## Friday, January 13, 2023

### The Four Maths of the PMO

Math may not be your favorite thing in the PMO, but hear me out.
There are four 'systems' of math you are probably using without thinking too much about them.
So, if that's so, why think about them now?
• Somebody may use the terminology around you, so informed is better than ignorant
• You may want to learn more about one or the other, so a look-up of terms is handy
Here's a quick read on the four:
1. Arithmetic and linear algebra: Arithmetic is the add-subtract-multiply-divide thing you have been doing all you life; linear algebra is just using arithmetic in a systematic and rules-based way -- in other words, formulas -- to find some values you might not have but need  (that conveniently lie along straight lines (thus, 'linear')

This is really useful stuff for adding up costs, figuring out schedules durations, and solving for resource unknowns, not to mention (gasp!) working forecast with earned value formulas

2. Exponentials: See my post on this topic. Exponentials form the world of non-linearity (no straight line). Exponentials are seen in the project office explaining  the non-linear "utility" of the project's value proposition, escalations in communications complexity, discounts for future risks, discounted cash flow (DCF) methods, and other useful stuff

3. Statistics: Statistics, and its close cousin 'probability', let us deal with uncertainty in project affairs. In this domain, we find 'random numbers': that is, numbers that are a bit uncertain because of incomplete knowledge or because of random effects (for which more knowledge doesn't help).

We can't do arithmetic directly on 'random numbers' because we don't have certain knowledge of what to add or subtract from one random effect to the next. Thus, simulations of statistical effects are the best way to handle such requirements. The 'Monte Carlo' simulation that is built-in to many scheduling apps and some cost and finance apps is an example of handling statistical effects on schedule numbers with simulation.

Keep this idea of 'no arithmetic with random numbers' in mind when people come to you with a risk matrix that purports to multiply random numbers for uncertainty and impact. No can do!

4. And then there's calculus! You say: 'I can skip this; we don't use calculus in our PMO.' Actually, you do! Calculus is the math of 'change'. And there are always change and changing effects in the PMO.

One powerful idea from calculus is that we can add up the individual effects of change, usually a lot small effects, and we call this process 'integration'. Even more handy, we can specify the integration limits to include only those effects in which we are interested.

Here's an example of something you probably know about: The so-called "S" curve of accumulating probability. This curve is very handy for assessing confidence limits in risk management. It is actually an integration result straight out of calculus. Small increments of probability from a "bell curve" are integrated to form the S-curve. In other words, if we 'integrate' the "bell curve", the result is the "S" curve!

Of course, the ideas work in reverse: Given the "S" curve, we can 'differentiate' it into the "bell curve" which then provides visualization of central clustering, and visualization of the outliers on the tails where events happen infrequently.

The secret to understanding derivatives is that they are always ratios: "something per something". If the "per something" part is time, then usually the ratio is a velocity or an acceleration; otherwise it's a density, as in 'parts per million'. The bell curve, being a derivative of cumulative probability, expresses a 'probability density'.

But maybe you are working in Agile methods and are concerned for 'velocity' and perhaps even the need for 'acceleration' of the evolving product base. Agile product velocity is the "first derivative" of a unchanging base; 'acceleration' is the first derivative of velocity and the second derivative of the original position.
Got it all?
Now you are the PMO math person!

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