**'How many?'**

I often hear this question from clients who are eager to launch a new online business:

*How many products should I offer in an online store?*

A different version of the same question is:

*How many clients do I need for a new service?*

Technically, all you technically need is one, and you’re in business! But the real question here, isn’t so obvious. The real question is about risk mitigation:

The same fundamental question pops up in other contexts:

*How many people should I interview for feedback about this new product or service idea?**How many stocks should I have in my portfolio?*

Our initial question can be expanded to something like:

*How many streams of income are required to support the fixed overhead of a business, and mitigate risk of failure of any one stream?*

In this framing, revenue from sales of a single product or service can be thought of as a stream of income. To simplify, we need to assume all of those streams are the same; i.e. we have priced them the same, and they all have the same risk of failure.

For our question, we are trying to figure out what minimum number of products, clients, etc. by which to divide a fixed quantity (overhead required to ‘keep the lights on’), to mitigate risk from any one of the divisor 'failing' (i.e. client that leaves, product that doesn’t sell).

The fixed quantity being our overhead (at a minimum, the amount of money the business must make in order to survive).

For any given business, there may not be an exact answer. Often we're tempted think 'well, it's got to be a lot'. But that's not very helpful.

Instead we can use some simple math to get a good understanding of real tradeoffs. And when we do, it's reassuring to work with a number that is both finite, and...really not all that big!

## Theres a quirk about math that we can leverage here.

Bear with me here, this is actually really simple. No college algebra or calculus. Just to fully illustrate what I mean:

Take any fixed number, which represents our overhead costs. We are going to talk about relative changes and don’t need to be accurate for demonstration, so we’ll just use 1.

Plot on the x-axis the scale of 0 - 100. We're going to take our fixed number, and apply the four basic math operators to it; with the x-axis value as an addend, subtrahend, multiplier, and divisor respectively; and plotting the result on the y-axis.

The four functions are:

- y = 1 + x
- y = 1 - x
- y = 1 * x
- y = 1 / x

## One of these is not like the others.

Now, this math is really basic, and we take it for granted every day. But I go to this length to point out the weirdness of one of them, as compared to the other functions, to highlight an important nuance to think about for business.

## Addition is linear.

## Subtraction is linear.

## Multiplication is linear.

**Division produces nonlinearity.**

Any time we see nonlinearities, we should pay attention. They can alert us to something ominous (like global warming) or something advantageous (like compound interest).

[And division is, of course, not the only function that produces nonlinearity, but that's beyond our scope here.]

In this case, we can leverage the function's nonlinear result (the 'quotient series') to answer the question 'how many'; assuming having 'more' is more difficult or costly, and therefore we want to know what number achieves sufficiency without excess.

The division graph represents how far an incremental stream of revenue moves the needle towards having less risk weighing on any single stream, or 'risk mitigation' with each added.

But to get an answer that makes more sense, it helps to invert the graph (i.e. plot y = 1 - 1/x). For each stream added (increase along the x-axis), we’ll count the change in the y-axis value as a good thing: incremental reduction in risk, with a total possible of 100% (or '1' in the graph).

As it turns out, with a service business example, we will have mitigated about:

- 80% of our risk with 5 clients.
- 90% of our risk with 10 clients.
- 95% of our risk with 20 clients.

Ever higher numbers of clients result in diminishing returns, as we approach (but never quite achieve) a perfect 100%.

5 or 10 clients to get going, is a tractable number. Not impossible at all.

We get a LOT of leverage from just the first 5 clients; well more than half of the total achievable 'mitigation'. Imagine how much harder this would have been if we were dealing with a linear function! It's like the universe is on our side.

**Thanks to nonlinearity: once begun is ***more than *half done!

*more than*half done!

Have more questions or a special case to discuss? Let's connect.

Cheers!