The Tyranny of the S Curve

It’s no secret that growing a successful B2C business is hard. Failure rates are high and the companies that do survive can never rest on their laurels.

There are a myriad of well known reasons why many start-ups don’t succeed in this space — e.g., bad product/market fit, lack of capital to get off the ground, too much competition, etc.

Another reason is the tyranny of the S curve. The basic theory is that growth follows an S-shape (see below), which means that — even if a company has gotten off ground and is posting double digit growth rates — stagnation might happen sooner than you expect. But this is not all bad news: while the S curve spells trouble for many companies, it also means opportunity for those that find a way to defy it.

In this post I’ll demonstrate this dynamic with a simple toy model and run some scenarios to evaluate how marketing and retention affects the S curve.

The Toy Model

The model I’ll use for the various scenarios is a simple cohort-based model. Note that (a) I’ve abstracted away the details as much as possible (it’s a toy model after all), and (b) the model does not describe all types of B2C businesses.

• Each month, a new cohort of customers arrive. The size of the cohort depends on the natural rate of acquisition and marketing spend.
• Once the customers have made their initial purchase, their churn pattern follows a simple exponential curve.
• The revenue for a given cohort in a given month is calculated by multiplying the retention rate by price and engagement, where engagement is the average number of transactions customers make during a month when they’re active.
• The total revenue for the company for a given month is calculated by adding up the revenue curves for all the cohorts that arrived before or during the month.

Predicting future growth for a single cohort

Scenario 1 — Baseline Growth

First, let’s run a five-year growth scenario for a fictitious company, using the assumptions listed below (for those that are interested in playing with the inputs, it’s easy to change the values in the code).

• The churn rate is 15% after the first month and then 10% for each subsequent month. This means that the monthly retention curve looks like this: 100%, 85%, 77%, 69%, …
• The average price of a transaction is $30 and active customers make two transactions on average in a given month. The gross margin is 40%. (Note that if we combine the survival curve with price, engagement and gross margin, we get a two year net LTV of $210.)
• The company consistently allocates 20% of revenue to marketing.
• The marketing elasticity is 30%. This means that if we increase marketing spend by 10% we get 3% more acquisition. It also means that marketing has diminishing returns as spend increases.
• Not all acquisition is due to marketing. For example, at a bare-bones monthly marketing budget of $40k, the company will still acquire 24k new organic customers each month. This is due to word of mouth, PR, etc.
• The company has found a product to market fit and moved past the initial part of the S curve.
• Last, but not least, I’m not assuming any erosion in cohort quality over time.

Let’s see how it plays out:

(Recall that the model does not include the early part of the S curve)

After growing rapidly during the first three years, the company hits a plateau — growing only 4.4% from year 4 to year 5. Despite hitting a top line of almost $1B in year 5, most investors would see this trend as a red flag.

Why is this happening? The short explanation is that absolute number of customers churning is outpacing acquisition over time. This is the essence of the tyranny of the S curve!

In order to see this, let’s start by looking at acquisition cost over time:

The left chart shows the average blended CAC — which is simply marketing spend divided by the total acquisition volume (paid+organic). The chart to the right shows the marginal incremental CAC — i.e., cost of acquiring one more paid customer at the current level of spend.

Clearly, due to the aforementioned diminishing returns, acquisition cost is going up as marketing spend increases (recall that marketing spend is pegged to revenue in this scenario). Also, as a side note, the marginal CAC chart above shows that, after year one, the marginal cost exceeds the two year net LTV. This is why looking at the marginal efficiency is so important and relying solely on the blended average CAC can be misleading.

Next, let’s look at churn. As the total customer base grows and cohorts age, the absolute number of customers churning will grow steadily:

Combine this with the rising CAC and we have a situation where churn is outpacing acquisition — despite the steady increase in marketing spend. This illustrated in the chart below:

Churn divided by acquisition

Scenario 2–Increase Marketing Spend

Now let’s see what happens if we increase the marketing allocation to 30% of revenue after year 3. This is fairly easy to do; just crank up the dial and let the ad impressions flow.

(Recall that the model does not include the early part of the S curve)

The good news that, in this scenario, the company is able to hit $1.14B in revenue in year 5 — 17% better than the baseline scenario. The bad news is that we only managed to delay the flat part of the S Curve. Also, the CACs are exploding. This is what happens when you’re addicted to marketing!

Scenario 3–Boosting Retention

In this scenario I’m assuming that the company is able to decrease the monthly churn rate from 10% to 8% for all cohorts joining in year 3 and onward. The initial drop off rate of 15% remains the same as the previous scenarios and the monthly marketing spend is copied from scenario 1.

(Recall that the model does not include the early part of the S curve)

The good news is that this scenario produces similar revenue growth to scenario 2, but without exploding the CACs. The bad news are that (a) churn is still outpacing acquisition, and (b) retention is not a lever we can simply pull when we need it. Increasing retention is difficult since the majority of churn is due to reasons that you cannot control. It can also be expensive if you’re using price as a lever.

Putting it All Together

The S curve is real . Even though stagnation can seem unthinkable during times of rapid growth, young companies must prepare for a paradigm where churn starts to outpace acquisition.

Here’s a summary of the main learnings from the scenarios:

• Boosting retention certainly helps to sustain growth rates, but it’s no easy feat and can’t be accomplished overnight.
• Marketing is an easy lever to pull and will “delay” the flat part of the S curve. But it also creates an addiction that isn’t sustainable and CACs will accelerate. If we do choose to increase marketing spend to drive growth, it should be coupled with strong retention efforts to get long term benefits.
• Perhaps the best way to drive continued growth is to think big! Find new S curves to climb by entering new markets and launching new business lines.
• Last, but not least, don’t rely solely on blended average CACs when tracking marketing efficiency; marketing is not responsible for all acquisition and marginal costs are almost always higher than the average costs. However, measuring marginal costs requires statistical modeling and continuous experimentation.

If you’re interested in playing with the model, go to: https://github.com/klarsen1/Pretend_Company_Growth. The file called scenarios.R has the code to run the scenarios in this post.

In the next part of this blog post series I’ll use this model to explore the trade-off of price versus marketing to drive growth.

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