# Why 21% = Monte Carlo simulation-like results

Using the SPERT-7 Rule, you can create a Statistical PERT estimation for a bell-shaped uncertainty and achieve surprisingly good results by choosing “Medium-high confidence” for your subjective opinion about how likely the most likely outcome really is.  “Medium-high confidence” corresponds to a 21% Ratio Scale Multiplier for the Statistical PERT standard deviation formula, which is:  (Maximum – Minimum) * Ratio Scale Multiplier.

Let’s choose three estimation examples.  One will be for a symmetrical estimation, one will be for an estimate skewed to the left, and the other will be skewed to the right.

Here are the 3-points we’ll use:

1. 5000, 8000, 11,000 (symmetrical)
2. 1000, 8000, 11,000 (left-skewed)
3. 5000, 8000, 25,000 (right-skewed)

Using the Statistical PERT template, the estimates with 85% confidence are, respectively:

1. 9,306
2. 9,510
3. 14,686

Using a Monte Carlo simulation of the same 3-point estimates and specifying the PERT distribution (in Palisade’s @Risk program, that’s the RiskPert function), the resulting estimates at the 85th percentile are, respectively:

1. 9,260, a decrease from the SPERT estimate of 0.50%
2. 9,310, a decrease from the SPERT estimate of 2.15%
3. 14,027, a decrease from the SPERT estimate of 4.70%

Using a symmetrical 3-point estimate led to very close results between SPERT and Monte Carlo simulation, which is rather (pleasantly) surprising because the 21% Ratio Scale Multiplier used by SPERT was just a number of convenience (it’s evenly divisible by seven).  Left-side skewing broadened the difference, but only by about 2%.  Right-side skewing created the biggest difference.  Why was that?

We’ll look into that in the next post.