Steve posted a comment on a previous post that spurred me to put on my physics and systems engineer hat for a moment.

The power law notion presented in the previous post by Andrew Filev is useful in many domains.

The Power Law is applicable IF, one quantity is dependent on another raised to a "power." What Andrew did was to assume this is the case then build an example. In the statistics world this is called a Post-Hoc argument. It goes like this, "Let's assume there is a power law relation between the number of small (no defined unit for small) and large (no defined unit of large) and possibly mega (again no defined unit) then the "power law could be tested - not assumed post-hoc.

Here in the space and defense business a "notional" concept is used all the time. But the little joke is "I see you're making a notional description of the problem at hand, nice power point presentation, where's the real numbers?" The classic is the Power Point pictures of flying to the moon, then to mars in the 500 page backgrounder called Constellation, were one of the programs we work derives the Orion manned vehicle avionics, which will go to the Space Station in 2014 (maybe), From there it's only a 1,000 times scaling to get to the moon and only a ½ million times scaling to get to Mars. No problem, we got a nice PPT picture of how to do it.

**Now to the subject long tails in task durations **

Steve asked about long tails for task durations. Great question.

The use of Mote Carlo simulations is mandated in our domain (DID 81650 is the source document). The tools we use (Risk+ and @Risk For Project) provide probability distributions that can be tuned for the specific task modeling. There is a principle in this practice that say "any longer than 35% or so to the right requires management intervention, don't use that in your model."The triangle distribution is usually the starting point. The boundaries of the Triangle in Risk+ are the 0 and 100 end points, in @Risk they are the 10% and 90% end points. This provides the ability to describe an asymmetric shape for the task durations.

But, and this is critical, the "long tails" don't exist in the planning process. Independent of their possible existence. This is the role of the Integrated Master Plan - to reduce the probability that there are "unknowns," in the plan. The real long tails - the unknown unknowns have been addressed in previous iteration of the program - during Milestone A and Milestone B. The work of system development - Milestone C - is working toward the low rate initial production.

The second rule - in our domain - is you plan and mange at the Work Package level, not the task level. Task management is the accountability of the Control Account Manager, or her designated Work Package Manager. Work Packages con only cross one accounting period. These means they are limited to 60 calendar days. Like Vegas, what happens inside the WP says inside the WP. It's the measure of physical percent complete we're after.

The reason for this is the WP is on baseline and if the tasks need to be rearranged for what ever reason - good or bad - we don't want to impact the baseline - 'cause there's too much paper work and we're essentially lazy.

**Power Laws Abound, But Make No Assumptions Without a Test**

Power Laws describe relationships that are "scale independent." Physics is one place to start. Having grown up in the particle physics world, power laws are used in the Standard Model of particles. As well a REALLY good power law in classical physics (thermodynamics) is the cooking time of a turkey. It is a power law related to the surface area of the bird.

There are Power Laws in Economics, in biology related to ecological complexity, power laws everywhere.

So in the end- yes power laws are real IIF (if and only if) there is a exponential relation between one variable and another. Assuming there is first without a basis for that assumption and then making an argument (in the mathematical sense) about something is simply bad math.

The common approach in some domains - like this example - is to use a notional graph - Kent Beck did this - to make a point. But the point may not actually have a factual basis. It's a notional point. An interesting dinner conversation piece. But trying to make managerial decision from notional graphs is real sporty business where I work.

Your mileage may vary