Mathias Brandewinder on .NET, F#, VSTO and Excel development, and quantitative analysis / machine learning.
by Mathias 1. October 2008 17:22

In my previous post, I described how the Bass model can be used to forecast the market potential for a newly introduced product, using limited post-introduction data. In this post, I will apply the method to a real-world situation, to see how the method holds up in practice, what practical problems may arise, and how to address them.

The data

My objective is to evaluate the long-term share of internet traffic of Chrome, the new Google browser. I will be using actual traffic data from a medium-sized website, the technology blog of Donn Felker. In case you wonder why I didn’t use my own data, unfortunately my own traffic is not steady enough to get a “statistically decent” sample of Chrome users, and Donn was gracious enough to share his data with me (Thank you!).

The data I will be using is the percentage of visits coming from users using Chrome as a browser. It covers September 2 to September 17, 2008, the 2 first weeks of Chrome on the market.


by Mathias 23. September 2008 17:37

On September 2, 2008, Google launched its browser, Chrome, with great buzz in the geekosphere. I gave it a spin, but stayed with Firefox (old habits die hard), and did not give it more thought until I came across this post where Donn Felker ventures his gut feeling for what the browser market will look like in 2009.

I believe that his forecast, while totally subjective, qualifies as an “expert opinion”, and is essentially correct, and wondered what quantitative analysis methods would add to it – and decided to give it a shot.

The Bass adoption model

Properly representing the introduction of a new product on the market is a classic problem in quantitative modeling. At least two factors make it tricky: there is only limited data available (because it’s a new product), and the underlying model cannot be linear (because it starts from 0, and has a finite growth).

In 1969, Frank Bass proposed a model which is now a classic. It represents adoption as the combination of two factors: innovation and imitation. Innovators are the guys you see in line at the Apple store when a new iGizmo is launched; they have to have it first, regardless of how many people have it already. Imitators are the cautious ones, who will jump on board when enough people are using the product already – the more people already adopted, the more imitation will take place.

In terms of dynamics, innovators determine the early pick-up of the product, and create the initial critical mass of users– and imitators drive the bulk of the growth, going from early adoption to peak.

The mathematical formulation of the model goes like this:



It is a very elegant and lightweight model, which takes only 3 parameters, and is surprisingly good at replicating actual adoption. The Excel model attached provides an illustration of the dynamics of the model, depending on its input parameters, the total population, and the rates of innovation and imitation.

Bass.xls (27.50 kb)


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