I cannot remember where I read this statement: "When looking out for trends, watch out for the big and the small S-curves". However, I have been studying S-curves for quite sometime now. I have used it in projecting how technologies could emerge.
When 3G mobile handsets were emerging in Singapore - and there were some data on the first six months of 3G handsets' penetration from the IDA - I tried my hand on modeling how the eventual penetration of 3G handsets were going to be. I was asked by a journalist from one of the leading newspapers when I thought it would hit critical mass - and I said "in the next 3-6 months".
She guffawed and didn't believe me.
(I checked back a few months after that conversation in 2005 [or was that 2006] - I was right. It's just that, ownership of a 3G-enabled handset didn't necessarily mean usage of 3G technologies. That's for another day.)
When I was also trying to look at the penetration of new technologies - such as social-networking sites in some of the countries in the Southeast - I managed to fit them in an S-curve.
During a conversation with a potential employer, I blurted out that "I loved S-curves!" Well, that's probably an exaggeration - but I find it to be very useful.
S-curves, I think, are very helpful. It describes social and tech phenomena quite nicely - for example, how rumors, epidemics, new technology, and new ideas spread have been modeled using S-curves. The proverbial "last straw that broke the camel's back", "tipping point", and "critical mass" can also be thought of as the inflection point of the S-curve.
There are a number of S-curves that I know of. Most are quite complicated. The logistic/sigmoid function is one of them - very powerful, very interesting, and very useful specially if one is working with individual level data.
One of the S-curves that I found really interesting is Frank Bass' Diffusion Curves. It uses 3 parameters:
- The maximum capacity, which in the case of "penetration" figures, would be 100.
- The Coefficient of Innovation
- The Coefficient of Imitation
I typically explain the Coefficient of Innovation as the innate power of a new technology (or product/service) to generate a following amongst the target population. It's the innate or initial momentum that the technology (for example, Google's search engines back in the early 2000s) to be used by others.
The Coefficient of Imitation is the impact of others using the same technology. It could be in the form of "perceived peer pressure" - a person's circle of friends upgrading to a 3G-enabled handset and therefore influencing that person to upgrade as well. It could be in the form of word-of-mouth or endorsements.
The diffusion curves of Bass, I think, explains a lot - and does so elegantly and simply. (Of course, there's more to the model than just mere projections and S-curves.)
Anyway, I have set up a spreadsheet called SCurves.Xls that would help in estimating S-curves given at least three data points (in percentage) using the diffusion curves of Frank Bass.
These data points may or may not be continuous or complete. For example, you may have data for Year-1, Year-5, and Year-10 - this simple spreadsheet should still work. Of course, the more data you have, the better.
(And if you have sufficient data, then reserve about 20% of these data as "counterchecks" or "validation data".)
You should have Excel's SOLVER Add-In enabled, though, for it to work. (If you want the unlocked file, let me know by leaving a comment and I'll send it through to you by email. You'd be surprised how simple it is.)
I cannot guarantee that the spreadsheet would work in all versions of Excel. I have only one version at home (Office 2000 for XP). I also cannot guarantee that there are no viruses. I have pretty much a good antivirus in my system - but I could be wrong - so if you don't trust me enough, don't download it.
Below is a screenshot of the outputs: It shows the Innovation and the Imitation Coefficients, the projected % at time, t, (which could be years, months, days, hours...), and a ghastly chart. The chart is 'unlocked' and therefore, you can change and beautify it.
You enter your data in the yellow region. In the file, there are 7 hypothetical data points entered. These were not "continuous data" points. But they seem to be working.
Try it out and let me know if it works. If it doesn't, let me know, too.