The S-shaped curve

Further notes from E M Rogers’ Diffusion of Innovations, originally published 11/2/2007 on my Open University blog, during H807.

When social researchers first started looking at how innovations diffuse through social systems in the 1940s, they noticed that the pattern of spread of a new technique or idea was very similar to that described by epidemiologists in studies of how infections spread through populations. That is to say, the rate of spread starts off slowly, accelerates through the mid range of the graph, and then slows down and levels off, forming an S-shaped curve.

The S-shape is caused by the fact that the innovation – whether it’s a technology or a pathogen – has first to come in from outside the social system, and that means relatively few people are susceptible to begin with. Once the innovation is established within the system, more and more people come into contact with it, and the rate of spread increases. Eventually, so many members of the community have been affected (adopted the innovation or caught the infection) that the system runs out of unaffected members, and the rate of spread slows and eventually stops.

S-shaped curves have a critical ‘take off point’, at between 10% and 20% of the system, where a sufficiently large number of people in the community have adopted (or been infected) to make the rate of growth turn upward and continue climbing until the system begins to run out of unaffected members. (Malcolm Gladwell took this idea – in fact the whole notion of innovation diffusion behaving like epidemics – and used it as the foundation of his book The Tipping Point.)

The S-shaped adoption curve applies to virtually all innovations, but something interesting happens when the innovation in question is a communication technology like mobile phones or the internet. When a non-interactive innovation spreads through a system, early adopters don’t get any extra advantage from subsequent adoptions (apart from additional people to chat to about the new toy!). But with a communication technology Metcalfe’s law dictates that each new adopter adds value to the innovation for everyone in the system. So a cycle of positive feedback sets in which makes the adoption curve accelerate still faster. This is partly why the world wide web has grown from zero to a billion users in little over 15 years.

Another interesting point that Rogers makes about this process concerns the different influences affecting early adopters and later ones. The first members of a community to take up an innovation must necessarily learn about it from outside the social system, and so are more dependent on indirect knowledge transmission via newspapers, books or other media. However as the innovation spreads through the community, more and more people are able to learn of it directly from neighbours, workmates, friends or family members – and this direct, personal contact is much more effective at persuading people to try out the innovation. This is another reason why the S-curve typically starts to speed up at between 10% and 20% adoption; and also helps to explain why the internet – which makes direct, personal contact possible even when individuals are 1000s of miles apart – has diffused worldwide so quickly.

Rogers, EM, 2003. “Diffusion of Innovations”, 5th edition, Free Press, New York