S-Curve Expansion: A New Framework For Growth
Guest Post

S-Curve Expansion: A New Framework For Growth

Daniel Shi
October 6, 2022

We're excited to feature Daniel Shi as a guest writer - Daniel Shi is an angel investor. Previously, he spent six years as an operator at Remitly, an international payments company, from early stage until IPO. He's also worked at Tencent and Amex Ventures, investing in gaming, e-commerce, and Fintech.

Recently, he wrote an article Growth Frameworks, and we think this could benefit more founders.


A lot of recent attention in the news has been around “What happens when companies slow down?” From giant public companies to hot startups, many of the headlines circulating have been around slowing growth, hard pivots towards profitability, and layoffs. Obviously, the law of large numbers makes it difficult to continuously compound at the same rate forever. But somehow, we always end up being caught off guard. Why is that?

My theory from talking to many founders and operators is that many have the wrong framework for thinking about growth. Things go well the first few years, but then in the out years, they are suddenly surprised when growth slows. Founders and investors start to ask existential questions. Employee morale starts to get shaky.

“Why did we slow down?”

“How did this happen to us?”

I think if a startup can reframe the way that they think about growth, they can see around corners and start to make investments that sustain growth in the longer term. I think a better, but under-appreciated, way to think about startup growth is that it is an attempt to stack S- curves.

To begin with, let’s think about what the typical startup growth slide looks like. It is usually something like this:

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What’s wrong with the above? First of all, where does the line stop? It certainly can’t continue linearly forever, and definitely not exponentially. Clearly, if you extrapolate far enough into the future, there needs to be a flattening of the line. But “exponential growth” and “the hockey stick” have become synonymous with startup growth.

Enter, S-curves. Also known as “sigmoids”, they are represented by what’s known as a logistic function as opposed to linear or exponential functions. They start off flat, shoot upwards, then start to slow down, and eventually level off at some upper limit. (Fun fact: sigmoids are also a key part of several machine learning algorithms.)

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This chart maps very well to the lifecycle of a startup. The initial flat line is the search for product market fit. Assuming the startup is able to find it, then it starts to experience growth as customers clamor for their product. And that’s usually when the first slide gets drawn and the startup begins pitching investors. The exponential curve is actually just the left hand side of the S-curve.

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Eventually, they will hit the inflection point in the middle of the S-curve and start to slow down. The reason that the line starts to flatten can be varied:

  • Competition starts to heat up. Maybe you are a disrupter in a space, but then incumbents start to notice you and react. They may react slowly at first, but eventually they learn how to adapt and slow you down.
  • You may hit a natural saturation point for your product in the market.
  • Even for companies that are monopolies, you eventually acquire all of your customers.
  • The cost of acquiring the marginal customer is higher than their LTV.

And that’s when the startup needs to start thinking about different ways of stacking on S-curves. Because what looks like a continuously growing business is in actuality a series of different S-curves stacked on top of each other.

It is impossible to violate the “laws of physics”. Meaning, for a linear (or exponential) curve to continue up and to the right forever. But it is possible to continuously stack new S-Curves over time, so that the sum total of your business continues to grow.

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But, how do you think about the individual S-curves and how they fall into the lifecycle of a company?

Reflecting back on my time at Remitly, I would propose a generalized framework around “S-curve expansion” that might be useful for founders and operators to think about where they are at and how they should be investing their resources. They are as follows in order of increasing difficulty and risk:

  • Segment expansion
  • Channel expansion
  • International expansion
  • Product expansion

Segment Expansion

Segment expansion is taking the same product from one set of customers, and trying to generalize it to another set of customers. For example, let’s say you have a consumer product business that’s well suited to Gen Z. It could quickly be expanded to Millennials. Or say you have a B2B business. A common form of segment expansion would be to go from “mom and pop” businesses towards “mid market” companies. I would also argue new payment methods is a form of segment expansion. The product and messaging may change, but still stay largely the same.

Channel Expansion

Channel expansion comes from expanding to different customer acquisition channels. Many tech companies follow a path of starting on Google AdWords, then Facebook, and then YouTube. The “channels” may also take the form of strategies. Meaning, they may start off with referrals or a waiting list mechanic that is “zero CAC”, but then they will eventually start to expand into paid strategies, which may require more robust analytics and different talent. The product stays the same.

International Expansion

Next is international expansion. This was actually an area I worked on at Remitly and enjoyed: helping launch our China and European markets. Now, you are taking a product and marketing strategy that works in one country, and searching for other markets where that same strategic combo can work. These expansions can be really deceptive because they may look like very juicy jumps in total addressable markets, but teams consistently underestimate the amount of localization and competition they will face when they enter those markets. Yet, when done right, it can be incredibly rewarding because then you start to enjoy the benefits of global scale (for customers and talent). Furthermore, your business can become more durable in the face of different shocks.

Product Expansion

Finally, arguably the hardest expansion to undertake is product expansion. This is the one where you need to start and find product market fit all over again. This is very hard. Many companies resort to M&A, as opposed to trying to build from scratch. Even if you are leveraging some shared assets or customers, you are effectively starting over with the search for product market fit. And that search is just as risky and unlikely to happen as the original startup idea at the inception of the company. There will also often be organizational challenges to overcome, now that the startup is now longer a startup anymore, but a scaled company with millions of customers, looking to find that entrepreneurial spark once again. However, successful product expansion can be tremendously rewarding. Look at examples like Amazon Web Services (which positively disrupted Amazon’s margin profile) or Cash App (which gave Square an entire multi-billion dollar consumer business).

Over time, as you stack these expansions, the overall S-curve continues to go “up and to the right”, even though the initial product that sparked the startup's growth may have flattened out long ago.

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Having laid things out, it’s important to be strategic and customer centric as you approach each of these expansions. For each of the above S-Curve expansions, there are risk and reward trade offs to consider. Each expansion takes resources. Those resources may also be coming from other initiatives that are working. The upper limit of those S-Curves may also be quite disappointing as well. Not every expansion is worth it.

S-curves are not a new idea in business by any means. But for whatever reason, I have found them to be rarely used in pitching and operating businesses, especially early stage businesses. Maybe it’s because talking about flattening growth at the jump is a bit of a downer. But hopefully, this will prove to be a useful framework for growth.

This article was originally published on Daniel Shi's LinkedIn.

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