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## 6th Edition PMBOK® Guide: Process 11.4 Perform Quantitative Risk Analysis: Tools and Techniques (2)

In yesterday’s post, I discussed the “generic” tools and techniques associated with this process 11.3 Perform Quantitative Risk Analysis, that is, those that are also used in conjunction with a number of other planning processes:  expert judgment, data gathering, and interpersonal and team skills.

Today let’s talk abut the remaining tools and techniques which are specific to this process.

11.4.2  Perform Quantitative Risk Analysis:  Tools and Techniques

11.4.2.4  Representations of Uncertainty

When you are dealing with uncertainty in regards to estimates for duration, cost and resources, the model of how to deal with this is a probability distribution.   Let’s take two examples that should be familiar if you know about the three-point estimates used in estimating duration and/or cost estimates.

Take an example of estimating how long it takes for you to get to work.   If you are asked by your boss to give him or her an estimate of how long it takes you to get to work, you may give that person a single figure, a one-point estimate, say 30 minutes.   That’s the estimate you use if everything is going well with regards to traffic–no accidents, no road construction, no weather hazards, etc.

Now let’s say that your boss says you have to be at a start-up meeting at a certain time, and that your success on the job is critically depending on being there on time.   Will you leave your 30 minutes ahead of that meeting time?   If you are me, and you are being risk adverse, you will want to leave a little earlier.   How much earlier?

Here’s where the three-point estimate comes in.   The 30-minute estimate is actually just the most likely (M) estimate.   A pessimistic estimate (P) is based on what happens if a negative risk occurs, such as one of the things I mentioned above such as a traffic accident that slows traffic down.    These things happen infrequently, but if they do occur, it could mean a delay of at least 30 minutes, meaning a total of a 60-minute commute.   An optimistic estimate (O) is based on what happens if a positive risk occurs also known as an opportunity.   There may be less traffic than normal on a given day, perhaps because it is a federal holiday which most people get off but you don’t.   The only positive aspect of being one of the few who have to work on that day is that traffic is similar to weekend traffic, and you may find yourself zipping to work in only 20 minutes.

How do calculate the three-point estimate based on the most likely, pessimistic and optimistic estimates?   Well, here’s where the probability distribution comes in.

If you have a triangular distribution, you count the pessimistic, optimistic and most likely EQUALLY.   You take their average the normal way with three items that are of equal weight, namely (P + O + M)/3 = (60 + 20 + 30)/3 = 35 minutes.   But if you are using a beta or weighted average distribution, this gives 4 times as much weight to the most likely estimate.   Why?  Well, that’s why it’s called the “most likely”, because it is most likely to happen as compared to the scenarios behind the pessimistic and optimistic estimate.   In this case the weighted average is then (P + O + 4M)/6.   Why do you divide by 6 instead of 3?   Because it’s like there are six different terms, with four of them being the same one, the most likely estimate.   In this case, then, the weighted average becomes [60 + 20 + 4(30)]/6 = 33.3 minutes.   So you would give yourself an extra 3.3 minutes head start to get out the door rather than an extra 5 minutes in the case of the triangular or regular average.

Now there are other probability distribution such as the “normal” distribution or “bell curve” distribution that represent the normally occurring distribution of probabilities in naturally occurring phenomena like height in populations, etc.   Other types of probability distributions are listed on p. 432 of the 6th Edition PMBOK® Guide.

Another way for uncertainty to be represented in the case of individual project risks is something called expected monetary value or EMV.   Let’s say there is a 10% risk of something happening, but the impact if it does happen is that it will cost the project \$10,000.   How much money should you put aside for a risk response?   With EMV you simply take the probability of 10% and multiply it times the potential impact of \$10,000, and you get \$1,000 as the money that should be put aside.   This risk response is an example of a contingency reserve, or money that is put aside in case an individual project risk occurs that has been predicted beforehand in the risk register.   If you take the various probabilistic branches for all the individual project risks, you get something close to the simulation described in the next tool and technique called “data analysis.”

We’ll talk about that set of techniques in the next post.