Give forty interconnection requests a 20% chance each and the arithmetic says you will get eight, give or take two and a half. That arithmetic assumes the forty are independent. They are not, and I measured how badly — on a book concentrated in one technology, the standard 80% confidence interval is wrong more than a third of the time.
1,637 active requests across MISO, CAISO, NYISO and ISO-NE. 355 GW under call.
A probability per project answers “will this one be built?” It does not answer “how much will my forty deliver?” The distance between those two questions is entirely the independence assumption, and it is almost always made silently, by multiplying.
Projects in the same queue share an ISO study cycle, a transmission owner's capital plan, an equipment supplier, a state policy regime. When one of those turns, it does not move one project. It moves all of them at once. Independence cannot represent that, so it produces a distribution that is far too narrow — confident, tidy, and wrong in exactly the tail you are trying to protect against.
A model of shared shocks invents risk if there are no shared shocks. So before fitting one: do outcomes inside a group vary more than independent draws would?
The test compares each group's build count against a permutation null — same predicted probabilities, same group sizes, group membership shuffled. That detail matters more than it sounds. The underlying model is miscalibrated: it says 65% and means 49%. A textbook chi-square test would have read that miscalibration as clustering and “found” correlation that was not there. The permuted null carries the same miscalibration, so only real structure survives it.
| outcomes shared by | groups | observed | permuted null | inflation |
|---|---|---|---|---|
| fuel type | 13 | 13.23 | 3.24 | 4.09× |
| state | 27 | 5.64 | 2.15 | 2.62× |
| ISO study cycle | 59 | 7.41 | 3.93 | 1.88× |
| county | 132 | 2.14 | 1.19 | 1.80× |
| ISO | 4 | 15.41 | 8.77 | 1.76× |
| transmission owner | 22 | 4.32 | 2.51 | 1.72× |
Every level significant at p < 0.00025, the floor at 4,000 permutations. Note the nulls are 1.19 to 8.77 rather than the 1.0 a table would assume — that gap is the miscalibration, and it is the size of the mistake the naive test would have made.
That is the commercially useful part. Tariffs, cell prices and turbine lead times hit every project of a type simultaneously, wherever it sits. A book spread across ten states but concentrated in solar is far less diversified than it looks.
Correlation being real does not mean a given model of it predicts better. So the structure was chosen by out-of-sample test, not by picking the largest effect: draw books of 40 from held-out data, and check how often the truth lands inside each model's 80% interval. The target is 80%.
| the book you actually hold | independence | shared shocks |
|---|---|---|
| diversified, drawn at random | 78.7% | 89.0% |
| all in one state | 74.5% | 88.1% |
| all in one technology | 62.6% | 81.5% |
Independence is tolerable for a diversified book and dangerous for a concentrated one — which is the realistic case for a developer, a lender, or anyone whose thesis is a single technology. Its “80%” interval contains the truth 62.6% of the time.
All 1,637 requests still active across four grid operators, 355 GW queued. Both models agree the expected delivery is about 102 GW. They disagree completely about how sure of that anyone should be.
| GW delivered | p10 | p50 | p90 |
|---|---|---|---|
| independence | 94.9 | 101.7 | 108.7 |
| shared shocks | 73.3 | 102.3 | 133.9 |
Same centre. 4.3× the spread. The one-in-ten bad case is 21.6 GW worse than the independent arithmetic implies — and 21.6 GW is roughly the entire active queue of ISO-NE and NYISO combined. That is the number a lender sizing a facility, or a manufacturer sizing a factory, is currently getting wrong.
Two measured reasons the centre of that distribution deserves less trust than its width. Both were found while building it and neither is fixed.
Calibrating on projects is not calibrating on capacity. Probabilities tuned so that each project is right overstate delivered capacity by 20.8% out of sample, because the gigawatts sit in large projects and large projects fail more inside every size band. Re-fitting the calibration weighted by megawatts cuts that to 6.1%. Adding project size as a feature does not help — the bias is within size bands, not between them.
The live book is 68% MISO by capacity; the training history is 19% MISO. So the headline leans heavily on one operator's record being representative. 18% of the book's capacity sits in operator×technology cells with fewer than 40 resolved historical requests.
The dispersion result is a ratio, and it survives both problems. The central estimate does not. So the honest claim here is narrow and deliberately so: not “103 GW will be delivered”, but “whatever the centre turns out to be, the spread around it is more than four times what independence tells you.”
Random-intercept logistic model fitted by marginal maximum likelihood, integrating the group effect out with Gauss–Hermite quadrature. Fixed effects held at the already-validated walk-forward model, so the shared effect cannot quietly absorb ordinary lack of fit. Study cycle carries a frailty of τ = 1.06 on the log-odds scale, an intra-class correlation of 25.5%. Levels are fitted one at a time and therefore overlap, which is precisely why the combination was chosen by out-of-sample coverage rather than by adding up the largest ones.