Simulation, Modelling and Probability Management


Project Planning and Risk Assessment:
Simulations, Models, Realistic Estimates.

Eliminate the Flaw of Averages

Calculating uncertainty with averages and other single numbers results in systematic estimation errors. That is, on average, the average is wrong.

Stanford's Dr. Sam Savage called this the The Flaw of Averages. These errors cause projects to be late and over-budget, resources to be short of need, and risks to be underestimated.

Probability Management

The solution is Probability Management – a discipline focused on quantifying, communicating, and calculating uncertainty. It overcomes the Flaw of Averages. is a non-profit institution created to coordinate efforts to improve the way we compute uncertainty and risk, through research, education, best practices, and standards.

For risk-defying models and simulations that foil the flaw of averages, and give you control of your probability of success, all you have to do is call.

Quantify uncertainty and risk

"What will it cost?" "How many can we sell?" "How long will it take?"

The answer in each case isn't just one number; it's a whole bunch of numbers, each with it's own probability. When we reduce all those numbers to an average or percentile, we throw away a lot of information we're going to need.

For example, consider a project with two tasks, both with the same expected time to complete. "Expected time" is the estimated average time over hypothetically many repetitions of the project. That means each task has about a 50% probability of finishing on time or early. That's like flipping a coin; heads you're early, tails you're late.

Even if you're comfortable with 50%, you have a problem: The project isn't done until both tasks are done – that's like flipping two coins and getting two heads. The probability that both tasks will finish on time isn't 50%. The probability that both task1 and task2 finish on time is 0.5 x 0.5 or 25%. You just lost your comfort zone.

You need to give yourself more time to finish the project. How much more time? Insufficient data.

Using SIPmath, the computational aspect of Probability Management, we keep the numbers that the average is the average of. Instead of a single value, we have a vector of values, a SIP (Stochastic Information Packet) that makes the connection between values and their probabilities. Calculations with SIPs can do any operation that's legal for scalars and the result is other SIPs, so we never throw away information.

Calculating Uncertainty

Simulation, modeling and calculating with SIPmath is fairly simple if you have the right tools. I use Excel/VBA. It's on millions of PCs, and it has some powerful (if poorly documented) capabilities for calculating with vectors. My book on the subject, Calculating Uncertainty is available as a free PDF. You can also get a paperback edition at Amazon.

SDXL - code for manipulating SIPs

I have a library of open source code for working directly with SIPs at