Earlier in the week John Cook tweeted something about Coxeter circles, so I clicked the link and was surprised by the following figure. The relationships between the diameters or radii of the circles is the same as what one would expect from a factor analysis. The first factor is the steepest and longest. The next less steep and shorter than the first. Subsequently, each factor is less steep and shorter than the previous factor. The particular angles and lengths will differ, but the subsequent factor will always be less steep and shorter.

The circle labeled zero is your firm. The circle labeled one would be your category. If you are focused on managing your revenues, your monetization generating your revenues would determine your category. If you are focused on something other than revenues, then place yourself in a category relative to that. The circles labeled two or three, any number above one, would be macroeconomic considerations.

A factor analysis typically covers 80% of your variance with three factors. They would be labelled with negative numbers. The area of a given circle hint at how much variance that factor covers. The factors would, as circles get smaller, or in a line graph get flatter and shorter. The statistical studies of your variance beyond those three factors gets more expensive, so your budget would constrain the number of factors your effort could be managed with. The budget is both monetary and managerial focus driven. The independence of the variables and the complexity of the data fusions giving rise to each factor would impact managerial focus.

The Coxeter circles here represent two levels of macro economic factors, your category, your firm, and your product. For wider product portfolios there would be more circles with negative numbers. Imagining this in three dimensions, as collections of spheres would demonstrate some interesting relationships.

In a firm that stretches across the technology adoption lifecycle (TALC), the factors would migrate in an animation, live and die as Ito memories and oscillate between carrier and carried considerations. In such a firm, the population considerations could be a parallel factor analysis anchored around each population’s relevant product. Economies of scale do not allow expression of the TALC.

Factor analyses need not be firm centric. The economic return on a given set of factors, places a given firm in a given value chain. In a value chain, the larger, aka steeper and longer factors may be outside of your managerial focus. A small factor for your customer would be a very large factor for your company. The key reason to outsource is to preserve managerial focus. When you tell your supplier how to do business, you are not preserving managerial focus. I realize a product manager wouldn’t do this, but when it happens it enters into your matrixed product organization.

Ad serving might be your only monetization, so you need to get and keep eyeballs, and deal with the standardized ad serving infrastructure. Your factor analysis would have holes in it. Your factor analysis would have discontinuities in it. Fast followers would have similar factors, whole product factors, and supplier factors.

In the figure, two whole products are shown: one for web, and another for mobile. One fast follower is shown. A fast follower may compete with you on a single factor. All ad serving monetized businesses might use this supplier.

The arrowheads indicate convergences defining the world size of a given value chain. That is similar to convergences in probability distributions. A factor analysis looks like a power law distribution or a long tail.

Where you have discontinuities in your value chain, you will have to establish well defined interfaces, as well as deciding how soon you would want to follow changes to the definitions of those interfaces.