Navigation:  Consolidations > Understanding the results

Understanding the results is by no means the easiest part of using REP. It can be even harder to explain what they mean to others. This section makes a brief attempt.

The important thing to remember is that for undrilled prospects (i.e. where the chance of success is less than 100%) there are two numbers AT LEAST which must be used to describe the possible outcomes. These are: chance of success and, in the case of success, some measure of volume. Most commonly, the measure of volume used is the mean; some prefer the P50 or median. REP calculates these and all the other P levels (P90, P10 etc.) and these should always be to hand.

The results of prospect/field evaluations, play analysis and consolidations are similar in presentation. On the results sheet you will find a numerical summary, and a graph.

The graph has two curves: the cumulative probability distribution, which starts on the left at 100% probability, and drops to the right to 0%. The other curve, usually a distorted bell-shape, is the relative probability distribution. These two curves have the same meaning for input as for output and are discussed, in the former context, in the section titled 'Entering Probability Distributions'.

From the cumulative curve you can read the probability that a particular reserve level will be exceeded. On the reserves (x) axis choose the reserve level, and read off on the probability (y)-axis the probability that this value will be exceeded. Alternatively, work the other way to discover, for any probability level, the associated reserves. The numerical values for unrisked P90, P50 and P10 shown in the table are simply readings from the cumulative probability curve.

Note that REP only shows the unrisked curve: earlier versions of the program also showed the risked curve, and tabulated values of risked P90, P50 and P10. These were removed, because they tended to cause confusion.

The relative probability curve is rather less useful, but its shape does give an idea of the uncertainly associated with the calculations. The tighter the shape, the less the uncertainty. The highest point of the curve is the mode, or value most likely to occur. The mode should not be confused with the mean, which is the average of all the iteration results.

You can think of the relative probability curve as a histogram of the results of each Monte-Carlo iteration. Note that the curve does not have a particular y-axis scale, and in fact REP adjusts it so that the modal value always corresponds to a y-axis value of 75. For presentation reasons it is highly smoothed.

The mathematical relationship between the two curves on the graph is that the cumulative curve is the integration of the relative probability curve.

Most calculations of reserves result in a skewed distribution, tending to log-normal shape. In this case, the mode is less than the P50, which is less than the mean. This begs the question: if one value is to be used, which one should it be? Most commentators prefer the mean and this seems to be generally used in the industry; however, some people do prefer to use the P50, especially in the case of proven reserves. The mode is never considered; but given the fact that all the studies that I know of show that companies overestimate their expected discoveries by a factor of about 50%, perhaps more consideration should be given to its use.

In general it is true to say that the difference between the mean and the P50 is due to the "romance" of the prospect. Most geologists like to include in their thinking the possibility, however remote, of a wonderful success. This very high risk, very high outcome case affects the mean much more than the P50. Perhaps this is why you will often find engineers and accountants using the P50 and explorationists using the mean. The problem for the engineers and accountants is that every now and again (and often to their chagrin), the romance case is realised (as an engineer, I know that there is nothing in the world more irritating than an explorationist who has been proved pessimistic).

One measure of how much romance is in the air is the probability level at the mean, shown on the table of results ("P-level at mean"). It will normally be around 35-45 %, If it is lower than this, you should be asking the question, 'if I only have a one-in-three (or less) chance of achieving the mean, is the mean the right figure to use?'

The risked mean (also known as the expectation) is the product of the unrisked mean and the geological chance of success. It is an unpopular figure with some people. Indeed, they say that anyone who uses this number should be locked up and if they additionally use the term expectation then the key should be thrown away! The present writer considers this to be harsh but fair. The reasons for the custodial sentence are, firstly, that risk (chance of success) and reward (discovered volume) are quite separate issues - almost orthogonal - and both must be considered. Only if you are rather stupid and cannot grasp two numbers at the same time should it be necessary to fudge things and multiply them together. Secondly, it a number without physical meaning (and especially without anything to do with expectation.) For example, you could have a prospect with a minimum reserve of 20bcf, an unrisked mean of 50bcf and a chance of success of 10%. The risked mean is therefore 5bcf, less than the minimum possible. This can really irk the purist.

The risked mean is used for prospect ranking. Other things being equal, it is best to drill up the prospect with the highest risked mean. The trouble is that other things are never equal. All ranking must always be done on a money basis. Even then using the highest risked NPV ignores vital human factors such as corporate strategy, political risk and personal bias.

However, so popular is risked mean that REP does calculate and display it.

If you are using economic criteria, two other key statistics are shown. The mean with economic cut-off is the mean value with the economic criteria only (i.e. without the geological risking). It is equal to the unrisked mean times the chance of economic success. It will, of course, be lower than the unrisked mean.

The mean of economically successful cases is the mean result of all economically (and therefore technically) successful cases. It is always higher than the unrisked mean.

The chance of economic success shown on the results sheet is the chance of economic success assuming technical success. The overall chance of success is the chance of technical success times the chance of economic success.

The results of consolidations are analogous but not the same as those of prospect/field calculations. This is because in consolidations there are no unrisked figures - not because they cannot be calculated but because they are almost meaningless. Instead of "unrisked", consolidations use the concept of "success". A success case in a consolidation is one where one or more of the fields or prospects being consolidated is successful. As with the unrisked case in prospect calculations, the success case in consolidations has a non-zero minimum - by definition, you have discovered something. However, it does not mean that every input prospect has been a discovery.

You can see this quite clearly if you consolidate two risky prospects of significantly different sizes. The relative probability curve will show two peaks - a "bimodal" distribution. The lower peak represents the cases where only the smaller prospect is successful, the higher peak the cases where only the larger is successful. Somewhere - probably lost - in the high end of the graph will be the rare cases that both are successful.