Invisible Asymptotes: The Part of the Growth Curve No One Talks About

Eugene Wei was Amazon’s first analyst in strategic planning, which means he focused on forecasting the company’s future—anywhere from a month to a decade down the road.

He recently wrote an article, Invisible Asymptotes, about what he learned in that role. I strongly encourage everyone to read his full post because it’s one of the best things I’ve read this year. It is a long read, so I thought I’d distill some of his major points. Below is my simplified take on Eugene’s complex and thought-provoking article.

Eugene starts off by saying that one of the most difficult aspects of a financial analyst’s job is to forecast a company’s adoption rate. Why? Every successful business experiences an S-curve. Most companies and their investors tend to focus on when they’ll hit the inflection point towards hockey-stick growth. But, few think about the shoulder that comes soon after; the point when, inevitably, a company’s growth flattens.

At Amazon, Eugene helped identify that shoulder—an “invisible asymptote,” which he defines as a ceiling that a company’s growth curve will eventually bump up against if it continues down its current path.

For Amazon? That ceiling came down to one thing: shipping fees. People strongly dislike paying for shipping fees. In an effort to address this pain point, the e-commerce giant tested out multiple models, such as: adjusting their checkout process, offering Super Saver Shipping (i.e. receiving free standard shipping for orders of $25 or more), and ultimately, introducing Amazon Prime.

While Amazon Prime may seem like an obvious idea in hindsight, upon launch, the concept of getting people to pay more than $100 up front for a year of free shipping (as well as myriad other—but less well known—benefits) was a crapshoot. Bezos, by the way, decided to forego testing and just go for it with Amazon Prime, employing a “fix it later” mentality.

Amazon Prime has worked out incredibly well for the company; as Eugene puts it, “on net, the dramatic shift in the demand curve is stunning at game-changing.”

Here’s where Eugene’s analysis of invisible asymptotes gets juicy, though.

He notes that for many companies, it’s not as easy to identify what will cause growth to level off—or when it’ll happen. Social networks, for example, don’t necessarily have clear and trackable metrics like TAM (Total Addressable Market). What exactly is the shoulder of the curve for a company like Twitter, Snapchat, Instagram, or Facebook?

He goes on to break down each of those four big social networks and identify their potential asymptotes from a macro perspective. Here were his thoughts about each company:


Twitter’s new user growth has leveled out—that’s obvious to anyone paying attention. Why is it happening? And can the asymptote Twitter is experiencing be overcome?

There’s a theory, popularized by Geoffrey Moore in his 2006 bestseller Crossing the Chasm, that one way to propel product growth is by getting more users to experience what power users or early adopters experience.

In the case of Twitter, Eugene thinks this theory is wrong. To cut to the chase, he doesn’t think any more meaningful user growth is possible. In his words, “the core experience of Twitter has reached most everyone in the world who likes it.”

That said, he views Twitter as two separate things: a product and a service. The former is the platform us users interact on. The latter is a public messaging protocol.

It’s the product portion of Twitter that Eugene believes doesn’t have any room left to grow.

The service portion, however, has potential. But, to unlock that potential, Twitter likely needs to nourish a third party developer program. They have one—but it’s hard to say they’ve nurtured the growth of it. There are a number of reasons Twitter took this path, and it likely has to do with the tech company wanting to own all of its ad inventory and restrict others’ ability to build clones of the Twitter platform through APIs.

To address these concerns, Eugene suggests tailoring a third party developer program to offer two options:

  1. For every X number of tweets a developer pulls, they have to display a Twitter-inserted ad unit. The developers get to pull the tweets, and Twitter still gets the benefit of ad revenue.
  2. For every X number of tweets pulled, a developer would pay some fixed fee. This forces the developer to come up with their own monetization scheme—and Eugene believes there are plenty of enterprising developers that could come up with monetizable use cases effectively.

The big lesson? Don’t mistake one type of business for another. If you don’t separate out Twitter the product from Twitter the service, it’s much harder to see that the latter is where the opportunity for continual growth remains. Product-market fit for the social platform itself may have reached a point of saturation, but the service still has boundless potential.

Eugene’s main thesis: If Twitter wants to continue to grow, it has to focus primarily on the service—not the product.


This social media giant has also hit the shoulder in its growth curve. Eugene’s take: It’s less about the product’s feature set and more about a generational divide.

The product itself is not intuitive to use, which actually may have served the company well early on. Part of the reason Eugene thinks Snapchat took off is because it rose to popularity at a time when the parents of younger millennials started joining Facebook. It’s like throwing a party for your college friends and having your parents crash unexpectedly. So, through that lens, it’s easier to see why a service that wiped out your messages and was less intuitive to older generations became so popular with a younger audience.

Snapchat has iterated on their product over the past several years in an effort to make it easier to adopt, and to better distinguish the one-way “news” portion of the site from the two-way “social” function. But, Eugene’s point is that making the Snapchat interface more intuitive and easier to use probably won’t move it past the shoulder of the S-curve in its growth.

Snapchat was built for a younger audience, and trying to broaden its user base to incorporate different generations is likely a futile effort. Even that the default opens to a front facing camera would be a turn off to an older audience that grew up communicating via text. To attract a wider audience would require a total redesign of the product—and that would, ironically, drive younger users off the platform.

As Eugene says so well, “The stronger the initial product market fit, the more vociferously your early adopters will protest when you make any changes.”

Snapchat’s best bet for stimulating growth:

Figure out how to retain and build frequency among their younger users—and plan in advance for how they will get the next generation to engage with the platform rather than adopt a brand new one (similar to what younger millennials did with Snapchat as almost a rebellion against Facebook, which attracts an older audience).


When it comes to Facebook, Eugene starts by saying this:

Because Facebook is the largest social network in history, it may be encountering scaling challenges few other entities have ever seen.”

Eugene talks specifically about the US market in his post—though he rightly notes that one of the reasons it’s so difficult to analyze Facebook is that it serves so many different needs in different countries and markets.

As far as the US market goes, one of the challenges is its enormous scale. I’ve personally noticed that fewer and fewer people I’m connected to on Facebook are sharing. Eugene makes an interesting point about why this might be that I had not thought about before:

The more people you’re “friends” with, the less inclined you are to share—unless you’re a celebrity, marketer, or part of the small group of users who feels oddly comfortable sharing everything about their lives publicly.

Think about it: If you were in one room with your family, friends, acquaintances, business contacts, college friends, clients, and so on…wouldn’t you behave differently than if you were just in a room with close friends, or at a family dinner, or in a business meeting?

The point is this: Facebook defaults to sharing with everyone, but most of us maintain multiple identities for different audiences in our lives. So, as one acquires more “friends,” it becomes increasingly likely that they won’t share as readily. It’s too hard to figure out what to post—and not to post—given a user’s wide audience on the platform.

Another challenge for Facebook? Trolling.

Facebook is less susceptible to this kind of interaction since the model is predicated on a bi-directional friending model rather than a one-way follow model. Still, trolling happens on the social network—it just probably looks more like opinion dissention than impersonal, vitriolic feedback. In short, the more friends you have, the more likely you are to piss someone off or trigger them in an unintentional way when you share your thoughts, feelings, and experiences.

Eugene believes Facebook can get past its invisible asymptote by more effectively utilizing a “groups” function, where users can subdivide their connections in more meaningful ways. In other words, imagine throwing a party—but your family, friends, colleagues, acquaintances, and so forth are all in separate rooms. You don’t have to uninvite anyone, but you still have room to tailor how you interact with each group given the meaning they hold in your life and the identity you assume when you’re with them.


In the case of Instagram, it’s harder to figure out where the company’s invisible asymptote even is. Currently, it is growing without a clear shoulder in sight.

Trolling is a challenge—but less so than Twitter because photos “tend to soften the edge of boasts and provocations.” It still happens, but it’s less likely on Instagram than other platforms. Unless, of course, you’re a Kardashian.

The company has iterated on the product in ways that have likely helped them avoid several asymptotes they otherwise might have hit by now. They include: allowing non-square photos, videos, and more ephemeral Instagram Stories.

Introducing Stories was particularly significant; content creators can share more without negatively impacting a more curated image on their feeds, while also skirting around the guilt associated with posting too much. I’d guess the average user posts more on Stories now than on their actual feed.

The other fascinating thing about Instagram:

There probably isn’t another platform that makes ads feel less intrusive and annoying. As Eugene puts it, “the visual nature of Instagram absorbs the signaling function of social media in the most elegant and unified way.”

Like every product, Instagram will inevitably hit its natural ceiling. What asymptotes might the company be missing right now? One is, potentially, its messaging function. There are rumors that Instagram is considering a separate messaging app, similar to what Facebook did with Messenger. It just might make sense to do this since there is only so much you can do with a single app.

Another possible asymptote for Instagram is the lack of what Eugene calls “structured interactions and content units.” A check-in, for example, would be a type of content unit.

It’s easy to fill gaps in a person’s free time the way Instagram is currently structured—like a never-ending feed. But, it’s harder to demand a person’s time unless you enable them to ingest content in a more structured way. Options help people get what they want faster—and make them feel like they have more control in the process.

It’ll be interesting to see how Instagram iterates on its product moving forward. Is it possible that Instagram will be the Amazon of social applications, ever-growing and amazingly adept at addressing invisible asymptotes before they hit?

It wouldn’t surprise me.

What’s Next for Amazon?

Back to the e-commerce giant. Amazon has made incredible progress addressing the challenge of shipping fees. But, what other barriers to growth should it be prepared for?

Eugene thinks it’s shipping speed.

Now that customers have come to almost expect free shipping, the speed of shipping will likely be the next hurdle.

Bezos said it best in his most recent annual letter to shareholders:

One thing I love about customers is that they are divinely discontent. Their expectations are never static – they go up. It’s human nature. We didn’t ascend from our hunter-gatherer days by being satisfied.”

The other possible growth barrier: stimulating desire. Amazon is built to be a platform of instant search, find, and purchase. Unlike walking into a grocery store or shopping mall, you’re more likely to buy exactly what you came for. Improvements in machine learning are sure to help—but this has been a sticky point for tech companies for a while. The better Amazon gets at sourcing meaningful product recommendations, the more likely users are to buy things they didn’t even know they needed.

Personally, I’ve seen Amazon’s recommendation engine effectively lure me into buying books I otherwise wouldn’t think to buy. But, this hasn’t carried over into other departments on the platform yet. For instance, if I’m buying an alarm clock, Amazon might nudge me into buying a specific one—but it won’t convince me to buy two. Another example: If I came to the platform to buy a knife set, I’m probably less inclined (at least the way Amazon is currently structured) to buy other kitchen accoutrements than if I were walking around a Williams Sonoma store.  

If Amazon can find a way to source better recommendations at the right time, it wouldn’t shock me if the average amount a consumer spent on the platform each year increased in a meaningful way.

What Amazon does next is any outsider’s guess, but given their commitment to being the most customer-centric company in the world, I’d bet they will find interesting ways to plan for and breakthrough the potential asymptotes that lie ahead.

How do you identify your invisible asymptotes?

Eugene offers up a few strategies you can use for identifying your own invisible asymptotes:

  • Ask your customers. It’s true that customers can’t always articulate what they want, but they are very good at sharing what they don’t like or want. It’s your job, then, to take your customers’ frustrations and find viable solutions to improve or work around them. Customer research isn’t a foolproof strategy, but it will help you get a more accurate picture of the problems you should focus on solving.
  • Look for the limits in your own product. Eugene asserts that one useful question to ask is this: “Why doesn’t every person in the world use your product or service?” You’re likely to come up with all sorts of answers—and the end result will be more clearly defining the borders of your total addressable market (TAM).
  • Product intuition. This strategy comes with a major asterisk because it’s so rare to execute, but here it is: It’s possible to avoid invisible asymptotes just by creating an insanely brilliant product. Steve Jobs is the godfather of product intuition—but, of course, so few have that same special product intuition Jobs had. Eugene’s advice? Employ a healthy mix of intuition backed by data and feedback.
  • You can’t over serve on user experience. Given the ever shifting and increasing expectations consumers have, it is relatively impossible to serve them completely or understand them fully. But, it’s important to stay engaged and try. The continual effort to put customers first and always change in an effort to stay relevant will get you as close as you can to meeting user wants and needs.

In addition to following Eugene’s advice on identifying your invisible asymptotes, I’d add one more question that I think it’s important for all founders to ask themselves:

What would the most ideal customer experience entail if the cost of us providing it were zero?

It’s a powerful question because it forces you to think through how to optimize the product itself, rather than lean on costly acquisition and retention strategies. It’s not that the latter isn’t important, but when it comes to anticipating why and when your growth might stagnate, you have to look at the root structure of your product and business model.

I enjoyed Eugene’s article because I think it gives language to a challenge all successful companies inevitably face but rarely think about and plan for: the leveling out of growth. Hitting an invisible asymptote isn’t a matter of if but when—which is why Eugene’s article is such an important read for all founders. Again, I can’t recommend reading the full version enough.

Here was the biggest takeaway for me:

If you want to grow a successful company, you have to plan in advance for the invisible asymptotes. They won’t always be easy to identify, and they often won’t be easy to change. But, it’s better to start the hard work of figuring out what they are—and iterating on your product accordingly—now.

The shoulder of your company’s s-curve will eventually come—and it’s better to be prepared for it sooner rather than later.

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