## Friday, February 12, 2010

### Random Numbers on the WBS? OMG!!

Yikes! who said random numbers belong on the WBS? Well, actually everyone who knows a lot about this business, and for that matter, a bunch of others who usually weigh in, say that single-point estimates are a poor choice, indeed in most situations they're a bad choice.

What's better? 'They' say: A three-point estimate--most optimistic, most pessimistic, and single trial most likely--is much 'better' for forming estimates and thereby budgets.

And, 'they' are right! Why so, why 'better'? A lot of reasons, but an obvious one is that there is simply more information, and so more information usually means a better outcome.

But, alas, a three point estimate is really three random numbers. A random number is really a number pair: < event value, event probability >, so what do you do when your work package managers hand you a bunch of charts that plot these number pairs on orthogonal axis', or just as bad, hand you a bunch of bivariate estimates?

You can't pass along a bunch of charts to your sponsor. You can't arithmetically add the number pairs--you can only convolve them. Egads! Convolution does not sound like program management--do we need a system engineer here?

You could outsource the whole thing to your project analysts and have them run a Monte Carlo simulation which does the convolution for you. However, that may be expensive and not timely, and certainly does not work off the back of an envelope.

The thing to do is what John Schyuler recommends in his excellent text on decision analysis, entitled "Risk and Decision Analysis in Projects", to wit: convert those three pesky random number estimates to a risk weighted average for each work package and then add them up!

That means doing the simple arithmetic to multiply the value times the value probability for each random number; then add all three for a risk weighted average.

There is actually rigorous proof for this idea that you can find in most applied handbooks on statistics, but it works well enough for project management without looking into the proof.

In the approximate world of ONE-SIGMA project management, 'risk weighted average' is what passes for expected value, the most powerful idea in statistics for the average project manager.

Of course, you may get asked about your confidence in the WBS budget as a weighted average. That takes a little more arithmetic, but that's all it is. However, that calculation is for another time.