Notes on the Normal Distribution

Pragmatism Slices and Sales

Progress through the technology adoption lifecycle happens in terms of seats and dollars. If you use alternate monetizations, rather than sell your product or service, drop the dollars consideration. Beyond those monetizations even if you sell your product or service, dollars are flaky in terms of adoption. But the x-axis is about population, aka seats.

Sales drive the rate of adoption in the sense that a sale moves the location of the product or service, the prospect’s organization(s), and the vendor’s organization(s) under the curve. By sales, I mean the entire funnel from SEO to the point where the sales rep throws the retained customer under the bus. But, I also mean initial sales, the point where prospects become customers. That sale moves from adoption from the left to right, from the early phases towards the late phases, from category birth to category death.

But, there are two kinds of sales: the initial sale, aka the hunter sale, and the upgrade sale, aka the farmer sale. What struck me this week was how the farmer sale does absolutely nothing in regards to progress through the various entities locations under the adoption curve. So let’s look at this progress.


People in a pragmatism slice reference each other. They do not reference people in other pragmatism slices.

In the figure, the hunter sales move the adoption front across the adoption lifecycle from left to right. The hunter sales rep made four sales. The farmer sales rep made four sales as well that generated revenues, but no movement across the lifecycle.


The size of the normal representing the addressable markets in the technology adoption lifecycle is fixed. It does not grow. A single company has a market allocation that tells us how much of that normal they own. With discontinuous innovations, that allocation to the market leader maxes out at 74%. Beyond that, antitrust laws kick in. Such a market leader would be a near-monopolist. Their market leadership will be the case until they exit the category, or face a Foster disruption. Intel was the market leader until NVIDIA brought a different technology to market. With continuous innovations, we are dealing with many players in a commodity market. The allocations are small. Market leaders can change every quarter.


In this figure, I started with a standard normal distribution (dark yellow) representing 100% of a category’s market. I represented the near monopolist’s market allocation of 74% as a normal distribution (light blue) inside of the larger normal. Then, I drew the circles (orange and blue) representing the curvature of the kurtoses of these distributions. The light blue distribution cannot get any larger. It is shown centered at the mean of the category’s normal. It could be situated anywhere under the category’s normal. Once a vendor has sold more than 50% of its addressable market, that vendor starts looking for ways to grow, ways to move the convergence of the vendor’s distribution as far to the right as possible. They try to find a way to lengthen the tail on the right. They run into trouble with that.

While a normal distribution represents the technology adoption lifecycle, the probability mass gets consumed as sales are made. The probability mass to the left has been consumed. So there is very little mass to allocate to the tail. In placing those curvature circles, I looked for the inflection points and made the circles tangent to the normals there. For the proposed tail, I drew its curvature circle. The thick black line from the mean to the top most inflection point doesn’t leave enough probability mass to allocate to the tail so the tails would be lower and the curvature circle would be larger. The thick red line from the mean to the bottom most inflection point leaves enough probability mass to allocate to the tail. It’s important that the curves represented by the black and red lines be smooth.

The points of convergence for the 74% normal, the 100% normal, and the long tail appear below the x-axis of the distribution. The mass between the convergences of the 100% normal and the long tail are outside the category’s normal distribution. The normal under the normal model used a kurtosis of zero. But, with the long tail, the kurtosis is no longer zero. That growth is coming from something other than the product or service of the vendor. And, the mass in the tail would not come from the normal inside the category’s normal. The normal was deformed when the mass was allocated towards the tail. But, again, that still does not account for the mass beyond the category normal. That mass beyond the category normal is black swan like and hints towards skew risk and kurtosis risk. Look for it in the data. These distributions just show a lifecycle of the category and vendor normals. The data should reflect the behaviors shown in the model. The pragmatism slices move as well. Taking a growth action that concatenates the tail can dramatically change your phase in the technology adoption lifecycle. Each phase change requires some, possibly massive, work to get the products and services to fit the phase they find themselves addressing.

Booms stack the populations in the technology adoption lifecycle. See Framing Post For Aug 12 Innochat: The Effects of Booms and Busts on Innovation for that discussion.

I drew my current version of Moore’s adoption lifecycle.

The Technology Adoption Lifecycle

Moore built his technology adoption lifecycle on top or Rodgers’ model of the diffusion of innovation. Rodgers identified the populations involved in technology adoption like the innovators, early adopters, early and late majorities, and laggards. Moore went further and teased out technical enthusiasts, and the phobics, Moore changed the early majority to vertical markets and the late majority to horizontal markets. Moore identified several structural components like the bowling alley, the chasm, and the tornado.

I’ve made my own modifications to Moore’s model. The figure is too abundant. Another incidence of my drawing to think, rather than to communicate.

TALC setup

The technology adoption lifecycle provides the basis for the figure. The technology adoption lifecycle is about the birth, life, and death of categories that arise from discontinuous innovation. This leaves aside the categories that can be created via management innovation discussed in an HBJ article over the last year. A category is competed for during the Tornado and birthed when market power selects the market leader. Immediately after the birth of a category, the competing companies consolidate, or exit. Their participation in the category ends. The category can live a long time, but eventually, the category dies. Its ghost disappears into the stack. The horse is still with us. Disruption is a means of killing a category, not about competing in the disrupted category. Disruption happens to adjacencies, not within the category sponsoring the disruptive discontinuous innovation.

The populations are labeled with red text. Most of the phase transitions are shown with red vertical lines. The transition to the early majority is shown with a black line, also labeled “Market Leader Selected.” The vertical labeled with red text consists of the early adopter (EA) and the next phase that Moore called the vertical market. Some technical enthusiasts would be included in the vertical as well, but are not shown here as such.

Notice that I’ve labeled the laggard phase device and the phobic phase cloud. The cloud is the ultimate task sublimation. The device phase is another task sublimation. These are not just form factors. They are simpler interfaces for the same carried use cases. The carrier use cases are different for every form factor. Moving from early majority to late majority phases also involved task sublimation, as described by Moore. Laggards need even simpler technology than consumers. Phobics don’t want to use computers at all. The cloud provides admin-free use. The cloud is about the disappearance of both the underlying technology in the carrier layer and the functionality in the carried layer. Notice that after the cloud the category disappears. There are no remaining prospects to sell.

The technical enthusiasts, as defined by Moore, was a small population at the beginning of the normal. But, there are technical enthusiasts in the Gladwell sense all the way across the lifecycle. They are a layer, highlighted in orange, not a vertical slice, or phase. I’ve shown both views of the technical enthusiasts. The IT horizontal people would show up as technical enthusiasts if the product or service was being sold into the IT horizontal. This distinction is made in my Software as Media Model. The technical enthusiasts are concerned with the carrier layer of the product or service.

Moore’s features are shown as brown rectangles. These features include the chasm, the tornado, and the bowling alley. Specific work, tactics, and strategies address the chasm, the tornado, and the bowling ally. These are labeled as pre-chasm, pre-tornado, and keeping the bowling alley full. They show up as blue rectangles. Another feature stems from de-adoption, the “Need (for a) New Category,” and appears as a blue rectangle. This latter feature happens, because nothing was done to create a new category before it was needed. Or, such an effort failed. The point of keeping the bowling alley full is to create new categories based on discontinuous innovation on an ongoing basis. I’ve seen a company do this. But, these days discontinuous innovation is very rare. Discontinuous innovations can, but not always, cause (Foster) disruptions. Christensen’s disruptions happen in the continuous innovation portion of the adoption lifecycle.

The lifecycle takes a discontinuous innovation to market and keeps the category on the market via continuous innovation. Plant the seed (discontinuous), harvest the yield (continuous). This division of the lifecycle is labeled in white text on a black rectangle towards the bottom of the figure. Discontinuous innovation generates economic wealth (inter-). Continuous innovation generates an accumulation of cash (intra-). A firm does not own the economic wealth it generates. that economic wealth is shared across firms. I am unaware of any accounting of such.

At the very top of the lifecycle, the early and late phases are annotated. The early phases constitute the growth phase of the startup. The late phases constitute the decline phase. The decline phase can be stretched out, as discussed in the previous section. When the IPO happens in the early phases, but not before the Tornado, the stock price sells at a premium. When the IPO happens in the late phases, the stock price does not include such a premium. The Facebook IPO bore this out. It’s typical these days, these days of continuous innovation, that no premium is involved.

Founders, at least in carrier business, with discontinuous innovation are engineers, not businessmen, so at some point, they have to hire them to put the biz orthodoxy in place. VCs these days require a team that is already orthodox. The hype before the Shake Shack IPO demonstrates that innovation has moved on from software. Orthodox businesses are now seen as innovative, but only in the business model, continuous innovation sense. Shark Tank and VCs don’t distinguish the technology startup from other startups. The innovation press confuses us as well. It used to be that the CFO and one other person had an MBA, now everyone has one. But, in an M&A, the buyer doesn’t want to spend a year integrating the business they just bought. The merger won’t succeed unless the buyer can launch their own tornado and bring in new customers in the numbers they need. The Orthodoxy needs to be in place at least a year before the IPO, or the stock price will underperform the IPO a year after the IPO.

From a statistical point of view, the process of finding a new technology involves doing Levy flights, aka a particular kind of random walk, until that new technology is found. It should not be related to what you are doing now, aka to your install base. You are building a brand new company for your brand new category. Google’s Alphabet does this. Your company would become a holding company. Managing the diversity inherent in the technology adoption lifecycle becomes the problem. “No, that company is in a different phase, so it can’t do what our earlier company does now.” Contact me to find out more.

After the Levy flights, we search for early adopters. Use Poisson games to look at that. The Poisson distributions tend to the normal. Those normals become higher dimensional normals. The standard normal has six sigma, the later normals in later phases of the lifecycle have more than six sigma. These divisions translate into geometries. The nascent stages of the lifecycle occur in a hyperbolic geometry where the distant is small from a Euclidean perspective generated by the inherent L2 geometry of linear algebra. Artists see the distant as small reality in perspective drawings. They call that foreshortening. We foreshorten our financial forecasts and small is bad. But, as the Poisson become a normal, those financial forecasts stop foreshortening. The idea we threw away becomes obviously invaluable after the founder builds a market, a technology, a product or service, a company, value chains,… The distributions change, and the geometries change. Once you move beyond six sigma, the geometry becomes spherical. In such geometry, there are many ways for followers with different strategies to win. We start with a very narrow way to win in the hyperbolic, arrive at the one way to win in the Euclidean, and find ourselves in the many ways to win in the Spherical. Or, damn, so many fast followers, geez.

Last but not least, we come to the Software as Media model. Media is comprised of carrier layers and carried content layers. The phases of the adoption lifecycle change layers when they change phases. The technical enthusiast is about the carrier layer; the early adopter, the content layer; the vertical, the content layer; the horizontal, the carrier layer; the device, both; and the cloud, carrier. At the point where you need another category, it could be either. But, these oscillations involve the market and the way the vendor does business. Each phase is vastly different. The past has nothing to do with the present. Yes, the practices were different, but they fit their market. They were not better or worse unless they did not fit their market.

Designers whining about the 80’s were not around then. They take today’s easiness for a given and think the past should have been done their way. The past taught. We learned. And, as we cross the technology adoption lifecycle, the Ito process that crossing, the memories are deep. We learned our way here. And, when we repeat the cycle, our organizations are not going to start over. They don’t have to if properly structured. Call me on that as well. But, usually they don’t start over from scratch, but should, because they forgot the prior phase, as they moved to the next.



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