Interactive Bass Diffusion Model

Click here to launch Interactive Bass Diffusion Model

The Bass diffusion model was developed by Frank Bass and describes the process how new products get adopted as an interaction between users and potential users. The model is widely used in forecasting, especially product forecasting and technology forecasting. Click here for the full description on Wikipedia.

The function describing Sales S(t) is given by



Ultimate market potential



Coefficient of imitation



Coefficient of innovation

Click here to launch Interactive Bass Diffusion Model

The Xcelcius dashboard allows users to interactively vary the parameters of the diffusion model. This is useful when doing ‘what if’ analysis during product portfolio planning stage. The sales profile is more realistic and can be embedded into the interactive portfolio or we can create a Monte Carlo income statement with distributions to describe uncertainty in ultimate market potential (m), coefficient of imitation (p) and coefficient of innovation (q).


5 Responses to Interactive Bass Diffusion Model

  1. Mathias says:

    To paraphrase Napoleon, “a good interactive dashboard is worth a thousand words”! Very nice way to illustrate how the parameters of the Bass curve influence the curve.
    As an aside, I was initially thrown off by the time of peak sales value. I am convinced now the number you return is correct, but it took me a bit of thinking to reconcile it with the time scale of the chart. You would expect a peak sales occurring at time, say, 7.67 (that’s what you get for parameters 0.01; 0.5), to correspond to a peak in period 7 of the chart, which is not the case. I realized after a bit that period T covered time T-1 to T, so 7.67 would actually occur in period 8…

  2. George says:

    One thing I still can’t figure out is WHAT units are defined by time. So I can make my S curve work, but is the time periods days, week, months, years, decades. Or do I also have to figure out WHEN penetration will have occurred, and back out from there. eg using the famous .03 and .38 share doesn’t go up much after time units hit 20. So if really I thought market will be saturated in five years, then I just relabel my time axis? Sorry to be so dense about this, but it seems that understanding the timing of this, is as important as the peak, and I don’t know how to get my arms around thinking about the units other than to throw out the whole equation and just consider the shape. Any thoughts here? Thanks!

  3. Ashish Chaudhary says:

    plz help me how can we estimate parameters(p & q) in bass diffusion model with LMS(least mean square method)

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