Predicting the speed of technology introduction (Dr. Jordi Robert-Ribes)

The Bass model of technology diffusion. Interactive prediction, past innovations examples, formulas, references.

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  Introduction in: 2014
  Degree of Innovation: standard
  Degree of Imitation: standard

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Air Conditioner Room air conditioner Telephone answering device Black & White TV
Black & White TV (2) Cable television Calculators Camcorder
CD player 1986-1996 Cellular telephone 1986-1996 Electric coffee maker 1955-1965 Colour TV
Colour TV (2) Colour TV (3) Colour TV (4) CT Scanner
Dishwasher 1949-1974 Clothes dryer 1950-1960 Freezer 1949-1959 Mammography 1965-1976
Microwave oven 1972-1990 Overhead Projectors PC Home PC 1982-1988
Radio 1922-1934 Refrigerator Toaster 1923-1979 Tractors (thousands of units) 1921-1931
Ultrasound Ultrasound imaging 1965-1977 Video Cassette Recorder 1981-1994

(Published in Australian Venture Capital Journal, 131 (May 2004), ISSN 1038-4324, pp34-36.)

Predicting the Speed and Patterns of Technology Take-Up

By Jordi Robert-Ribes, PhD, Manager Strategy - B33hive Pty Ltd, and
Phillip Wing, PhD, General Partner - Technology Venture Partners.


When assessing the attractiveness of a technology investment, either as an external investor or when building a business case for internal funding, a key element of the analysis is the rate at which customers will take-up or adopt the technology. Often, the entire business case is premised on a gross level assumption such as, "assume that the new technology will be used by 5% of the population of final users in less than four years time." This approach is based on the "large market fallacy" that argues, the market is big, we therefore only need a fraction of that market to adopt the technology in order to reach break even or return the investment, and therefore the potential upside is massive!

This is hardly a realistic or satisfactory approach and the underlying market assumptions typically have no validity if this approach or some variant on it is used. The purpose of this article is to introduce the theory of "diffusion of innovation" and how it can be practically applied to the assessment of investments in new or emerging technologies.

Central to the argument in this article is that the speed with which a new technology can be introduced and accepted by the market is crucial to;

       assessing the risk profile of the opportunity, and

       understanding both the capital and organisational capabilities required to successfully exploit the technology opportunity.

The related proposition is that there are multiple diffusion models and understanding the dynamics and applicability of varying models is also crucial to the investment analysis. The use of diffusion models is particularly useful for new or emergent technologies where no sales history is available and the nature of the offering to the market has a new or novelty dimension.


The major development of the DOI theory and practice is attributed to Rogers (1995) who framed innovation adoption as a life cycle involving;


       early adopters;

       early majority;

       late majority, and


Roger's research indicated that the spread of a new technology depends mainly on two factors; innovation or imitation. Innovators are driven by their desire to try new technologies or methods and the likelihood of an innovator using a new technology does not depend on the number of other users. On the other hand, imitators are primarily influenced by the behaviour of their peers. The likelihood of an imitator embracing a new technology, or new way of doing work, is dependent on the number of people who are already using it. Normally imitators are the main contributors to the diffusion or spread of innovation (i.e. early and late majority)

The innovation and imitation factors shape the speed at which the technology is accepted into everyday use. For example, the colour TV adopters were mainly imitators (and almost no innovators). On the contrary, for the frypan, innovators were more relevant to the uptake of the technology than imitators. You can see these patterns of introduction in Figure 1 and Figure 2.

Software: Microsoft Office

Figure 1. Colour TV introduction speed
(mainly imitation).

         Software: Microsoft Office

         Figure 2. Frypan introduction speed
         (mainly innovation).



As a starting point for the practical, commercial application of diffusion models, we suggest a broad understanding of the model developed by Frank Bass in the 1960s (the Bass Diffusion Model). Bass' original models were developed to predict the uptake of consumer products based on various advertising campaigns. The Bass Model quantifies the introduction of new technologies depending on the take up by innovators and imitators by estimating the introduction and acceptance rate variables. It is simple enough to allow a first assessment without the need for complex modelling; however, it is only one of the many models of technology diffusion (see references).


The authors have found the DOI useful in two broad applications - the initial feasibility of the investment via the modelling of take-up scenarios and the analysis of actual take-up rates post the investment being made.

The Bass Model has been used to predict technology introduction rates from a set of estimated values for the innovation and imitation factors. Such values can be dimensioned from comparable technologies that have been introduced in the past.

Figure 3 shows examples of past technology introductions. More examples are presented in

Figure 3. Levels of innovation and imitation for some past technology introductions

The nature of a technology, the target market and other ecosystem aspects affect the amount of innovation and imitation that fuels the diffusion of that technology. A high imitation factor occurs for technologies that have network effects (eg. facsimile) or that need high levels of common infrastructure investments. Regional and cultural differences also impact the innovation and imitation factors. For instance, collectivistic cultures tend to have higher imitation factors and countries with high purchasing power per capita tend to have higher innovation factors.

The implementation of the model available from lets you select an industry and develop up-take models for varying levels of innovation and imitation. The authors have used the Bass Model to predict technology introduction by using three sets of values for the innovation and imitation factors, which gives high, low and most likely scenario results. This allows to plot three curves (see Figure 4), which provide some orientation and an indication of the likely trajectory of the expected introduction rate.

Figure 4. Example of higher, average and lower predictions.

In a recent investment made by one of the authors in an early stage start-up technology company, the take up of the technology had been assumed to be a traditional innovation s-curve. After a slower than expected take-up, some primary data was collected that showed the diffusion curve was more likely to be bi-modal. That is the initial uptake by innovators was likely not to be sustained and in fact decrease until a second wave of innovators/early adopters used the technology. This insight provided significant additional information into the capital requirement of the business, the burn rate needed to sustain the customer and a major rethink on the competitive positioning of the company.

Figure 5. Traditional innovation s-curve.


         Figure 6. Bi-modal innovation curve



The Bass Model, along with other DOI models, has been enhanced in several ways from the basic up-take model of the 1960's. The patterns of successive generations of technologies can be modelled and the maximum market acceptance and the peak of introduction rates estimated. More recent research has looked at diffusion over time and has resulted in dynamic simulation models that attempt to isolate the key causes of differing adoption patterns over time.

Despite the sophistication of DOI models, data from all analytical models need to be treated with care. They are essentially just predictions from a model, which is driven by the initial set of assumptions. For instance, a new technology might be affected by competing technologies or a general economic down-turn that can result in its take-up being well below the lowest prediction of the model. A good example was a set of technologies developed in response to the introduction of GST. The technologies were developed to assist accountants and tax agents to process GST returns electronically and more cost effectively. Based on the market need and the previous uptake of electronic tax return lodgement, the diffusion models looked very promising. However the inertia of changing the ways of work and the use of relatively cheap para-professional staff to process GST returns made the technology economically unattractive and the business was not successful.

Another critical factor when applying DOI models to investment decisions is the delineation between total market and addressable market. The use of DOI models must reflect the introduction of the technology as a percentage of the total population that will use that technology, not of the total target market - the former being a subset of the latter. The concept of addressable market helps avoid the "large market syndrome" and will make the DOI models more robust and reliable.


The dynamics of the uptake curves and how the technology or its application diffuse into the market is a crucial analytic when assessing the business case for internal or external investments in new technologies.

For early stage investments or internal business cases for new products, it is essential to have some understanding of the likely diffusion of the technology. By not having a mental model to test against reality, the amount of capital, time to market and the window of opportunity can be grossly misjudged.

The authors recommend diffusion of innovation models as an important element of the tools for effectively assessing the merits of investing in technologies that are new or novel and do not have prima facie, predictable patterns of user up-take.


Bass, F.M., 1969, "A new product growth model for consumer durables", Management Science Vol 15.

Rogers, E.M., 1995, Diffusion of Innovations, 4th Edition, The Free press, New York NY.

Anotated references, examples and a model simulation are available at

(Published in Australian Venture Capital Journal, 131 (May 2004), ISSN 1038-4324, pp34-36.)

"Diffusion of innovation" (1st ed. 1962; 5th ed. 2003), E. Rogers, ISBN 0743222091.
A seminal work of diffusion of innovation.

"The aplication of an individual level diffusion model prior to Launch" (2000), J.M. Lattin, J.H. Roberts, Graduate School of Business, Stanford University, research paper 1663.

"Business Transformation Success: diffusion of innovation and the pivotal role of communication" (2001), P.J. Wing, PhD Thesis at Macquarie Graduate School Management (Sydney, Australia).

Bass's Basement Research Institute
A free graphical forecaster (web and excel) and many references.

"Diffusion models: Managerial applications and software" (1999), G. Lilien and C. Van den Bulte, Institute for the Study of Business Markets (University of Pennsylvania), ISBN Report 7-1999.
Introduction to the Bass Model and its extensions together with several examples of innovation and imitation factors for particular technologies.

"Want to know how diffusion speed varies across countries and products? Try using a Bass model"(2002), C. Van den Bulte. Visions Magazine.
Short overview paper with a good summary on the Bass Model.

"Telecommunications demand forecasting"R. Fildes.
Introduces and compares several forecasting models. Briefly discusses the calibration of the parameters in the Bass Model. It has an extensive bibliography. Forecasting May08 rev.pdf

"What's wrong with the diffusion of innovation" (2001), K. Lyytinen and J. Damsgaard. International Federation for Information Processing WG8.6. Conference, Banff, Canada.
Critical review of the underlying assumptions of the diffusion models.

"Diffusion Theory in Marketing: a historical perspective" (1999), F. Bass.
Extensive presentation of the Bass Model, its extensions and examples of applications.

"Investigating new product diffusion across products and countries" (2002), D. Talukdar, K. Sudhir and A. Ainslie. Marketing Science, 21(1).
Overview on how the innovation and imitation factors change across countries, cultures and disposable income.


F(t) is the cumulative fraction of adopters at time t
p is the innovation factor
q is the imitation factor

f(t) is the rate of diffusion at time t
p is the innovation factor
q is the imitation factor

From "Managing technology and innovation for competitive advantage", V. K. Narayanan (2001), Prentice Hall, page 101.

Jordi Robert-Ribes ©2004