discretisation remains widely used and for good reasons:
- **🖥 Computational Simplicity.**Many economic models, especially legacy spreadsheets or built-in field simulators, can’t process random variables. Feeding in 3–5 representative values is just easier.
- **👥 Human Interpretability.**Decision makers often prefer simple “High–Mid–Low” cases over probability density plots or 10,000-run histograms. Discretisation helps frame decisions in more digestible terms.
- **📑 Regulatory & Reporting Constraints.**SEC filings, PRMS submissions, and internal audit processes still require discrete case reporting using P10, P50, and P90. Sometimes, you discretise because you have to.
✅ Bottom Line
Monte Carlo simulation gives you the most complete view of uncertainty and should be used whenever feasible.
But discretisation, when done correctly, can still provide a practical, defensible, and communicable approximation.
📌 Just remember: discretisation is a modelling choice, not a shortcut.
Be deliberate. Preserve expected value. Communicate limitations. And if you can, run a Monte Carloalongside to test how well your three-point approximation holds up.
Reference:
Bratvold, R. B., & Begg, S. H. (2010). Making Good Decisions. Society of Petroleum Engineers. ISBN: 978-1-55563-258-8.