Why All Forecasts are Sigmoid Curves

STL Partners’ forecast for Open Radio Access Network investments--whether one agrees with the projections or not--does illustrate one principle: adoption of successful new technologies or products tends to follow theS curve growth model.

The S curve  has proven to be among the most-significant analytical concepts I have encountered over the years. It describes product life cycles, suggests how business strategy changes depending on where on any single S curve a product happens to be, and has implications for innovation and start-up strategy as well. 

source: Semantic Scholar 

Some say S curves explain overall market development, customer adoption, product usage by individual customers, sales productivity, developer productivity and sometimes investor interest. It often is used to describe adoption rates of new services and technologies, including the notion of non-linear change rates and inflection points in the adoption of consumer products and technologies.

In mathematics, the S curve is a sigmoid function. It is the basis for the Gompertz function which can be used to predict new technology adoption and is related to the Bass Model.

 I’ve seen Gompertz used to describe the adoption of internet access, fiber to the home or mobile phone usage. It is often used in economic modeling and management consulting as well.

Source: STL Partners

The following  graph illustrates the normal S curve curve of consumer or business adoption of virtually any successful product, as well as the need to create the next generation of product before the legacy product reaches its peak and then begins its decline. 

The graph shows the maturation of older mobile generations (2G, 3G) in red, with adoption of 4G in blue. What one sees is the maturing products are the top of the S curve (maturation and decline) while 4G represents the lower part of the S curve, when a product is gaining traction. 

The curves show that 4G is created and then is commercialized before 3G reaches its peak, and then declines, as the new product displaces demand for the old. 

source: GSA

Another key principle is that, successive S curves are the pattern. A firm or an industry has to begin work on the next generation of products while existing products are still near peak levels. 

source: Strategic Thinker

It also can take decades before a successful innovation actually reaches commercialization. The next big thing will have first been talked about roughly 30 years ago, says technologist Greg Satell. IBM coined the term machine learning in 1959, for example.

The S curve describes the way new technologies are adopted. It is related to the product life cycle. Many times, reaping the full benefits of a major new technology can take 20 to 30 years. Alexander Fleming discovered penicillin in 1928, it didn’t arrive on the market until 1945, nearly 20 years later.

Electricity did not have a measurable impact on the economy until the early 1920s, 40 years after Edison’s plant, it can be argued.

It wasn’t until the late 1990’s, or about 30 years after 1968, that computers had a measurable effect on the US economy, many would note.

source: Wikipedia

The point is that the next big thing will turn out to be an idea first broached decades ago, even if it has not been possible to commercialize that idea. 

The even-bigger idea is that all firms and industries must work to create the next generation of products before the existing products reach saturation. That is why work already has begun on 6G, even as 5G is just being commercialized. Generally, the next-generation mobile network is introduced every decade. 

source: Innospective

There are other useful predictions one can make when using S curves. Suppliers in new markets often want to know “when” an innovation will “cross the chasm” and be adopted by the mass market. The S curve helps there as well. 

Innovations reach an adoption  inflection point at around 10 percent. For those of you familiar with the notion of “crossing the chasm,” the inflection point happens when “early adopters” drive the market. 

source 

It is worth noting that not every innovation succeeds. Perhaps most innovations and products aimed at consumers fail, in which case there is no S curve, only a decline curve. 

source: Thoughtworks 

The consumer product adoption curve and the S curve also are related to the point at which early adopters are buyers, but before the mass market adoption starts. 

source: Advisor Perspectives 

Also, keep in mind that S curves apply only to successful innovations. Most new products simply fail. In such cases there is no S curve.  The “bathtub curve” was developed to illustrate failure rates of equipment, but it applies to new product adoption as well. Only successful products make it to “userful life” (the ascending part of the S curve) and then “wearout” (the maturing top of the S curve before decline occurs). 

We Will Overestimate what Generative AI can Accomplish Near Term

For most people, it seems as though artificial intelligence has suddenly emerged as an idea and set of possibilities. Consider the explosion of interest in large language models or generative AI.

In truth, AI has been gestating for many many decades. And forms of AI already are used in consumer applicances such as smart speakers, recommendation engines and search functions.

What seems to be happening now is some inflection point in adoption. But the next thing to happen is that people will vastly overestimate the degree of change over the near term, as large language models get adopted, just as they overestimate what will happen longer term.

That is an old--but apt--story.

“Most people overestimate what they can achieve in a year and underestimate what they can achieve in ten years” is a quote whose provenance is unknown, though some attribute it to Standord computer scientist Roy Amara. Some people call it the “Gate’s Law.”

The principle is useful for technology market forecasters, as it seems to illustrate other theorems including the S curve of product adoption. The expectation for virtually all technology forecasts is that actual adoption tends to resemble an S curve, with slow adoption at first, then eventually rapid adoption by users and finally market saturation.   

That sigmoid curve describes product life cycles, suggests how business strategy changes depending on where on any single S curve a product happens to be, and has implications for innovation and start-up strategy as well. 

source: Semantic Scholar 

Some say S curves explain overall market development, customer adoption, product usage by individual customers, sales productivity, developer productivity and sometimes investor interest. It often is used to describe adoption rates of new services and technologies, including the notion of non-linear change rates and inflection points in the adoption of consumer products and technologies.

In mathematics, the S curve is a sigmoid function. It is the basis for the Gompertz function which can be used to predict new technology adoption and is related to the Bass Model.

Another key observation is that some products or technologies can take decades to reach mass adoption.

It also can take decades before a successful innovation actually reaches commercialization. The next big thing will have first been talked about roughly 30 years ago, says technologist Greg Satell. IBM coined the term machine learning in 1959, for example, and machine learning is only now in use. 

Many times, reaping the full benefits of a major new technology can take 20 to 30 years. Alexander Fleming discovered penicillin in 1928, it didn’t arrive on the market until 1945, nearly 20 years later.

Electricity did not have a measurable impact on the economy until the early 1920s, 40 years after Edison’s plant, it can be argued.

It wasn’t until the late 1990’s, or about 30 years after 1968, that computers had a measurable effect on the US economy, many would note.

source: Wikipedia

The S curve is related to the product life cycle, as well. 

Another key principle is that successive product S curves are the pattern. A firm or an industry has to begin work on the next generation of products while existing products are still near peak levels. 

source: Strategic Thinker

There are other useful predictions one can make when using S curves. Suppliers in new markets often want to know “when” an innovation will “cross the chasm” and be adopted by the mass market. The S curve helps there as well. 

Innovations reach an adoption inflection point at around 10 percent. For those of you familiar with the notion of “crossing the chasm,” the inflection point happens when “early adopters” drive the market. The chasm is crossed at perhaps 15 percent of persons, according to technology theorist Geoffrey Moore.

source 

For most consumer technology products, the chasm gets crossed at about 10 percent household adoption. Professor Geoffrey Moore does not use a household definition, but focuses on individuals. 

source: Medium

And that is why the saying “most people overestimate what they can achieve in a year and underestimate what they can achieve in ten years” is so relevant for technology products. Linear demand is not the pattern. 

One has to assume some form of exponential or non-linear growth. And we tend to underestimate the gestation time required for some innovations, such as machine learning or artificial intelligence. 

Other processes, such as computing power, bandwidth prices or end user bandwidth consumption, are more linear. But the impact of those linear functions also tends to be non-linear. 

Each deployed use case, capability or function creates a greater surface for additional innovations. Futurist Ray Kurzweil called this the law of accelerating returns. Rates of change are not linear because positive feedback loops exist.

source: Ray Kurzweil  

Each innovation leads to further innovations and the cumulative effect is exponential. 

Think about ecosystems and network effects. Each new applied innovation becomes a new participant in an ecosystem. And as the number of participants grows, so do the possible interconnections between the discrete nodes.  

source: Linked Stars Blog 

Think of that as analogous to the way people can use one particular innovation to create another adjacent innovation. When A exists, then B can be created. When A and B exist, then C and D and E and F are possible, as existing things become the basis for creating yet other new things. 

So we often find that progress is slower than we expect, at first. But later, change seems much faster. And that is because non-linear change is the norm for technology products.

5G Uptake Will be an S Curve

Even if the 5G networks could magically spring up fully-deployed, with no construction obstacles, there would still be a lag between availability and customer acceptance. The reason is that not all customers are early adopters 

Early on, innovators and early adopters drive take rates. For them, the value of better performance is enough to create demand, even in the absence of compelling new use cases or applications. 

source: Researchgate 

Novelty does not create demand for mainstream customers, who need a value proposition oriented around some practical value beyond bragging rights. Mainstream customers must see a solution to some existing problem.

In some cases, that problem might be “predictability of service charges” more than “speed” as such. “No overage charges” is a value people understand. In other cases the lure might be “no additional cost video streaming subscriptions.” In yet other cases the value might be the ability to “use all the features of my new phone.”

The point is that mainstream consumers need tangible benefits, and those benefits might not flow directly from “faster speed” claims. 

The concept of the S curve describes consumer adoption behavior,  product life cycles, suggests how business strategy changes depending on where on any single S curve a product happens to be, and has implications for innovation and start-up strategy as well. 

source: Semantic Scholar 

Some say S curves explain overall market development, customer adoption, product usage by individual customers, sales productivity, developer productivity and sometimes investor interest. 

It often is used to describe adoption rates of new services and technologies, including the notion of non-linear change rates and inflection points in the adoption of consumer products and technologies.

In mathematics, the S curve is a sigmoid function. It is the basis for the Gompertz function which can be used to predict new technology adoption and is related to the Bass Model.

I’ve seen Gompertz used to describe the adoption of internet access, fiber to the home or mobile phone usage. It is often used in economic modeling and management consulting as well. 

The S curve also fits and explains consumer adoption of new technologies.

Actually, AT&T Did Quite Well in Content and Video Subscription Businesses

Many will criticize telco failures to "innovate." Many will pan diversification efforts such as that made by AT&T into content ownership and entertainment video services. By one reckoning, AT&T actually did quite well.

Many will criticize telco failures to "innovate." Many will pan diversification efforts such as that made by AT&T into content ownership and entertainment video services. By one reckoning, AT&T actually did quite well.

It actually took only a handful of attempts before AT&T was able to emerge as a significant provider of video content, video subscriptions and internet access. In fact, it did not actually take many tries before AT&T and Verizon actually created roles for themselves in content and video. 

On June 24, 1998, AT&T acquired Tele-Communications Inc. for $48 billion, marking a reentry by AT&T into the local access business it had been barred from since 1984. 

Having spent about two years amassing a position in local access using resold local Bell Telephone Company lines, AT&T wanted a facilities-based approach, and believed it could transform the largely one-way cable TV lines into full telecom platforms. 

That move was but one among many made by large U.S. telcos since 1994 to diversify into cable TV, digital TV, satellite TV and fixed wireless, mostly with an eye to gaining share in broadband services of a few different types. 

By some accounts, TCI was at the time the second-largest U.S. cable TV provider by subscriber count, trailing only Time Warner. TCI had 33 million subscribers at the time of the AT&T acquisition. As I recall, TCI was the largest cable TV company by subscribers. 

For example, in 2004, six years after the AT&T deal, Time Warner Cable had just 10.6 million subscribers. In 2000, by some estimates, Time Warner had about 13 million subscribers. That undoubtedly is an enumeration of “product units” rather than “accounts.” Time Warner reached the 13 million account figure by about 2013, according to the NCTA. 

Since 1994, major telcos had been discussing--and making--acquisitions of cable TV assets. In 1992 TCI came close to selling itself to Bell Atlantic, a forerunner of Verizon. Cox Cable in 1994 discussed merging with Southwestern Bell, though the deal was not consummated. 

US West made its first cable TV acquisitions in 1994 as well. In 1995 several major U.S. telcos made acquisitions of fixed wireless companies, hoping to leverage that platform to enter the video entertainment business. Bell Atlantic Corp. and NYNEX Corp. invested $100 million in CAI Wireless Systems.

Pacific Telesis paid $175 million for Cross Country Wireless Cable in Riverside, Calif.; and another $160 to $175 million for MMDS channels owned by Transworld Holdings and Videotron in California and other locations. 

By 1996 the telcos backed away from the fixed wireless platforms. In fact, U.S. telcos have quite a history of making big splashy moves into alternative access platforms, video entertainment and other ventures, only to reverse course after only a few years. 

But AT&T in 1996 made a $137 million  investment in satellite TV provider DirecTV. 

Microsoft itself made an investment in Comcast in 1997, as firms in the access and software industries began to position for digital services including internet access, digital TV and voice services. In 1998 Microsoft co-founder Paul Allen acquired Charter Communications and Marcus Cable Partners. 

Those efforts, collectively, are well within the “one success in 10” rule of thumb, for any single firm, and close to it for the entire industry. More significantly, the amount of revenue generated by those efforts come well within the “one in 100” rules of innovative success for “blockbuster” impact. 

AT&T, remember, continues to own 70 percent to 80 percent of its former Time Warner content assets. It continues to benefit from the cash flow of DirecTV and its fixed network video services. It continues to drive cash flow from HBO Max.

And all that was achieved with far fewer than 10 attempts. By standard metrics of innovation, that clearly beats the odds.

What most will miss is the difficulty of making successful change in any organization, on a routine basis. As a rule of thumb, only about one in 10 efforts at change will succeed. Quite often, only about one in 100 successful innovations is truly consequential in terms of organization performance.

source: Organizing4Innovation 

That means we must tolerate a high rate of failure before we can hope for successful change. And we must fail quite a lot before we encounter a successful innovation with the power to change a company's or a whole industry's fortunes.

Of all the innovations connectivity providers have attempted--and been criticized for--how many have had industry-altering implications? Not many. Fixed network voice; mobile phones; internet access and possibly entertainment video subscriptions have been transformative.

Deregulation, privatization and competition have been historically transformative. But one might argue that was something that "happened to" the connectivity business, not necessarily an innovation of the industry itself.

Yes, we have seen many generations of business data networking services and business phone systems and services. But few have revenue magnitudes so great they change the fortunes of the industry or whole firms. In 150 years, only mobility and internet access have had clear industry-altering implications.

We all are familiar (even when we do not know it) with the sigmoid curve, otherwise know as the S curve, which describes the normal adoption curve for any successful product. We are less familiar with the idea that most innovations fail, whether that is new products, new technologies, new information technologies or business strategies. 

S curves apply only to successful innovations.

Most new products simply fail. In such cases there is no S curve.  The “bathtub curve” was developed to illustrate failure rates of equipment, but it applies to new product adoption as well. Only successful products make it to “userful life” (the ascending part of the S curve) and then “wearout” (the maturing top of the S curve before decline occurs). 

source: Reliability Analytics

Though nobody “likes” to fail, there is good reason for the advice one often hears to “speed up the rate of failure.” The advice is quite practical. 

Only about one in 10 innovations actually succeeds. Those of you who follow enterprise information technology projects will recognize the pattern: most efforts at IT change actually fail, in the sense of achieving their objectives. 

source: Organizing4Innovation 

“We tried that” often is the observation made when something new is proposed. What almost always is ignored is the high rate of failure for proposed innovations. About nine out of 10 innovations will probably fail. Most of us are not geared to handle that high rate of failure. 

Unwillingness to make mistakes almost ensures that an entity will fail in its efforts to grow, innovate or even survive. 

Those of you who follow startup success will recognize the pattern as well: of 10 funded companies only one will really be a wild success. Most startups do not survive. 

 

source: Techcrunch 

Connectivity providers are not uniquely free from the low success rate of most innovations. Innovation is hard. Most often efforts at innovation will fail. Even smaller efforts will fail nine times out of 10. An industry-altering innovation might happen only once in 100 attempts.

The more failure, the more the chances for eventual success. Many would consider telco initiatives in content and video subscriptions to have "failed." It is more accurate to call them an innovative success, given the relative handful of attempts to lead that business.

AT&T continues to own 70 percent of its former Time Warner content assets. It continues to benefit from the cash flow of DirecTV (about 71 percent ownership) and its fixed network video services. It continues to drive cash flow from HBO Max.

And all that was achieved with far fewer than 10 attempts. By standard metrics of innovation, that clearly beats the odds.