Percent Growth from Zero

An interesting (or possibly not) question came up as some colleagues and I were discussing % growth.

The logic flows thusly:

A = previous total
B = new total.

Simple % growth = (B - A)/ A.

So, if we had 100 widgets in March and 150 widgets in April, that with by a 50% growth (150 - 100)/100 =.50.

So how do you define it, if at all, if you start from zero.

You’ve got 0 widgets in February and now you’ve got 100 widgets in March. What’s the % growth? Can’t divide by zero. Undefinable?


It’s a definition problem. As you define it, you need infinite growth because only infinity multiplied by zero gives you any kind of result.

if you definbe it as the change divided by the final number, then you have 100% growth, which is a real number, but equally useless in giving a sense of the increase.

The point is that percentage growth only makes sense if you have a nonzero start, since you’re essentially giving your final number in terms of your initial number. If you start with zero, it’s not a meaningful metric. It probably isn’t meaningful if your starting number is vastly smaller than your initial number, too.
So it’s not that it’s “indefinable”, it’s that you’ve chosen an inappropriate measure of increase .

Concur. This is a situation where you should report the raw number, not the statistical change.

Of course, you could also fudge it and say that after the first widget was sold, you experienced a 10,000% increase.

This is a variant of the Small Base Problem. One discussion is on page 355 of this document:

If exponential growth could somehow get started from zero, it would be impossibly inconvenient. All the bank accounts that had never been started by people who never existed would swell uncontrollably - to say nothing of all the unstarted credit card accounts, which would swell so much faster. Physical variables everywhere that were already in equilibrium would constantly be equilibrating. Pencils that were lying on their sides would all be moving away from balancing on their points. How could we live in such a state?

Are your colleagues in marketing? I think, “infinite month-on-month growth” is pretty catchy. Imagine the projections into the future!
Obviously, the “% growth on previous time period” concept is sort of dumb to start with.

Why weren’t you selling as many widgets before? Why are they selling now? Why do you think it indicates your present success rather than your prior mismanagement? Let’s start with asking how many widgets you should be selling considering the size of the market, before patting anyone on the back.

You could say, “we were achieving 0% of our potential in March, but are now shipping to 10% of the expected market in April. That’s a rise of 10 points, and we’ll reach saturation by Christmas!” That’d be a nice-sounding analysis.