"Inflection points"

June 27, 2008 Jack Repenning

GAaaaaahhh!  Marketspeak!!!

There are 22 messages in my inbox that misuse the idea of an “inflection point” in a growth curve.

No, really, I counted them. And I try to keep my inbox completely
cleaned out, we’re just talking about the incoming ones over the last day or so (while I’ve been travelling).  There are over 200 in various other mail folders, that I’ve been forced to keep for various archival reasons despite their annoying innumeracy.  Every single one of them means, I’m quite sure, “a point where the growth really starts to take off.”  And every single one of them is wrong, because an inflection point on a growth curve is just exactly the opposite: it’s the point where growth begins to slow down.

Look, “an inflection point, or point of inflection (or inflexion) is a point on a curve at which the curvature changes sign. The curve changes from being concave upwards (positive curvature) to concave downwards (negative curvature), or vice versa.”  If it was growing, it is now growing less rapidly.  If it was shrinking, it is now shrinking less rapidly.

What that means in ordinary speech depends on the shape of the curve, of course.  What can we say about that?  Well, we’re talking about “growth.”  There are two kinds of growth curves.  If there are no limits to the growth, then the growth is “exponential.”  Whether any product actually has unlimited, exponential growth is a whole other story, not to be explored here.  Suffice it to say that “exponential growth” sounds good, is just the sort of thing marketspeakers like to say, so might be what they want to mean, and anyway real growth often looks exponential in the beginning.  But exponential growth does not have inflection points: it doesn’t change from “growing rapidly” to “growing slowly”; so long as it’s exponential, it just keeps growing more and more rapidly.

So if you claim an inflection point in your growth, you’re claiming the other curve, the logistic curve.  A logistic curve has an inflection point.  The inflection point is the point at which it changes from “growing ever more rapidly” to “growing ever less rapidly,” and is therefore the point at which its growth rate is at its maximum.  It will never again grow as rapidly as it was just recently.

A logistic curve also has a maximum value, limited by some factor in the environment.  The inflection point typically appears at about 50% of the maximum possible value.  So if you’re calling an inflection point on a growth curve, you’re saying “this product already has half the market it’s ever going to have; it will never have more than twice its present market.”

And I just don’t think that’s the message these 220 messages actually intended!

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