Why 7% = Near Certainty

The SPERT-7 Rule says that to obtain a standard deviation for any bell-shaped uncertainty, find the range between maximum point-estimate and the minimum point-estimate, then multiply the range by 7%.  The product is a standard deviation to be used when the estimator is nearly certain that the most likely outcome will actually occur.

Why is that?  What’s so special about 7%?  Why not 5% or 8%?

In Statistical PERT, the ratio scale multiplier — for conditions where there is very high confidence in the most likely outcome — is found by distributing 100 hypothetical trials across only three possible outcomes (the minimum, most likely, and maximum estimates) by using a 1-98-1 split.

Think of a bell-shaped uncertainty with a three-point estimate.  In Excel, in cells A1 to A100, distribute 100 hypothetical trials of that uncertainty using only the values identified in your three points using a 1-98-1 split, where one cell contains the minimum point-estimate, one cell contains the maximum point-estimate, and the remaining 98 cells contain the most likely outcome.

Then, use STDEV.P to find the standard deviation for that data set (so, =STDEV.P(A1:A100).  To obtain the ratio scale multiplier, divide the standard deviation by the range between the maximum point-estimate and the minimum point-estimate.  The result will be somewhere pretty close to 7% (assuming your three-point estimate doesn’t show extraordinary skewing to the left or right of the mean).

Now, try changing to a different three-point estimate by changing the values in cells A1 to A100, but retain the 1-98-1 split showing very high confidence in the most likely outcome.  You’ll still get a ratio scale multiplier of about 7%.

If your three-points suggest a skewed normal curve, the ratio scale multiplier might be a little higher, like 8%, but for a normally-shaped normal curve, a 1-98-1 split of a three-point estimate will yield a SPERT ratio scale multiplier around 7%.  Hence, the start of the SPERT-7 rule.

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