Three curves and a lie

January 2026

SiriusXM has 33 million subscribers. Every year, 18% of them leave. That’s roughly 6 million people walking out the door annually, which means SiriusXM has to acquire 6 million new subscribers before it even breaks even on subscriber count, let alone grows.

Most PMs look at that number and think: retention problem. Fire up the cancellation flow. Offer a discount. A/B test the win-back email sequence. Classic stuff. And sure, that thinking isn’t wrong, but a 2025 paper in the International Journal of Research in Marketing, by Barak Libai (Tel Aviv/MIT Sloan), Eitan Muller (NYU Stern), and Verena Schoenmueller (ESADE), argues it’s dangerously incomplete.

Because those 6 million churned subscribers didn’t just stop paying. They took something else with them.

The framework nobody’s using

Here’s the core argument: when you build a subscription product, you’re not really building one growth curve. You’re building three, and they all behave differently.

This sounds obvious when you say it out loud. Of course there’s a difference between someone who signed up once and someone who’s actively using your product. But here’s the thing: most growth models, including the classic diffusion models that underpin how VCs and boards think about TAM and market penetration, were built around physical products. They track adoption events. You buy a car, you’re an adopter. You don’t un-buy the car.

Subscriptions don’t work that way. An adopter can leave. And when they do, the implications ripple in ways that the standard model doesn’t capture at all.

The hidden tax on future growth

This is the part that should make you sit up. The paper introduces a distinction between two types of churn that most companies conflate into one:

Overt churn is the customer who leaves. You can count them. They show up in your churn rate. You can try to win them back. This is the churn everyone measures.

Covert churn is everyone who never signed up because someone else left. You can’t count them. They don’t show up anywhere in your dashboard. They are invisible.

“Churn will impact the adopter curve because the number of users affects growth due to social influence: word of mouth, observational learning, network effects.”

Libai, Muller & Schoenmueller, IJRM 2025

Think about what this means in practice. When someone cancels Spotify, they don’t just stop paying. They stop talking about Spotify. They stop being the reason their friend signed up. If they go negative, telling people the product wasn’t worth it, they become active drag on acquisition. The word-of-mouth engine doesn’t just slow down. It can start running in reverse.

Back to SiriusXM: those 6 million churned subscribers represent 6 million voices that are no longer in the market evangelizing the product. That’s covert churn. It doesn’t show up on a retention dashboard. It shows up, months or years later, as a slower-than-expected growth curve that your growth team scrambles to explain.

Why Netflix’s password problem was actually a churn story

Here’s a real-world case the paper doesn’t mention, but maps cleanly onto its framework. When Netflix cracked down on password sharing in 2023, the conventional read was: they’re converting freeloaders into paying customers. Which was true.

But the less-noticed risk was covert churn. Password sharers were users: people embedded in Netflix’s product, watching content, building habits, forming opinions. Kicking them out of the ecosystem didn’t just eliminate a free rider. It removed a social signal. A college student who watched Netflix on a parent’s account is someone who recommends Netflix, argues for it over Disney+, and eventually becomes a paying subscriber when they get their first apartment. Severing that relationship early in the funnel has a cost that doesn’t show up for two years.

Netflix ran the numbers and decided it was worth it, and the subscriber growth proved them right, at least in the short term. But the paper’s framework gives you the vocabulary to have that conversation explicitly, rather than treating password-sharing crackdowns as a pure upside play.

The cashflow trough problem

There’s a third wrinkle the paper surfaces that’s particularly brutal for early-stage products. In subscription businesses, you spend money to acquire a customer before you make money from them. Acquisition costs hit day one. Revenue trickles in over months or years. This creates what they call a cashflow trough: a dip between when you pay to get someone and when they’ve generated enough revenue to cover that cost.

High churn makes the trough deeper and longer. If customers are leaving before they’ve paid back their CAC, you’re not just losing future revenue, you’re locking in a loss on every churned customer. And the faster you grow (which means acquiring more customers), the bigger the trough gets.

The paper puts it starkly: the shift from reporting customer retention to reporting Net Revenue Retention (also called Net Dollar Retention) across the SaaS industry isn’t just metric fashion. It reflects a dawning recognition that the money curve is what actually matters, and that you can’t read it from the adopter curve alone.

What this means if you’re actually building something

Let’s be concrete. Three things fall out of this framework that should change how you operate.

First: your churn rate is understating the cost of churn. If you’re calculating churn impact as “lost customer × average LTV,” you’re only counting overt churn. The paper’s argument is that every churned customer also reduces your market potential by eliminating their word-of-mouth contribution. For products where virality matters, which is most consumer products, the true cost of a churned customer is higher than the CLV model suggests. Probably significantly higher.

Second: early cohort quality matters more than early cohort size. The paper finds that high churn reshapes the entire market diffusion curve: pushing the peak later, changing the ratio of early adopters to mass market. In plain English: if your early adopters leave, you don’t just lose their value. You slow down the momentum that converts a product from “early adopters use it” to “everyone uses it.” This is why obsessing over Day 1 and Day 7 retention isn’t just about LTV. It’s about whether you ever cross the chasm.

Third: freemium users are not freeloaders. The paper specifically flags that in freemium models, free users sustain the ecosystem that paying users depend on. Spotify’s free tier isn’t just a conversion funnel, it’s a social proof machine. The discovery playlists, the shared links, the “did you hear this?” conversations: those come from free users. Churning them with heavy-handed conversion pressure or ad load can damage the paid tier’s growth in ways that only show up quarters later.

“Don’t view churn in isolation. It’s not just about the value of the person leaving, it’s about their effect on the entire network of customers.”

Barak Libai, via Up Next Podcast

The metric you actually need

So what do you do with this? The paper doesn’t hand you a new metric, it’s academic, not a dashboard template. But the implied framework is fairly clear: you need to track all three curves, separately, and understand how churn is affecting each one.

For most teams, that means: subscriber/user count (curve 2), NRR or revenue per cohort over time (curve 3), and, hardest to measure, referral rate and virality by cohort (the proxy for what covert churn is costing you on curve 1). If your referral rate is declining for a specific cohort, that’s an early signal that churn from that cohort is starting to suppress future adoption. You’re seeing the covert effect before it shows up in headline numbers.

The companies that do this well, Duolingo is a good example, or Notion, treat retention not as a single team’s KPI but as the organizing logic of the entire product. Every feature decision gets filtered through “does this keep people in the product long enough to become advocates?” Not because advocacy is a nice-to-have. Because advocacy is what fills curve 1. And without curve 1, curves 2 and 3 starve.

The thing most PM dashboards miss

Here’s the simplest version of what this paper is saying: your churn rate is a lagging indicator of a leading problem. By the time high churn shows up in your metrics, the covert damage, the missed word-of-mouth, the slowed diffusion, the suppressed market potential, is already baked in. You’re reading the financial statements of a fire that happened six months ago.

The companies that get this right don’t just measure churn. They treat retention as a compounding asset. Every month a customer stays is a month of potential referrals, network effects, and social proof that brings in customers you’d never have reached with paid acquisition. And every month they leave early is a month of that value that simply never gets created: not for them, not for your growth curve, and not for the people they might have brought with them.

None of this means “obsess over retention at the expense of acquisition.” The paper’s point is subtler: the two are more connected than most models assume. Your ability to acquire future customers is partly a function of how well you retained past ones. The user who never churned is still out there, quietly making new users possible.

That’s a different way of thinking about what retention is for.

Source: Libai, B., Muller, E., & Schoenmueller, V. (2025). “The effects of churn on the growth of subscription services: Adopters, users, money.” International Journal of Research in Marketing. DOI: 10.1016/j.ijresmar.2025.03.005 · ScienceDirect →