Please email me to report any problems, small or big, to john1@maxvalue.com. Thanks for reading the book!

**Decision Analysis for Petroleum
Exploration, 3.0 Edition**

Upcoming nomenclature changes:

Upon checking several authoritative sources (e.g., Wikipedia, Wolfram Research), it seems only half the world uses lower-case for distribution abbreviations (Wikipedia authors have used mostly but not always lower-case). With no clear choice, I've decided to start capitalizing (which I much prefer). Capitalized abbreviations are much more visible in text. So pdf's will become PDFs, cdf's will become CDFs, etc.

This seems to be the dominant notation, though not at all universal. See notes (1 and 2) for 2.016, next, for other notation changes I'll be making in future editions.

**3.0.6 version released Mar 2015**

2.016 Probability Mass Function

The cumulative probability mass function figure is the conventional <= form and was mislabeled as <.

Wikipedia has a disambiguation page saying that "cumulative density function" is self-contradictory. https://en.wikipedia.org/wiki/Cumulative_density_function

I'm not sure that I agree. Since perhaps high school, I've used "CDF" where the "D" stood for "density." Either the meaning of CDF changed at some point or I've always had it wrong.

After checking several authorities, I have decided to go with the flow. Here are the forthcoming changes:

1. The present and widely-accepted meaning of CDF is *cumulative distribution
function*. This applies to both continuous, discrete, and mixed-type
distributions.

2. Similarly, I have been using "rcdf" to represent *reverse cumulative
density function*. Some prominent software packages (still) use
*reverse* for labeling frequency distributions. However, especially with
density functions, the more-accepted term appears to be *complementary cumulative
distribution function* (CCDF). I'll be using that and, similarly,
CCFD to represent *complementary cumulative
frequency distribution*.

2.316 Beta Distribution

Apparently, this kernel form is more-popular (with, e.g., @RISK, Crystal Ball):

And the normalizing factor denominator is:

The distribution now has these simple properties (Thanks to Palisade Corp. for the excellent @RISK documentation):

6.320. Typical Value of Information Problem (p. 441; the error is on p. 445):

In the paragraph above the last tree, "EMV is $60 million (80-20) higher with the Do Pilot Alternative." should read "EMV is $57 million (77-20) higher with the Do Pilot Alternative."

The table, below, details the VII calculation.

**3.0.5 version released December 2014**

2.017. Frequency distribution

The Retrieval Code for the corrected Excel-produced frequency distribution
chart is **uqueqk**

5.214. Sensitivity Chart

The 100% W.I. line starts at DHC (~–$40 million) at Ps = 0 and is the Discovery Value ($175 million) at Ps = 1.

Index entry "ME2"

These are supposed to be "Excel" (the dummy name was used in a
search-and-replace operation and not restored).

**3.0.4 version released August 2014.**

2.060. Correlation Coefficient

All three equations for σ_{xy}, σ_{xx}, and σ_{yy} : The summation
terms (Σ's) should all be preceded by 1/n.

**3.0.2 version released April 2014.**

2.231. Bayes by Probability Tree

In the subsection, "Conditional probabilities on the tree" subsection. The
first three joint probabilities at the top portion should be switched with the
bottom three:

As examples, P("DHI" | HC) = .50 and P("DHI" | no HC) = .10.

2.701. The reader can ignore the obsolete references to Table
3.1 and Chapter 6 that can be ignored. An expanded discussion of the same
example (except monetary outcomes were multiplied by 100) is available with
Retrieval Code **vrza**.

2.720. Again there is a reference to Table 3.1 and to original chapter numbers. Some of the properties of EV are discussed in 2.130 Algebraic Properties of EV."

2.731. Assessment Challenges. This is mostly about subjective assessments and biases. Please see 2.354 Subjective vs. Objective Probabilities and 2.730 Cognitive and Motivational Biases.

2.733. Risking Petroleum Exploration. This section has been dropped. For judgments see 2.354 Subjective vs. Objective Probabilities and 2.730 Cognitive and Motivational Biases. We have seen companies use multi-criteria scoring methods; we advise that rough economic evaluations be attempted instead.

2.735. Resource Distributions. There are only Figures 3 and 4 in this topic.

**2.1 Edition and Earlier**

*Decision
Analysis for Petroleum Exploration, Second Edition *and
Earlier

Special thanks to Larry Killion, PE, J.D., BHP Billiton Petroleum, who noticed and reported quite a few typographical errors.

*Some of the recent and more-important
revisions are listed immediately below:*

Feb 4, 2013. Minor
calculation errors in table 2.1 (2nd edition, 2009 printing and
earlier)

June6, 2008. Value of information, several typos, pages 520-522
(2nd edition, 2007 printing and earlier)

June6, 2008. Exponential decline formula error, page 467 (2nd
edition, 2007 printing and earlier)

June6, 2008. Combined EV formula error, page 77 (2nd edition,
2007 printing and earlier)

June6, 2008. References to Appendix A, page 29 et al. (2nd
edition, 2007 printing and earlier)

Mar. 18, 2007. Frequency histogram figure 6.12, page 256
(printings prior to 2007)

Sep. 28,
2006. (Update) Rethinking the PV Discount Rate and Decision Policy, pages 25
and 568.

Dec. 14, 2005. Revised 3-event Addition
Rule formula, page 232.

Nov. 16, 2005. Revised
Bayes' Theorem formula 6.16, page 318.

The text box in the left margin truncates the last word and should read: "Petroleum exploration is a classic case of decision-making under uncertainty."

(Somehow, the computer didn't print the figure.)

Here is link to download an MS Word file for the page: dapepage16.doc

Right-click on the link for some download options.

**Total New Revenues:****Prospect A: $485,500 should be $485,450.****Prospect B: $589,000 should be $589,282.**

The "Appendix A" references direct the 1st Edition reader to present value tables. We now have Excel and financial calculators, so the appendix was dropped in the 2nd Edition.

I have long maintained that *EMV* of a project, properly
evaluated, provided a measure of the value added to the corporation. In prior
efforts to model project and company value from the shareholder's perspective,
a persistent problem has been the inconsistency with the shareholder's
** time value of money** and the typical capitalization rates inferred
from stock prices (papers HEES3 and HEES5). A fundamental premise in the decision
analysis approach is that the PV discount rate should represent only time value
of money, and that risking should be done with probabilities.

In developing an example for the latest in a series of papers
(HEES6), I was working to reconcile *EMV*
per share versus share price. Using Value Line Investment Survey data for nine
oil and gas producers, I was finding that share price was typically about half
of the PV per share of forecast ** free cash flow**. I used a
multiplicative factor to represent an additional

My current (as of Sep. 2006) thinking is:

*EMV*_of a project or the company should be based upon modeling the project's contribution to the company's free cash flow.*EMV*_of a project, properly evaluated, measures incremental*EMV*of the company.*EMV*_of the company (calculated from*free cash flow*) ´**MVD**factor = market capitalization of the company.**Shareholder value**added by a project equals the project*EMV*times the**MVD**factor.- Replacing
*EMV*with**certainty equivalent**(*CE*, page 204) will be somewhat better. This will incorporate investor's risk aversion as to the outcome levels. Use the exponential utility function and scale-up the typical investor's risk tolerance coefficient to the company level. Normally, this will be a minor adjustment. - The "optimizer's curse" bias (see inset) needs to be estimated and adjusted-out.

In my opinion, the appropriate ** free cash flow**
consists of the cash amounts that can be

Yet another detail affects our use
of the EMV decision rule: The "optimizer's curse." Tim Nieman
brought this to my attention recently, and I've referenced the source
paper, summarized the concept, and prepared some demonstration
calculations into Tip 113 (which links to a
PDF file). Investment candidates with slightly-positive EMVs
should not be approved. Forecasts of a project's value-added will
probably be too high. Even if our evaluations are unbiased, random
errors will introduce an optimistic bias when we select the better
projects. Bayesian calculations are needed to adjust-out this
bias. |

If you have any comments or suggestions as to a better approach, please contact me:

I hope to wrap-up this topic in yet one more paper or article. It will be mainly about the optimizer's curse and reversing this bias in a consistent approach to capital investment decisions and portfolio optimization.

Near the bottom,

"Finally, the gain per year in excess of making an earnings rate of is computed as ... " should read

"Finally, the gain per year in excess of making an earnings rate of 10% is computed as ... "

The last paragraph, "Table 3.6 shows the ratio calculations." Because the table wasn't numbered in the 2nd edition, this should read

The table on page 104 shows the ratio calculations."

About the middle of the page, "Equation 5.1 states ..." should read "The equation above states ..."

"[such as Figure 5.1 (c)]" should be "[such as Figure 5.5 (c)]".

The second paragraph ends with "probability of a discovery is 1/10 or 0.10." and should instead read "probability of a discovery is 1/11 or 0.0909."

**Page 232, P(A+B+C)
formula **(prior to the
2007 printing)**.**

The formula is missing the P(C) term and should read:

P(A+B+C) = P(A) +P(B) +P(C) -P(AB) -P(AC) -P(BC) +P(ABC)

**Page 256, ** **Frequency Histogram: Wrong figure printed** (2nd edition, 2007 printing and earlier):

Table 6.6 has a typo in the middle row. The frequency of the wells with thicknesses 110-150 should be 5, not 6.

Figures 6.12 and 6.13 are the same. Figure 6.12 (update version below) is supposed to have the y-axis in 'Number of wells having thickness values in each range.' That is, the y-axis should be units that are number of 'counts' in each histogram bin.

Most every reader would recognize that "The are of the triangle is (base)(height) ..." should be "The area of the triangle is (base)(height)/2 ... " about 2/3 down the page

The last column header should read: *p _{i}*
(

**Page 298, Figure 6.25. Log probability graph
**(prior to the 2005
printing)**.**

The data are permeabilities (in millidarcies), not porosities, on the y-axis.

The formula in the book is missing the P(E_{i}) term
in the numerator of the center form. It also had a B term in the denominator
which should be A. Sorry about that. How embarrassing!

I also added the simpler, equivalent form at the right. P(A • E) is the same as the numerator, center. P(A) is the same as the denominator, center. This is much easier to remember, isn't it? If you have a joint probability table, conditional probabilities are always the ratio of a joint probability (inside the table) divided by a marginal probability (at the margin of the table). This is the Bayes' rule method that use in classes.

Page 467, (6.) formula for recoverable reserves per well (2nd edition, 2007
printing and earlier)

The right-hand side is missing the * a* denominator.
The formula should read:

About the middle of the page is a reference to a 5-column table method for solving Bayes' theorem. Table 6.17 was in the first edition and deleted from the second edition. The method is shown in the tables on page 323 and 521.

In the last paragraph,

"That is, the
column 3 values we need are P(B | E_{1})and P(B | E_{1})." should read

"That is, the
column 3 values we need are P(B | E_{1})and P(B | E_{2}).

**Page 521, Table has truncated labels**

The lower-right annotations should be:

← P(E_{1} | B)
and

← P(E_{2} | B)

**Page 522, Notation typo**

P(E_{1}) = 0.3 should
read

P(E_{2}) = 0.3

Perhaps you figured out the different symbols, where I forgot to label the symbols:

Hollow squares represent investments approved, subject to
a budget constraint.

Hollow squares plus solid circles represent acceptable projects (better
than the rightmost dotted contour, which represents the boundary between
acceptable and unacceptable projects).

Hollow circles represent unacceptable projects.

On page 565, the third paragraph, "Figure 11" should be "Figure 11.5."

Please email me to report any problems, small or big, at . Thanks for reading the book!

Back to Decision Analysis for Petroleum Exploration

revised 16-Sep-2015