The Bass Model & Forecasting Product Adoption (Part II)

This is a continuation of the previous post.

Estimating m, p, q
Accuracy of the Bass Model relies heavily upon the modeler’s estimation of m (the market size), p (the “coefficient of innovation” and q (the “coefficient of imitation”). Because determining these values is a rather arduous task, anyone constructing a Bass Model typically looks to analogous products. In the previous post we suggested that the iPod’s analogous products included portable radios, walkmans, and portable CD players. This is quite literally, prediction by analogy, and this is precisely why it fails for the truly novel. (personal note: for the hackers out there, this is a bit like proving a problem is NP-Complete by reducing it to another previously proven NP-Complete problem.)

The first step, therefore, is to identify analogous products and either (1) search the literature for their previously documented p, q, and m values or (2) to derive m, p and q through analogous products’ actual sales data. Taken from reference [2], for example, the p, q values for CD players between 1986 and 1996 are p = 0.055 and q = 0.378. If you have multiple analogous products, then simplest thing would be to take a weighted average of the figures. If market size data for analogous products does not exist, or if the target market isn’t obvious (as a result of the product’s novelty as is the case with technology-based products), the best you can do is guesstimate through consumer surveys. Unfortunately, the inherent subjectivity seems somewhat unavoidable!

Assessing the Impact of Marketing
For the purpose of this post, I’m assuming that marketing comes in two forms (1) generating consumer awareness and non-promotional events, and (2) promotional events in the form of price discounts.

Note that in the Bass Model, neither consumer awareness building efforts nor promotional events impact the “coefficient of innovation” p, or the “coefficient of imitation.” Both of these values are constant. The “coefficient of innovation” is the probability that an innovator will adopt the product and, in its calculation, includes the impact of awareness building efforts. The “coefficient of imitation” simply represents the probability that your friends will adopt the service if you did. The extended Bass Model is therefore modeled as:

• S(t) = [p + (q/m) * N(t-1)] * [m - N(t-1)] * X(t)
• X(t) = the impact of both consumer awareness building efforts and promotional events.

Modeling Consumer Awareness & Non-Promotional Events

• A(t) = advertising in time period t
• alpha = percentage increase in diffusion speed resulting from a 1% increase in advertising
• alpha * [[A(t) - A(t-1)]/A(t)]

Modeling Promotional Events

• P(t) = the product’s price in time period t
• beta = percentage increase in diffusion speed resulting from a 1% decrease in price
• beta * [[P(t) - P(t-1)]/P(t)]

Putting It All Together

• X(t) = (alpha * [[P(t) - P(t-1)]/P(t)]) + (beta * [[A(t) - A(t-1)]/A(t)])

The Bass Model & Competition
Phew, now that we got through the math, lets touch very briefly on assessing the impact of competition. In the Bass Model, competition for first-time adopters, be they innovators or imitators, impacts m, the total market size, i.e. the total number of people who could adopt the product. Given a market size of m, and competition over those individuals, the only question that remains is one of market share. What percentage of the total market will your product capture? If it’s 10% then simply replace the m in the model with (.10 * m). Yup, it’s that simple. If you are wondering how to forecast market share capture, don’t worry, we have left that exercise for another, undoubtedly lengthy post.

Happy Memorial Day!

References
[1] Frank M. Bass, “A New Product Growth Model for Consumer Durables,” Management Science 15:5 (1969): 215-227
[2] Elie Ofek, Peter Wickersham, “Forceasting the Adoption of a New Product,” HBS Case No. 9-505-062
[3] Wikipedia, “Bass Diffusion Model,” http://en.wikipedia.org/wiki/Bass_diffusion_model
[4] Gary L.Lilien, Arvind Rangaswamy, and Arnaud De Bruyn, “The Bass Model: Marketing Engineering Technical Note1,” A supplement to materials in Chapters 1, 2, and 7 of Principles of Marketing Engineering

Tags: bass model, business, business modeling, forecasting, innovation, methods, product design, sales forecasting

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