SPERT on a scratchpad

Next week after the Labor Day holiday, I’ll return to regular posts on Statistical PERT and estimation in general.  I just returned from a short vacation in Washington DC, welcoming incoming graduate students to George Washington University’s MSPM program.  Fun times!

In wanting to show someone how Statistical PERT works and how relatively easy the concepts are behind it, I used just a pen and paper — not Excel! — to create probabilistic estimates using statistical principles, rules, and assumptions.

Suppose there’s a room full of project managers, and all of them have their PMP credential.  And I asked you, “About what percent of the room are project managers who are 55 years old and older?”  You can’t see the room.  All you can do is make some assumptions and use whatever expert knowledge you have.  (You left your laptop back in the hotel room.)

What information do you know?  Not much.  You don’t even know how many people are in the room!

But you know that PMPs have real-life work experience and perhaps many, in not most, have 4-year college degrees.  If someone graduated from college in four years and immediately began work as a full-time project manager, they might be able to attain their PMP credential by, say, the age of 25, right?  A 25-year-old PMP is possible, but highly unlikely in a room of profesional, PMP-credentialed, project managers.

How about the upper-end?  How old might be the oldest PMP credential-holder?  Age 60 is certainly possible, and I know people who work even after their normal retirement age, so how about 70 years old?  There might be a PMP older than 70, but in a room of project managers, let’s just say that a reasonable estimate of the oldest PMP credential-holder is 70 years old.

What might be the most likely age of a PMP credential-holder?  Most probably, it’s not going to be someone in their 20s.  Or 60s.  Though many more PMPs are in their 30s than in their 20s, my experience is that a PMP is more likely to be in their 40s than in their 30s.  That leaves PMPs who are most likely in their 40s and 50s.  My personal gut feel is that the most likely age of an actively-engaged PMP is probably in their 40s, so I’ll say that the person is most likely 45 years old.

We’ve got a 3-point estimate:  25, 45, 70.  That’s about all we need to use SPERT estimation!

Let’s calculate the mean (arithmetic average) using the PERT formula:

[Min + 4(Most Likely) + Max] / 6.

So:  [25 + 4(45) + 70] / 6 = [25 + 180 + 70] / 6 = 275 / 6 = about 46 years old, nearly the mode of 45 years old (which was my most likely estimate).

Let’s calculate the standard deviation using the SPERT-7 Rule and the SPERT standard deviation formula which is:

[Maximum – Minimum] * Ratio Scale Multiplier

The SPERT-7 Rule uses ratio scale percentages corresponding to subjective opinions about the most likely outcome, where 7% = Nearly Certain, 14% = High Confidence, 21% = Medium-high Confidence, 28% = Medium-low Confidence, 35% = Low Confidence, and 42% = Guesstimate.  And we know that a Monte Carlo simulation using the PERT distribution (a special form of the beta distribution) is equivalent to using the Medium-high Confidence ratio scale multiplier of 21%, so let’s use that.  Since I’m using mental math at this point, not even a scratch pad or Windows calculator, I’ll round it to 20%.

The SPERT standard deviation formula, then, is:  [70 – 25 * 20%] = 45 * 20% = 9 years.  I did that all in my head as I typed this out!

Now let’s use the well-known 68-95-99.7 Rule in statistics.  One standard deviation from the mean covers 68% of the area under the curve.  The PERT mean is 46 years.  Let’s add and subtract one standard deviation of 9 years from the mean; that creates a range between 38 years and 55 years.  The remaining 22% of the area is evenly split between the left-side and right-side tails, but we’re only interested in the right-side tail.  So, 11% of the area under the curve is to the right of 55 years.  That’s my answer!

In a room full of project managers, all of whom hold the PMP credential from PMI, about 11% of them will be age 55 or older, and 89% would be younger than 55.

The concepts behind Statistical PERT are easy enough you don’t even need Excel (but you get much better and robust results, naturally, when you do use Excel)!

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