Richard Pike is an old BP hand, whose maths is sound. The proved reserve is often defined as that low amount which is 90% likely to be recovered, i.e. almost certain, and is called P90. Proved and probable reserve, or P50, is the amount which is 50% likely to be recovered. P10 also includes the possible, and is only 10% likely to be recovered.

Pike’s point is that while you can simply add P50 values arithmetically, to get national or global P50 values, you can’t just add the P90 values together to get aggregate P90 proven reserves. The true aggregate P90 is higher than their arithmetic sum, but less than P50.

P90 means that there is only a 10% chance of recovering less than the proven reserves. But if you consider two fields, how likely is it that both will only yield this low amount? As Pike notes, the probability of throwing a 1 with a die is 17%, but the probability of throwing two 1s with two dice is only 3%. By analogy, the probability of getting only the P90 proven reserves from each of a number of fields quickly shrinks – in aggregate, they will almost certainly exceed this.

Why have we not recognised this effect in the past hundred years of the oil industry? Well, perhaps we have, in one way. The phenomenon of reserves growth might stem in part from this statistical effect. But the following reasons suggest that the effect on global peak oil is marginal.

1. As a field is produced, its reserves become constrained by its behaviour. The difference between P90 and P50 rapidly shrinks, which would reduce the error of adding P90 values.

2. Industry’s estimates of a field’s reserves before it enters production are unfortunately often inaccurate anyway. The bulk rock volume, net-to-gross reservoir, oil saturation, mean porosity and oil recovery factor are all initially poorly constrained, yet each has to be assigned a mathematical probability. The effect of possible problems such as compartmentalisation or lateral variability may be little more than guesswork at first. This can result in very precise estimates of P50 and P90for a field which are, however, quite inaccurate. Put bluntly, you can’t apply rigorous statistics to educated guesswork.

3. 75% of global conventional oil reserves are held in OPEC countries, and they are subject to much greater uncertainties than this. For political reasons, or for lack of any particular need to do so, few OPEC states have made any meaningful re-calculations of reserves since the mid-1980s. The published reserves data may bear no resemblance to either P90 or P50.

4. Models of peak oil would not use P90 values where P50 values are available, simply because P50 is the most probable outcome. As Pike notes, companies use P50 reserves to plan developments and write reports to host governments, and (outside OPEC and certain other states) these numbers then get published in the press and company reports. He’s wrong in suggesting that they are seldom available to public, although you do have to hunt for them.

To use UK data as a guide to this possible effect, BERR reported proven (i.e. P90) UK reserves to be 479 million tonnes, or 700 million tonnes of proven + possible (i.e. P50) in December 2006. The BP Statistical Review reported 532 million tonnes, or somewhere between the two. I see the effect as real but not globally significant for peak oil modelling.