Industry: Oil and Gas Product: ModelRisk Application: Exploration success rates
Across the wildcat record of the past two decades, exploration teams have consistently declared pre-drill Pg numbers that run a little ahead of the realised hit rate — a systematic over-optimism that compounds across a portfolio. Layer onto that the assumption of independent well outcomes — the default in nearly every spreadsheet exploration model — and a 10-well annual programme can carry a far larger probability of negative aggregate NPV than the independence math suggests. The exploration team rebuilt its programme analytics in ModelRisk around two corrections that point estimates cannot make: a calibration audit of declared Pg against realised outcomes, and a Gaussian copula that couples wells within the same geological play.
The clearest single picture is what correlation does to the count of successful wells for an unchanged mean Pg — the independence assumption is the green curve, the realistic correlated case is the red one:
Both cases have the same mean — about 3.1 successes out of 10 — but correlation widens the standard deviation from 1.41 to 2.11 successes and lifts the probability of zero successes from 2% to over 11%. That left tail, not the mean, is what breaks a capital plan built on a minimum number of discoveries.
A 400-well historical cohort — the firm's full multi-year wildcat record, each well with its declared pre-drill Pg and realised outcome (commercial discovery or dry hole) — is the raw material. Bucketing wells by declared Pg and computing the empirical hit rate in each bucket — with Jeffreys 95% binomial intervals per bucket — produces the audit chart every exploration committee should be looking at and few do:
The pooled declared mean Pg in this cohort is approximately 28%; the pooled realised hit rate is approximately 21.5%, a gap of roughly 6.7 percentage points — a clear, statistically robust over-optimism across 400 wells, no longer something a thin sample could explain away. The Jeffreys intervals on the larger cohort are tight enough that the bias is unambiguous: the prior the team has been using is systematically optimistic by about 15% of its declared value. The correction is mechanical: shrink declared Pg toward the realised hit rate by a calibration factor (the model applies a 0.85 multiplier to the true success probability), and re-run every prospect in the portfolio. A simulation with the uncorrected Pg overstates the expected number of discoveries across a programme — and the bias compounds in aggregate NPV.
The second correction is harder to make and harder to argue against. The textbook EMV calculation assumes wells in a portfolio fail and succeed independently — which is the modelling equivalent of assuming hurricanes hit Florida and Louisiana in uncorrelated years. Wells in the same play share the same geological story. If the regional source rock is not mature, every well in the play tends to fail; if it is, several tend to succeed together. The standard correction is a Gaussian copula at the play level: a per-play latent factor with within-play correlation ρ = 0.55 in this model, with idiosyncratic per-well noise on top.
For a 10-well programme split 5/5 between a shelf play (mean Pg = 0.44, NPV-given-success ~$280M, dry-hole cost $50M) and a deepwater frontier play (mean Pg = 0.19, NPV-given-success ~$1.1B, dry-hole cost $150M), the per-well mean EMV is unchanged by correlation. The distribution of total successes — shown at the top of this article — is not. Under independence the distribution is approximately normal (sum of independent Bernoullis), with mean 3.13 and standard deviation about 1.41 successes. Under correlation the standard deviation rises by half, to 2.11, and the probability of zero successes in the programme rises from 2% to over 11% — because all five wells in either play can now fail together. The mean is unchanged; the tail of total failure is five times more likely. For a company whose annual capital plan is built on at least two commercial discoveries, that tail is the number that matters.
The reshaping of #successes carries straight through to aggregate NPV:
Both curves have approximately the same mean, around $1.16B. The independence curve has the tighter body — the central limit theorem pulls 10 independent draws toward Normal — yet even here the heavy dry-hole costs leave a roughly 26% probability of negative aggregate NPV (P10 ≈ −$510M). The correlation curve is markedly wider: its P10 sinks to about −$1.0B, and the probability of negative aggregate NPV climbs from roughly 26% under independence to about 35% under realistic spatial correlation. The right tail also gets fatter (multiple co-arriving discoveries in the deepwater play, P90 ≈ $4.2B versus $3.2B), but in capital-allocation decisions the left tail is the binding constraint.
In exploration portfolios, the two largest sources of bias are not the geology — they are systematic Pg optimism and mistaken independence. Monte Carlo simulation in ModelRisk does not fix either silently; it makes both visible enough that the corrections become operational policy.