Bass Curves for the Diffusion of Innovations

by Jakob Nielsen on September 1, 1995

Sidebar to Jakob Nielsen 's column on growth of the Web, September 1995.

Experience from many earlier innovations shows that the spread of a new method or concept in a market can be characterized by the Bass formula :

Standard Bass formula for the diffusion of innovations

In this formula, N t indicates the number of companies (or people) using the innovation at time t .

The three parameters of the model are:

  • m = the market potential; the total number of people who will eventually use the product
  • p = the coefficient of external influence; the likelihood that somebody who is not yet using the product will start using it because of mass media coverage or other external factors
  • q = the coefficient of internal influence; the likelihood that somebody who is not yet using the product will start using it because of "word-of-mouth" or other influence from those already using the product.

The standard Bass curve (with the average values of p and q of 0.03 and 0.38, respectively) looks like this:

Standard Bass curve for the diffusion of innovations
The standard Bass curve for the diffusion of innovations over time.

Uptake of hypertext is likely to happen somewhat differently than the standard Bass curve. First, the market for hypertext use is highly dependent on the number of people who have computers with certain minimum capabilities (typically at least a graphical user interface; for WWW use it is also necessary to have Internet access). Second, the influence of other hypertext users is almost certainly not linear. In fact, it is likely that hypertext use follows a so-called non-uniform influence model as shown in this formula:

Revised Bass formula with non-uniform adapter influence

This model is identical to the basic Bass model except that the impact of the other adapters is not proportional with their number. For hypertext in general, and the Web in particular, it seems to be the case that the impact of having more stuff available grows faster than a linear scale. Thus, it is almost certainly true that the diffusion of hypertext will follow a non-uniform formula with a value of delta that is substantially greater than one. Some analysts think that delta should be two, since the number of possible connections in a hypertext network grows by the square of the number of nodes. In reality, though, many of these connections are useless and lead to information overload, so it may be more reasonable for delta to approximate 1.5.

Taking these revised assumptions into account results in a curve somewhat like this for the spread of hypertext use in the industrialized world:

Revised technology transfer curve showing probable diffusion of hypertext
Revised technology transfer curve showing the probable diffusion
of hypertext use in the industrialized world.

In the above diagram, Year 0 for hypertext use has been set equal to 1986 since the first commercial hypertext program (Guide) shipped that year. The use of hypertext prior to 1986 was confined to research labs and other experimental situations.

Currently (1995), there is probably about 1 percent of the population in the industrialized world using the WWW and about 4 to 5 percent using other hypertext systems (mainly online documentation and CD-ROM encyclopedia).

Actual developments will almost certainly happen differently than the predictions in the above curve. In fact, I suspect that the adaption of the WWW will happen faster than indicated by the curve and reach maybe half a billion people by the year 2000. One thing seems certain, though: it is still early times on the Web!

Reference

For more information about the Bass curve, please see
Mahajan, V., Muller, E., and Bass, F.M. New product diffusion models in marketing: A review and directions for research. Journal of Marketing 54, 1 (January 1990), 1-26.


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