When it comes to oil, addition is hard

Have we underestimated total oil reserves?, from New Scientist (and, it appears, every other source in the British-speaking world).

Richard Pike, of the Royal Society of Chemistry and previously of the oil industry, points out that it's generally the convention in the oil industry to give, as a one-number estimate for the output of a particular oil, the 10th percentile of the distribution that they expect. This is an inherently conservative estimate. That's fine -- but then when they combine the estimates from every oil source they do it by just adding those together. If I'm understanding this correctly, the estimates that are out there of how much oil there is correspond to what happens if every oil well, etc. performs only at the 10th percentile of its expected distribution -- which just isn't going to happen. The 10th percentile is called the "proven reserves", the 50th "proven plus probable reserves".

I don't know what the underlying distributions are, but it seems like they generally report the 10th, 50th, and 90th percentiles of the underlying distribution -- so says Pike at this friction.tv video. They add these distributions together correctly internally but Pike claims that governments don't want to think about the probabilistic logic. Pike then claims that security analysts use the resulting very pessimistic estimates; perhaps the current run-up in prices is a result of this, although I'm not sure if he'd say this. (It sounds like it's not a secret that this is the way things is done, and perhaps the analysts know this.)

Mathematically, the idea is simple. Let's say that a certain oil field is expected to produce 4 megabarrels, and the production is normally distributed with standard deviation 1 megabarrels. The tenth percentile of a normal distribution is 1.28 standard deviations below its average, so the "proven reserves" of this field would be 2.72 megabarrels, and the "proven plus probable" 4 megabarrels.

But now say we have four such fields. The oil industry's techniques would say that those fields together have "proven reserves" of 2.72 million times four, or 10.88 megabarrels. But for uncorrelated distributions -- and I'm going to assume that the distributions here are uncorrelated -- the variances add. The variance of the distribution for one field is 1 megabarrel², so for four fields it's 4 megabarrel²; the standard deviation is the square root of this, 2 megabarrels. The mean is still 16 megabarrels, but the 10th percentile is now 13.44 megabarrels. The chances of getting as low as 10.88 megabarrels are about one half of one percent; this is what Pike means when he calls this a pessimistic estimate. And of course with more fields the pessimism becomes more extreme.

The first reference I can find to this is a May 2006 press release of the Royal Society of Chemistry, referring to a June 2006 article by Pike in Petroleum Review but it seems to have swept through the British blog world in the last few days after the Times of London made a quick reference to it in an article on North Sea oil, as this press release of the RSC mentions. (For some reason the Times article refers to "this month"'s issue of Petroleum Review, which I can't seem to see online even though Penn's library claims to have an electronic version.)

If this is true (I hesitate to think it is, just because it seems surprising that people wouldn't know this!) then it's good news and bad news. Good news because it means we're not going to run out of oil as soon as we think, which means less economic shock. But it also means more carbon for us to spew into the air before we finally run out.

I encourage you to not read the comments in most places where this has been posted, because it's basically people just ranting about global warming and saying either "we've reached peak oil, anybody who says we haven't is a poopyhead" or "we haven't reached peak oil, anybody who says we have is a poopyhead".

The moral here: probabilistic forecasting is tricky. See also Nate Silver's appearance on cnn.com regarding polling for the presidential election, which is totally irrelevant here except that it also goes to show how a lot of people don't know how to aggregate probabilistic data.