# SaaS Metrics: Negative Churn

Churn is one of the central metrics that SaaS companies should care about. It is typically quantified as a probability or percentage of customers lost annually, or in each subscription renewal period. Even moderate changes in churn can lead to a very big changes in the expected total revenue from each account, so reducing this number is very important in driving your companie value up.

This post is about **Negative Net Churn**. Negative churn occurs when the revenue lost from lost customers that leave is outweighed by the revenue expansion in the accounts that the company manages to keep. New Relic is a great example of this, with annual average revenue expansion of 14%. In theory this would allow New Relic to continue growing without ever adding more customers.

New Relic achieves this by offering pricing that is linked to the number of servers a client uses New Relic on. The number of servers per customer is very likely to grow over time, especially as their main clients are fast growing technology companies.

Other examples of negative churn include API marketplace Mashery: their pricing model was based on revenue share and number of API calls; and they worked with fast-growing tech companies whose revenues and API consumption tend to grow over time. Content Delivery Networks, like CloudFlare or Fastly, are another great example of revenue expansion: they charge based on data volumes consumed, which are growing at an exponential rate.

You can read more about why negative churn is so powerful and further examples on how to plan for it on Tom Tunguz's blog.

## What's the catch?

Negative churn means that the company would - on average - keep growing even when you stop adding accounts. This all sounds too good to be true. Indeed, the main catch here is that this growth only happens **on average** or **in expectation**. This simple interpretation ignores the randomness and variance around average behaviour. Unless the company has millions of customers, the actual revenue trajectory could look radically different from the average or expected behaviour. So valuing a company on the back of negative net churn can be a dangerous game.

### Net Present Value

To understand why negative churn is a risky thing to build a business on, let's take a look at the net present value (NPV) or discounted customer lifetime value of a single client. The net present value expresses the total future revenue that a single client acount generates, in today's money, accounting for inflation for example.

My simple model have four components:

- $r$: initial revenue run rate per unit time
- $g$: revenue expansion rate per unit time
- $c$: churn probability per unit time
- $i$: discount rate per unit time (for example inflation, or growth rate of S&P500 index)

The expected NPV is given by the following formula for the sum of geometric serices:

$$\hat{NPV} = \frac{r}{1 - (1-c)(1-i)(1+g)}$$.

Note that without the discounting term, negative net churn would imply that the average lifetime value of a customer is infinite, because *on average* the revenue is *expected to* keep growing in the future. This already shows that negative churn is just too good to be true, and that something is wrong with this simple model.

### Power law

Crucually, the formula above is only an expectation. It is a description average behaviour that ignores variance and uncertainty. The interesting features of negative churn will become apparent only when you start studying the randomness of $NPV$ and not just average behaviour.

For a single client, $NPV$ is not a deterministic number but in fact a random variable. This is because churn is assumed to happen at a random time in the future, we just don't know when. If you knew that the client will leave after exactly $L$ years (or units of time), the $NPV$ is going to be described as follows:

$$NPV(L) = r\frac{1 - {(1-i)(1+g)}^L}{1 - (1-i)(1+g)}$$.

$NVP$ becomes a random variable because it depends on the length of the contract $L$, which is modelled as a random variable.

So instead of just looking at its mean $\hat{NPV}$, we should look at the entire probability distribution. It is relatively simple math to show that

if you have negative net churn, the net present value of each client follows a power law distribution.

This is radically different from the behaviour of exponential distribution that is normally used to model churn.

### Being reliant on the single biggest customer

Probabily the most important consequence of a power-law NPV distribution is that when you look at a cohort of otherwise identical clients, the NPV of the whole cohort will be dominated by the NPV of a single, or only handful of clients. Essentially, the ever growing accounts that you can keep around for the longest will contribute most revenue in the future. This effect is very similar to why venture capital returns are typically dominated by one or two really good investments in a fund.

As a consequence, as the contribution of each account to total revenues becomes more uneven, the company's revenue stream starts to hinge on a handful of clients that it cannot afford to lose. Therefore,

negative churn does not mean that you can stop caring about churn, in fact you have to care even more, and you have to watch those few clients that become the primary drivers of your revenue.

Luckily, as you add more clients per cohort, your revenue from those cohorts will be a lot more predictable and closer to average behaviour thanks to the law of large numbers. You are still likely to have dominant clients, but their at least you have enough backup to survive if and when you lose those.

## Summary

Negative Net Churn is an amazing characteristic to look for in a SaaS business. The most common way to achieve this is to have pricing structure which grows with the client's:

- revenue/sales
- bandwith/data volume consumed
- number of servers
- number of employees

But even if your SaaS business has negative churn, keeping churn under control is very important. The picture that your company will grow itself in autopilot mode if you stop adding new clients is misleading and can lead to being overly reliant on the single biggest customer.

In fact as your account sizes grow with the client, it will be more and more crucial to keep the few clients that drive most of your revenues. In addition to keeping churn under control, try to keep an eye on how inequal your account sizes are.

And finally, to build a really robust business, revenue growth should be supported by growth in the number of accounts as well as account size expansion. This diversifies your portfolio of clients, and mitigates the risk of being too reliant on the fastest growing accounts.