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.

Amara's Law and Generative AI Outcomes: Less than You Expect Now; More than You Anticpate Later

Generative artificial intelligence is as likely to show the impact of Amara's Law as any other new technology, which is to say that initial outcomes will be less than we expect, while long-term impact will be greater than we anticipate.

Amara’s Law suggests that we tend to overestimate the effect of a technology in the short run and underestimate the effect in the long run.

Source

Amara’s Law seemingly is the thinking behind the Gartner Hype Cycle, for example, which suggests that initial enthusiasm wants when outcomes do not appear, leading to disillusionment and then a gradual appearance of relevant outcomes later. 

lots of other "rules" about technology adoption also testify to the asymmetrical and non-linear outcomes from new technology.  

“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 and some people call it “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. So is Amara’s Law.