Older articles in our blog (here, here, and here) explore a simplified s-curve model in Excel to study user adoption. This particular post looks at two concrete examples.
To provide some context: since the pioneering work of Bass[1969], many models have been proposed to explain the time dependent nature of new product/technology diffusion.
I have used many of these to understand diffusion of technology, growth potential for industries, and to some extent, individual companies within an industry. Sometimes, the need for simulation software packages and the math behind these models kept clients from really taking ownership of the models that we as consultants developed. After I started “packaging” the s-curve model into a simple Excel formula on their own spreadsheets, I saw much more engagement.
On the article Throw your Life a Curve which I coauthored with Whitney Johnson, and published on the Harvard Business Review blogs, we presented the following chart on Facebook’s user base growth:
To construct it, we looked at publicly available data points such as when Facebook reached milestones of 100 million users, 200 million, etc. Then, we used the simplified s-curve model to fit and understand the growth trend. Because this model uses only 3 parameters, the discussions with analysts and managers tend to be more about the company than on the model itself. Starting out with a base assumption that saturation is around 1.3 billion users, we calculated through least-square curve fitting that takeover would occur within 5 years, with hypergrowth beginning in Q3 2008. If these terms don’t make sense to you, feel free to drop me a note, or check the posts mentioned earlier. Once we solved for these parameters, it is now easy to calculate the virality coefficient: how many users should be gained per each existing user in order to grow For Facebook, it came around 7-8%.
Now, let’s look at Dropbox. Because Dropbox is a much younger company, it is harder to make an assumption about saturation, to make a similar analysis. The resulting fitting parameters of assuming 200 million or assuming 500 million are substantially different. Using the company fundamentals, and other industry benchmarks, I chose 200 million as the saturation parameter for the following chart. With that, the hypergrowth date is Q1 2011, and takeover is 3 years.
Are these predictions accurate? In time we will know. But having a model to refer to, and particularly a simple one, allows executives to have focused conversations, and refine periodically their understanding of their company, competitors and industry.
Among many other applications, we have recently used these figures, for instance, to analyze startup business plans, and look for red flags and ask probing questions.
How would you use this? What are your thoughts? We’d love to hear your comments.
1 Zuckerberg, Mark (August 26, 2008). “Our First 100 Million”. The Facebook Blog. Retrieved June 26, 2010.
2 Zuckerberg, Mark (April 8, 2009). “200 Million Strong”. The Facebook Blog. Retrieved June 26, 2010.
3 Zuckerberg, Mark (September 15, 2009). “300 Million and On”. The Facebook Blog. Retrieved June 26, 2010.
4 “New navigation for users and 400 million active users announcement”. Facebook. February 4, 2010. Retrieved June 26, 2010.
5 Zuckerberg, Mark (July 21, 2010). “500 Million Stories”. The Facebook Blog. Retrieved July 21, 2010.
6 Carlson, Nicholas (January 5, 2011). “Goldman to clients: Facebook has 600 million users”. MSNBC. Retrieved February 11, 2011.
7 Socialbakers employee (May 30, 2011). “Facebook is globally closing in to 700 million users!”. Socialbakers.
8 Adam Ostrow (September 22, 2011). “Facebook Now Has 800 Million Users”. Mashable. Retrieved September 26, 2011.
Dropbox data points:
http://techcrunch.com/tag/Dropbox/page/2/
http://techcrunch.com/2011/11/01/founder-storie-how-dropbox-got-its-first-10-million-users/
http://techcrunch.com/2009/04/24/dropbox-now-effortlessly-syncing-files-for-1-million-members/