Jul30
Relationship between the Bass and the logistic market adoption models
The simplified market adoption model I described on previous postings (1,2) is an Excel implementation of a kind of logistic function. The Bass model is one of the most popular models used in marketing, and management of technology to think about product introductions. (See Wikipedia article). From a mathematical perspective, when the parameter p is 0, the Bass model reduces to the logistic function.
What is most interesting, from a business perspective, is how you arrive to each of those functions by modeling real-world interactions. On both models, you can conceptualize the world as two different pools of people (or stocks, in the system dynamics terminology). One is the pool of potential adopters, and the other is the pool of adopters. The flow between these two pools is controlled by the adoption rate, a variable that models how probable is that a potential adopter becomes “infected” by a current adopter. On the logistic model, it depends solely on how much they interact, how big the total population is, and how “contagious” the product is. On the Bass model, an additional parameter accounts for external factors, the most common being advertising. The Bass model overcomes what is called the startup problem of the logistic model: how a initial base of zero adopters can spread “infection” of the product.
There are more refinements that can be done to the Bass model: accounting for changes in the total population over time, learning and experience curves, etc. For projects where the sensitivity of the model to these factors is high, I definitely recommend to spend more time calibrating your model, understanding which of the different available curves fits better any data you may have, and most critical of all, whether the chosen coefficients for any of the functions have strong impacts on the critical business issues you want to model — capacity planning, pricing, profitability, etc.
For many projects like business plans, revenue projections, etc. I’m willing to sacrifice the ability to fine tune parameters in a model like the BDM for the clarity provided by a model like the Excel logistic function I described. I can generate more tangible conversations with executives by discussing what they believe will be the takeover time, when they believe it will be the start of the fast growth, how much share they believe will be reached in steady state, etc.
Bob Kitzberger Says:
Thanks, Juan. I’d have to agree that the parameters provided in your model are more intuitive and easier to use as the basis of substantive conversations (vs. the coefficients of innovation [p] and imitation [q] of the Bass model). The market mix levers of growth can still be discussed without quantifying them in the model.
Adriano Says:
Hi Juan,
I have found your blog posts re s-curves very informative.
I’m studying technological growth curves at present as part of some postgrad research at university and am interested in the application of such a model in industry.
I have read many of the papers in the Journal of Forecasting etc, and much of it seems quite esoteric and I don’t find it quoted that often by non-academics. Does the Bass model have a place in real world modeling of sales data?
Are there other models which perhaps I should consider too, which account for the marketing mix variables more directly?
BR,
chidinma Says:
Hi Juan,
I have this question that has been bugging my mind for a while now. I’ve read about the pros and cons of strategic modelling. but do you think strategic modelling can make a contribution to management decision making?
Thank you!
Juan C. Mendez Says:
@chidinma
Thanks for your message. In my opinion, modeling is more about the conversations that are generated when you model something than it is about the math of the model itself. Every model is a simplification of reality and will be, by definition, “wrong” or insufficient if you look at it from certain perspective. But we simply can’t escape models! When we as humans understand something, it is simply that we created a mental model about that something. Therefore, the value of strategic modeling is to have conversations that elicit each of the participant’s mental model about the problem, that make explicit some of the assumptions behind those mental models, and allow the group to have alignment conversations so it becomes a shared mental model. Once that is achieved, it doesn’t matter if the implementation of the models are scribbles on a blackboard, a Excel spreadsheet or a complex computer program. You won’t get far if the involved parties don’t trust and understand whatever model is used. What you and other readers think?
Stig Ottosson Says:
S curves are used also for planning of new product development (NPD) activities where the Y-axis gives the achieved performance (P) and the X-axis time (T). When P 100 % has been reached a NPD project is completed. Milestones (on the P-axes) are used to divide the total project in smaller pieces. Larger companies often also use “Gates” on the T-axis to evaluate if a project shall get a Go or Kill decision at the gates to continue into next development stage. However gained milestones are often lost and re-gained and lost again a number of times in real NPD projects if they are allowed to continue until P 100% has been reached. The theoretical linear S curves unfortunately give a falce mindsetting e.g. causing projects to be stopped when there are good possibilities for the future. Similar conclusions can be made for innovation diffusion.