I see S curves everywhere. They tell me where I should live, work, invest my time, my money, my efforts. I hope this article will help you see them too.
S-curve is basically a cumulative curve of the bell curve. So , like in marketing or innovation, first (Bell curve) we have innovators, then early adopters, then early majority - inflection point) , then late majority and laggards. In cumulative terms one gets S-curve. Another interesting story is time of transition from one S-curve to another . Like transition from vacuum lamps to transistors , etc. Or ICE to EV vehicles.
I tend to use the 10/80/10 rule. Around 10% of the population are risk takers and thrive on change, the innovators and early adopters are included in this group. The other 10% are the conservative, risk averse laggards, leaving the 80% to be swayed either way.
I think it is a social evolutionary phenomenon. Taking risks can get you killed, but still leave 90% of the population safe. It can also provide fantastic new discoveries or save you when the world changes rapidly and your species needs to adapt to survive.
Disclosure: I am one of the laggard 10% by nature, though I have learned to work around my naturally conservative instincts when I need to. I may try out an iphone one day.
Well, you clearly aren't a laggard with regards to Uncharted Territories!
What you say is true. If we pay attention to tech adoption curves, it's more like 10-60-30 or something like that, but your overarching point is still valid
The percentages are only rough estimates and vary according to the specific situation as you say. Adoption S curves do of course have relevance to the meta-conversation, as do the skills required to work around our natural instincts. I will add some thoughts on that thread once I've clarified them a bit.
Further disclosure: I have owned an android smartphone for 2 years now and can no longer imagine life without one.
I never though of it as a bell curve, great point. It makes me think - for products that don’t have S-curve adoption, does that say something about the distribution of the population? For example, ferraris - there wasn’t really an adoption S-curve. marginal costs are high, Supply is artificially constrained, and demand is inversely correlated to ubiquity (exclusivity) - no s curve. Another way to view that is that you’re only really ever getting early adopters part of the distribution - that first bump. So no exponential growth because you can’t ever tap that middle section of the population.
1. Companies' products ≠ entire industries. Many companies never reach product-market fit for example. Or grow very very slowly. Or have shocks that make them not look like S-curves. So they might follow S curves, but they're so noisy that they don't look like it.
2. As Pete says, some industries avoid S curves by design. Luxury is one of them. The very definition of luxury requires exclusivity. You can't have exclusivity if you saturate a market.
A long time ago - early to mid-50s, I think - Prof. Jay Forrester at MIT came up with the "bullwhip" or "whiplash" effect (later termed as the Forrester effect). This referred to very small perturbations (say, 2%) in customer purchases at checkout of specific products that cycled back through the entire supply chain in ever increasing amounts. What he evidenced was the increasing amplitude of demand-generated effects on supply all the way back through upstream vendors.
He theorized that the initial small dip or increase in sales of a particular item (itself possibly random) was subsequently misinterpreted by people in every preceding stage: first by the shelf replenishing clerk reporting to the store inventory head, who then inflated it some more while placing orders for the store at the local warehouse, that was then again inflated to the regional warehouse... And so on until it reached the manufacturer. The ripple effects took time and when the manufacturer finally increased production or invested in higher capacity, there was over-supply and unsold goods. All because the original blip at the checkout was just that: an inconsequential blip.
Of course, today's supply chain systems are architected for just-in-time using real time data. But the principles of human behaviours remain the same. And, for the purposes of this discussion, if one were to look backwards at the whiplash effect curve and smooth out the waveform, they do resemble the S curve - in reverse, or as mirror image.
You remind me of the class where I was taught the effect. They put us students in lines of 5, with each of us a step in the production process. we could only look at what we had and talk with those immediately on our sides. We communicated our needs for a product in rounds. After 6 or 7 rounds, the source supplier was in such oversupply that he went bankrupt.
Thank you, Tomas. It may be that the S Curve is probably as prevalent in nature as the Fibonacci series is. You can, for example, see the S curve in the Gartner Hype Cycle, the technology diffusion curve (the left half of the Bell Curve that really matters), fashion retail, incidence and spread of rumours, etc etc. In short, probably has to do with human behaviours.
I enjoy Tomas' articles but, as an Indian, wish to point to an error in the above article on S curves. He refers to a Chinese emperor in the context of a grain of rice in the first square on a chessboard that doubles with every subsequent square. Sorry - but that's not Chinese, it's an ancient Indian story that goes back a couple millenia at least. Mind you, Chess was created in India - it was referred to as "chaturanga", hence the word "chess" in English. The Chinese creation was Go, not chess and the story is intrinsically Indian - every Indian schoolboy knows this.
Kahneman's and Tversky's Prospect Theory curve has the S shape. They looked at it from the zero point to the right and to the left, but you can also consider how gains change the perception of value going from the bottom left corner towards the upper right corner.
It does sound like a completely different type of S curve, no? Nothing growing, no saturation, and I wonder how it behaves in the extremes (does it have asymptotes?)
You are right: the Prospect Theory representation is a different type of S curve. Your examples of S curves are tangible, they are rooted either in physical processes or observable economic behaviors. By contrast, the Prospect Theory curve represents perceptions of losses and gains. I was wrong in suggesting that you can look at the gains from the bottom left to the upper right. The perceptions don't rise along the S curve, they are rooted in the zero point ("Reference Point").
The question of asymptotes is interesting. In the bottom left end we have risk seeking in losses, where losses accumulate but the perception of risk does not increase. The end state is the demise of the actor who took took too much risk. In the upper right corner, the asymptote is the level of value that does not change with increase in the gains. For example, if your assets are $10,000 your subjective value of $1 million and $10 million is the same.
Your S Curves can be stacked. The Prospect Theory curve moves as your Reference Point changes. If your assets are $1 million your subjective value flattens after, say, $100 million.
The steep part of the Prospect Theory curve on the losses side is about 2.5 steeper than the same-magnitude gains on the gains side. It's a linear piece calculated in psychological experiments where people were asked about gambles they would accept. The rest of the curve is more notional than mathematical.
While my contribution to your topic ended up being irrelevant it was fun thinking about it.
Hahaha not at all! I love it. It might not have been pertinent, but it's certainly fascinating.
In fact I'd love to read something in depth about it. Thinking Fast & Slow is one of my favorite books, but I don't feel like I've ever read something that details the ins and outs, the ramifications of prospect theory. Wikipedia is too shallow and boring. That would be a welcome article!
"Thinking, Fast and Slow" elaborates on the Prospect Theory in Appendix B. I spent some time trying to understand it when I volunteered to give an introductory talk on Behavioral Economics to a diverse group of non-experts. As they say, if you want to learn a topic teach it.
On the fifth day of Christmas my truelove gave to me five gold rings
In 1970 those gold rings would have cost around $30. Today they would cost around $1600.
That price would seem shocking to someone in 1970, but today we think the price sounds about right. This is because of Gradualicity*, also known as the boiling frog effect. When things change very gradually, the human brain accepts each small step and that becomes the new normal. It is only by taking a step back and looking at the big picture that we can appreciate the true magnitude of the change over time and where we are on the curve.
The third and fourth days of Christmas were about balance and attention. It’s hard to get things back into balance if we haven’t even noticed that they are out of balance, and it is hard to notice that things are becoming unbalanced if it happens gradually.
*If people are allowed to use “normalcy” I think I should be allowed gradualicity.
I am modelling national vaccine rollout. I have a view that site availability and nurses per site will both be log decays (also for hesitancy). But now I wonder if they are not closer to reverse S curves. What would you think?
I'm probably not the best to ask. I've avoided doing mathematical modeling during the pandemic, as it's so easy to go wrong.
Personally, I think in many cases a mathematical model can be misleading. Unless you do know the underlying force is mathematical (eg, R is indeed mathematical), I'd be wary. I just take ranges based on what the curve is looking like, and what similar curves have done in other places or in the past.
Eg what happened with hesitancy in Israel? What happened in the communities of US states where the rollout was fastest?
S-curve is basically a cumulative curve of the bell curve. So , like in marketing or innovation, first (Bell curve) we have innovators, then early adopters, then early majority - inflection point) , then late majority and laggards. In cumulative terms one gets S-curve. Another interesting story is time of transition from one S-curve to another . Like transition from vacuum lamps to transistors , etc. Or ICE to EV vehicles.
That's right!
I tend to use the 10/80/10 rule. Around 10% of the population are risk takers and thrive on change, the innovators and early adopters are included in this group. The other 10% are the conservative, risk averse laggards, leaving the 80% to be swayed either way.
I think it is a social evolutionary phenomenon. Taking risks can get you killed, but still leave 90% of the population safe. It can also provide fantastic new discoveries or save you when the world changes rapidly and your species needs to adapt to survive.
Disclosure: I am one of the laggard 10% by nature, though I have learned to work around my naturally conservative instincts when I need to. I may try out an iphone one day.
Well, you clearly aren't a laggard with regards to Uncharted Territories!
What you say is true. If we pay attention to tech adoption curves, it's more like 10-60-30 or something like that, but your overarching point is still valid
The percentages are only rough estimates and vary according to the specific situation as you say. Adoption S curves do of course have relevance to the meta-conversation, as do the skills required to work around our natural instincts. I will add some thoughts on that thread once I've clarified them a bit.
Further disclosure: I have owned an android smartphone for 2 years now and can no longer imagine life without one.
I never though of it as a bell curve, great point. It makes me think - for products that don’t have S-curve adoption, does that say something about the distribution of the population? For example, ferraris - there wasn’t really an adoption S-curve. marginal costs are high, Supply is artificially constrained, and demand is inversely correlated to ubiquity (exclusivity) - no s curve. Another way to view that is that you’re only really ever getting early adopters part of the distribution - that first bump. So no exponential growth because you can’t ever tap that middle section of the population.
Interesting thoughts. A couple of reactions:
1. Companies' products ≠ entire industries. Many companies never reach product-market fit for example. Or grow very very slowly. Or have shocks that make them not look like S-curves. So they might follow S curves, but they're so noisy that they don't look like it.
2. As Pete says, some industries avoid S curves by design. Luxury is one of them. The very definition of luxury requires exclusivity. You can't have exclusivity if you saturate a market.
Thanks Tomas, good stuff. This was another great article - I really like your visualizations.
Ferraris Supply is designed (to my knowledge) to be just marginally below the Demand curve. So it's NOT designed for general (constraint-free) adoption and Bell curve does not apply. You are right. A decent treatment of S-curves in Technology adoption here: https://steemit.com/bitcoin/@cryptokate/bitcoin-goes-mainstream-s-curve-of-technological-adoption .
Thanks!!
A long time ago - early to mid-50s, I think - Prof. Jay Forrester at MIT came up with the "bullwhip" or "whiplash" effect (later termed as the Forrester effect). This referred to very small perturbations (say, 2%) in customer purchases at checkout of specific products that cycled back through the entire supply chain in ever increasing amounts. What he evidenced was the increasing amplitude of demand-generated effects on supply all the way back through upstream vendors.
He theorized that the initial small dip or increase in sales of a particular item (itself possibly random) was subsequently misinterpreted by people in every preceding stage: first by the shelf replenishing clerk reporting to the store inventory head, who then inflated it some more while placing orders for the store at the local warehouse, that was then again inflated to the regional warehouse... And so on until it reached the manufacturer. The ripple effects took time and when the manufacturer finally increased production or invested in higher capacity, there was over-supply and unsold goods. All because the original blip at the checkout was just that: an inconsequential blip.
Of course, today's supply chain systems are architected for just-in-time using real time data. But the principles of human behaviours remain the same. And, for the purposes of this discussion, if one were to look backwards at the whiplash effect curve and smooth out the waveform, they do resemble the S curve - in reverse, or as mirror image.
What a beautiful way to put it.
You remind me of the class where I was taught the effect. They put us students in lines of 5, with each of us a step in the production process. we could only look at what we had and talk with those immediately on our sides. We communicated our needs for a product in rounds. After 6 or 7 rounds, the source supplier was in such oversupply that he went bankrupt.
J Vasanjust now
Thank you, Tomas. It may be that the S Curve is probably as prevalent in nature as the Fibonacci series is. You can, for example, see the S curve in the Gartner Hype Cycle, the technology diffusion curve (the left half of the Bell Curve that really matters), fashion retail, incidence and spread of rumours, etc etc. In short, probably has to do with human behaviours.
I enjoy Tomas' articles but, as an Indian, wish to point to an error in the above article on S curves. He refers to a Chinese emperor in the context of a grain of rice in the first square on a chessboard that doubles with every subsequent square. Sorry - but that's not Chinese, it's an ancient Indian story that goes back a couple millenia at least. Mind you, Chess was created in India - it was referred to as "chaturanga", hence the word "chess" in English. The Chinese creation was Go, not chess and the story is intrinsically Indian - every Indian schoolboy knows this.
Ah, yes! Thanks!
Kahneman's and Tversky's Prospect Theory curve has the S shape. They looked at it from the zero point to the right and to the left, but you can also consider how gains change the perception of value going from the bottom left corner towards the upper right corner.
You're right.
It does sound like a completely different type of S curve, no? Nothing growing, no saturation, and I wonder how it behaves in the extremes (does it have asymptotes?)
You are right: the Prospect Theory representation is a different type of S curve. Your examples of S curves are tangible, they are rooted either in physical processes or observable economic behaviors. By contrast, the Prospect Theory curve represents perceptions of losses and gains. I was wrong in suggesting that you can look at the gains from the bottom left to the upper right. The perceptions don't rise along the S curve, they are rooted in the zero point ("Reference Point").
The question of asymptotes is interesting. In the bottom left end we have risk seeking in losses, where losses accumulate but the perception of risk does not increase. The end state is the demise of the actor who took took too much risk. In the upper right corner, the asymptote is the level of value that does not change with increase in the gains. For example, if your assets are $10,000 your subjective value of $1 million and $10 million is the same.
Your S Curves can be stacked. The Prospect Theory curve moves as your Reference Point changes. If your assets are $1 million your subjective value flattens after, say, $100 million.
The steep part of the Prospect Theory curve on the losses side is about 2.5 steeper than the same-magnitude gains on the gains side. It's a linear piece calculated in psychological experiments where people were asked about gambles they would accept. The rest of the curve is more notional than mathematical.
While my contribution to your topic ended up being irrelevant it was fun thinking about it.
Hahaha not at all! I love it. It might not have been pertinent, but it's certainly fascinating.
In fact I'd love to read something in depth about it. Thinking Fast & Slow is one of my favorite books, but I don't feel like I've ever read something that details the ins and outs, the ramifications of prospect theory. Wikipedia is too shallow and boring. That would be a welcome article!
"Thinking, Fast and Slow" elaborates on the Prospect Theory in Appendix B. I spent some time trying to understand it when I volunteered to give an introductory talk on Behavioral Economics to a diverse group of non-experts. As they say, if you want to learn a topic teach it.
Very much a core reason why I write this newsletter
On the fifth day of Christmas my truelove gave to me five gold rings
In 1970 those gold rings would have cost around $30. Today they would cost around $1600.
That price would seem shocking to someone in 1970, but today we think the price sounds about right. This is because of Gradualicity*, also known as the boiling frog effect. When things change very gradually, the human brain accepts each small step and that becomes the new normal. It is only by taking a step back and looking at the big picture that we can appreciate the true magnitude of the change over time and where we are on the curve.
The third and fourth days of Christmas were about balance and attention. It’s hard to get things back into balance if we haven’t even noticed that they are out of balance, and it is hard to notice that things are becoming unbalanced if it happens gradually.
*If people are allowed to use “normalcy” I think I should be allowed gradualicity.
I am modelling national vaccine rollout. I have a view that site availability and nurses per site will both be log decays (also for hesitancy). But now I wonder if they are not closer to reverse S curves. What would you think?
For others, here's how to use S curves in your models: https://blog.arkieva.com/basics-on-s-curves/
I'm probably not the best to ask. I've avoided doing mathematical modeling during the pandemic, as it's so easy to go wrong.
Personally, I think in many cases a mathematical model can be misleading. Unless you do know the underlying force is mathematical (eg, R is indeed mathematical), I'd be wary. I just take ranges based on what the curve is looking like, and what similar curves have done in other places or in the past.
Eg what happened with hesitancy in Israel? What happened in the communities of US states where the rollout was fastest?
Just my 2 cents.