S-curves (Theodore Modis)

 

Theodore Modis., Prediction : society's telltale signature reveals the past and forecasts the future, 1992.

pp.37-38

p.37

  Critics of S-curves have always raised the question of uncertainties as the most serious argument against forecasts of this kind.  

p.37

Obviously the more good-quality measurements available, the more reliable the determination of the final ceiling.  But I would not dismiss the method for fear of making a mistake.  

p.37

Alain Debecker and I carried out a systematic study of the uncertainties to be expected as a function of the number of data points, their measurement errors, and how much of the S-curve they cover.

p.37

We did this in the physics tradition through a computer program simulating “historical” data along S-curves smeared with random deviations, and covering a variety of conditions.  The subsequent fits aimed to recover the original S-curve. 

p.37

We left the computer running over the weekend. 

pp.37-38

On Monday morning we had piles of printout containing over forty thousand fits.  

p.38

The results were published,12  and a summary of them is given in Appendix B, but the rule of thumb is as follows:

  If the measurements cover about half of the life cycle of the growth process in question and the error per point is not bigger than 10 percent, nine times out of ten the final niche capacity will turn out to be less than 20 percent away from the forecasted one. 

p.38

The results of our study were both demystifying and reassuring.  The predictive power of S-curves is neither magical nor worthless. 

p.38

Bringing this approach to industry could be of great use in estimating the remaining market niche of well-established products with quoted uncertainties.  Needless to say life is not that simple.

p.38

If products are not sufficiently differentiated, they are sharing the niche with others, in which case the combined populations must be considered. 

p.38

Like any powerful tool, it can create marvels in the hands of the knowledgeable, but it may prove deceptive to the inexperienced. 

p.120

  The cases presented in this section depict deviations from the description of the natural substitution model.  In the work of economists and meteorologists such a situation ── evidence against a model ── would have resulted in modifications of the model itself.  With the ((process of natural growth)) in competition, however, the theory is fundamental; deviations, whenever they occur, must be explained in the way the model is used rather than raise questions about its [a model] validity. 

p.225

From half of a growth process one can intuitively predict the other half. 

p.234

Appendix B

Expected Uncertainties on S-Curve Forecasts 

p.235

In other words, a slower rate of growth correlates to a larger niche size, and vice versa.  This implies that accelerated growth is associated with a lower ceiling, bringing to mind such folkloric images as short life spans for candles burning at both ends. 

  (Prediction : society's telltale signature reveals the past and forecasts the future / Theodore Modis.,  1. forecasting., 2. creation (literary, artistic, etc.)

3. science and civilization.,  CB 158.M63, 303.49--dc20, 1992

, )

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