Sunday, February 24, 2019

It's a bell shape, unless it's not

Jurgen Appelo is, by his own description, "a Dutch guy" who is somewhat of a humorist, an illustrator, and a proponent of Agile. He also writes a lot about complexity, and the effects of complexity on systems and projects.

In his posting, "The Normal Fallacy", Appelo takes on both misconceptions and lazy thinking, and reinforces the danger of thinking everything has a 'regression to the mean'.

It's a bell, unless it's not
Appelo tells us to not have a knee jerk reaction towards the bell-shaped Normal distribution.  He's right on that one: the bell-shape distribution is not the end-all and be-all but it does serve as a useful surrogate for the probable patterns of complex systems.

Why?  Because many, if not most, natural phenomenon tend to have a "central tendency" or preferred state of value. In the absence of influence, there is a tendency toward the center. This really isn't lazy thinking; in fact, it's a useful default when there is a paucity of data.

But if no central tendency?
In both humorous and serious discussion he tells us that the Pareto concept is too important to be ignored. The Pareto distribution, which gives rise to the 80/20 rule, and its close cousin, the Exponential distribution, is the mathematical underpinning for understanding many project events for which there's no average with symmetrical boundaries--in other words, no central tendency.

His main example is a customer requirement. His assertion:
The assumption people make is that, when considering change requests or feature requests from customers, they can identify the “average” size of such requests, and calculate “standard” deviations to either side. It is an assumption (and mistake)...  Customer demand is, by nature, an non-linear thing. If you assume that customer demand has an average, based on a limited sample of earlier events, you will inevitably be surprised that some future requests are outside of your expected range.

Average is often not really an average
In an earlier posting, I went at this a different way, linking to a paper on the seven dangers in averages. Perhaps that's worth a re-read.

So far, so good.  BUT.....

What's next to happen?
A lot of stuff that is important to the project manager are not repetitive events that cluster around an average. The question becomes: what's the most likely "next event"? Three distributions that address the "what's next" question are these:

• The Pareto histogram [commonly used for evaluating low frequency-high impact events in the context of many other small impact events],
• The Exponential Distribution [commonly used for evaluating system device failure probabilities], and
• The Poisson Distribution, which Appelo doesn't mention, [commonly used for evaluating arrival rates, like arrival rate of new requirements]

Even so, many "next events" do cluster
But project managers are concerned with the collective effects of dozens, or hundreds of dozens of work packages, and a longer time frame, even if practicing in an Agile environment.  Regardless of the single event distribution of the next thing down the road, the collective performance will tend towards a symmetrically distributed central value.

For example, I've copied a picture from a statistics text I have to show how fast the central tendency begins.  Here is just the sum of two events with Exponential distributions [see bottom left above for the single event]:

Good enough
For project managers, central tendency is a 'good enough' working model  that simplifies a visualization of the project context.

The Normal curve is common surrogate for the collective performance.  Though a statistician will tell you it's rare that any practical project will have the conditions present for truly a Normal distribution, again: It's good enough to assume a bell shaped symmetric curve and press on.

Buy them at any online book retailer!