BUSINESS SIDE OF GEOLOGY
By PETER R. ROSE
A Case Against ‘Most Likely’
Figures courtesy of Peter R. Rose
Peter R. Rose is managing partner, Rose & Associates, LLP, Austin,Texas.
In the early days of E&P risk analysis, one of the most widely used terms was “most likely,” representing some perceived intermediate outcome.
Back when many firms employed triangular diagrams to characterize the ranges of uncertainty attending various prospect parameters (such as productive area, average net pay, gross rock volume, HC-recovery factor, porosity, etc.), the peaks of the triangles were labeled - correctly - “most likely,” corresponding to the statistical mode of the distribution.
But triangular distributions are poor proxies for the lognormal frequency distributions they purport to represent, leading in most cases to overestimating, i.e., optimistic bias (Figure 1).
Moreover, most prospectors just didn’t recognize how severely skewed such natural distributions really are - the correctly plotted peak of most lognormal frequency distributions usually lies far to the left of the peak of most counterpart triangular distributions.
“Most likely” began to mean different things to different prospectors.
Today, most explorationists use cumulative log probability distributions (Figure 2) rather than the frequency (or probability density) form of portrayal, because of their superior analytical and iterative capabilities.
For any estimated parameter, geoscientists can postulate tentative high-side and low-side outcomes, plot them provisionally at the P10 percent and P90 percent points, and then evaluate the plausibility of the consequential P1 percent, P50 percent, P99 percent and Mean outcomes. Taking all such values under consideration, geoscientists can then iterate and reiterate the cumulative probability distribution until a “best fit” is obtained, consistent with all pertinent data.
The location of “most likely,” however, is not apparent on the cumulative probability distribution - its position varies with the slope of each distribution.
Nevertheless, “most likely” - undefined - has stubbornly persisted in the operational terminology of prospect risk analysis. It is used regularly in the E&P vernacular, and it commonly appears as a formal prospect parameter in company evaluation data forms used to evaluate projects on which companies are prepared to spend millions of dollars!
Problem is, in most companies explorationists don’t agree about what “most likely” really means.
Does it correspond to the mean (= average) of the distribution?
The median (= P50 percent)?
Or does it simply represent the prospector’s best guess?
We regularly inquire of our classes as to what “most likely” means to them, as individuals. We also ask students to identify, on an example prospect, “most likely” values for parameters such as productive area, average net pay, HC-recovery factor and prospect reserves.
Results are startling: “Most likely” is used for a wide range of outcomes corresponding to probabilities ranging from about P90 percent to P20 percent.
Sad to report, we also hear a few cynical suggestions that “most likely” means whatever outcome is required to sell the prospect!
After reviewing hundreds of Industry prospects over the past 10 years, I cannot identify any meaningful or unique use in prospect risk analysis for “most likely.” All the important statistical measures for prospect reserves parameters can be expressed using the P1 percent, P10 percent, Mean, P50 percent, P90 percent, P99 percent convention.
Moreover, “most likely” can very easily lead to misleading, systematically biased prospect evaluations - and, consequently, unfortunate management decisions.
If you need to describe some subjective intermediate case that is probabilistically undefined, try “best guess” (which also has the virtue of intellectual forthrightness).
“Most likely” is a throwback to the past, a dangerous term because it is generally undefined, leading frequently to miscommunications. All it can do is get you in trouble.
Recommendation: Expunge the term from your E&P vocabulary.