Does your early-stage business rely on user growth to achieve the scale required to reach profitability? Then you need to understand Rτ+Kτ >1. It's a deceptively simple formula that can ultimately determine an early-stage company's success.

Here, we discuss the relationship between retaining users and acquiring new users virally at a rate sufficient to offset the inevitable creep of Customer Acquisition Costs (CAC) and impacts on Lifetime Value (LTV) and baseline profitability.


  • Growth for membership-driven business models is a battle, and the tools and metrics that increase and measure retention and virality are the weapons entrepreneurs need to win.
  • Rτ+Kτ >1 is a simplified way to consider how retention (R) and virality (K) work together to achieve an early-stage company’s growth and profitability.
  • Businesses cannot tackle these crucial metrics in isolation. No virality means your investments in paid growth will eventually become unsustainable, but virality without retention will ultimately result in business failure.
  • By incorporating R+K>1 early in a system’s development, early-stage companies can avoid blowing out their Customer Acquisition Cost (CAC) by implementing strategies and features to retain users, improve Lifetime Value (LTV), and deliver more organic inbound users through viral channels (K).

If you’re not familiar with the math, here’s a brief breakdown. If you are, just skip ahead:

Breaking it down

R = retention of members/users
τ = the period of time under consideration (6 months, 1 year, etc.)
K = coefficient of virality

Let's say I've launched a new app that relies on a freemium model. For the app to be successful, I need to acquire new users. Generally, I can do this in a couple of ways; either organically (users join and use the app without me having to pay to acquire them), or I pay for them (most often through platforms like Facebook, app stores, and Google advertising).

We know 'τ' represents a period of time, let's say one year, and 'R' is the number of retained users during that period. Therefore, 'Rτ' is a percentage (or fraction)—the retention rate over the period τ.

On day one of my app's launch (time, t = 0 months), I acquired 100 users. One year later (t = 12 months), how many people do I have left? Is it 20 percent (Rτ = 0.2)? 50 percent (Rτ = 0.5) ? Or, disastrously, zero (Rτ = 0).

In short, for τ of 1 year, Rτ is the percentage of users I initially acquired that stick around after a year.

Kτ, the coefficient of virality for an app over time period τ, simply answers the question, if I add a user (say by registering him/her) at the beginning of the period, how many new users will that initial user attract to be users of the app (say as registered users) by the end of the period τ?  For example, if you have a chat app, and you bring in exactly 100 initial users at the beginning of the year. At the end of the year, the initial users brought in (say, by inviting their friends to register on the app) 75 new users. Thus, τ = 1 year, and the coefficient of virality for the year, Kτ, is 0.75.

In an ideal world, if my app's retention rate Rτ is 1.0 (or 100 percent), and if the app continues to attract even a single new user at any point of time (i.e., Kτ > 0), then the app's user base will grow because people never leave the app's ecosystem.  (But, of course, there will be churn, and Rτ < 1 in the real world for most useful periods τ would represent.)

Simply put, R+K>1 in the scenario above means whenever I add a new user, and I don't change anything else, the user base will grow and keep growing.

Why R+K is important

Founders who want to build profitable membership-driven businesses need to apply R+K>1 from day one in their system's development, instead of waiting until the business has to start paying to acquire new users, which is arguably an inflection point for profitability if R+K has not been accounted for.

For example, let's say I want to get an app's user base to 500 users in a particular market like Singapore. If R+K is less than one, then I'm not going to reach that number. At this point, it may make sense to pay to acquire the users I want.

Let's assume the app's a first mover in its space, and to begin with, my Customer Acquisition Cost (CAC) is relatively low – say, about one dollar ($1).

I know that for every user I retain, their Lifetime Value (LTV) is $100, so my CAC is only one percent of the LTV of each user. It costs me $500 to acquire five hundred users, and I've generated $50,000 in value. That's a pretty good outcome.

However, the dream run of LTV to CAC rarely lasts.

It would not matter if the LTV/CAC ratio were 100; if you're targeting a specific type of user in a particular market, sector, or keyword grouping, eventually, you're going to hit saturation on platforms like Facebook and Google. At that point, your CAC will start to rise, and margins and the business's profitability start to drop.

How far margins and profitability fall depends on your competitors for the relevant ad inventory. If your business competes with companies more efficient in securing relevant ad inventory, your business could ultimately become unprofitable; i.e., LTV/CAC < 1.

The best defensive stance founders can take against this occurring is R+K>1.

This is why 'K' – the coefficient of virality—is so important. Suppose the app's functions—the hooks that get people to stay and spend time—also do a great job of turning users into advocates and provide them the functionality to share the app or app contents with other people easily. In that case, I'll have a set of powerful tools to increase 'K' and ensure my CAC doesn't creep into unprofitable territory.

Measuring and testing R+K>1

When it comes down to numbers, if it costs you more to acquire a user than you make off them, it doesn't matter how many users you have—you don't have a profitable business.

The scientific approach to cranking up 'R' and 'K' means constantly iterating new hypotheses, running experiments to see what works, reviewing results, tweaking methodologies, and running the process repeatedly.

And, as in science, the quality of your hypotheses and experiments correlates closely with how quickly you yield results.

Some of the most common hypotheses founders should test and measure center around questions like:

  • How can you crank up the viral coefficient (K) of your platform or app via design? Virality can be driven through features, content, incentives, communities, and gamification, to name a few. Consider the best fit for your business model and bake it in at a systems level. We call this approach Viral-by-Design—a deliberate design process that focuses on introducing viral elements into your product/platform. You'll find examples of viral-by-design features in products like Instagram, WhatsApp, Venmo, and Slack. These apps have virality built-in from the ground up, and their very usage drives their viral growth.
  • How can you improve retention? Engagement, user-generated content, and social nets are typically key factors of retention. The more you have of each, the higher your retention.
  • How can you make your product easier to use? Ease of use is a deciding factor in user engagement and retention. Perhaps it’s relooking at your user interface or A/B testing different features to optimize UX. Ease of use will improve retention.
  • Communications: how are you communicating with your current users, and what value are you adding beyond core functions and features? How can you tweak aspects of content and communications as part of the UX/CX to increase retention or make it easier for people to share your product with others? The key here is to build communities that result in user-generated content that drives higher retention and virality.

Importantly, testing hypotheses must originate from first principles: it's crucial to remember the value and pain points you're building your solution to solve and bring measurement back to key results, including LTV to CAC.

Further, in the product/engineering process, to ensure the product makes steady improvements in R and K, a significant fraction of the bandwidth of the product/engineering team needs to be dedicated to building, deploying, and measuring the R and K experiments. One single experiment might not give you the improvements you were hoping for, but a large enough collection of well-thought-out experiments will ... at least statistically.

R+K in action...

A few years ago, when MHV started interacting with a recruiting company, one of the CEO’s concerns was that CAC was a significant fraction of their operating costs. The founder recognized that CAC would continue to rise over time if they did nothing. The team focused on generating content that is very helpful to young professionals; they built communities and relationships with a large user base. In short, they executed a community and content strategy.

The result:
Over four years, the team has lowered the average CAC by about an order of magnitude. At this point, even if paid-LTV-to-CAC goes below 1, the business will still be in good shape.

Relevance to B2B Businesses

We used to think that viral-by-design was restricted to consumer-oriented businesses. That's because we lacked imagination. Over the years, we've seen multiple B2B businesses who have creatively designed how they do business so that their existing customers end up introducing more prospective customers to the company.

For example, when users of Slack form inter-company groups, the users who have not been exposed to the use of Slack get pulled into the Slack ecosystem. We've seen another SaaS business use a similar strategy to get their customers, who are main contractors, to solve their information flow challenges by requiring all their subcontractors to use the SaaS system. The result is that the subcontractors start to get used to the level of project tracking their systems provide. Within a year, they had significantly penetrated the contracting market.

If you run a B2B business, there are enough examples of viral-by-design products in the B2B world that you owe it to yourself to explore the possibilities of building high-virality features.

An email exchange ...

QUESTION: R+K>1 is a great formula; basically you mean to say that you need some virality to compensate for natural churn being non-zero, right? It's such a simple idea but founders should really remember it as a fundamental way to measure growth.  The black magic of virality is usually the product team's main source of angst too.  Sometimes even in our company, things we've counted on to be viral have not been viral, and things we did not expect to have a viral effect have had the inkling of being one.  You're right that experimentation and iterations are really the only way forward.  I am curious as to your thoughts on how to measure LTV in a business whose primary KPIs do not yet include revenue generation? Would you say then get to revenue generation fast, in whatever way, so that you can start measuring LTV?

Yes, churn will be greater than zero.  If you have a set of KPI's that don't include revenues (and hence no LTV measurement) ...  then, actually, you don't have a real business.  Even when R+K>1, when you turn on revenues, will R+K stay above one? We don't know.  It's a complex system.  Whatever KPIs you have, at the very least, you need to have a strong view (perhaps a historically backed view) as how those KPIs can predictably convert to revenues.  E.g. when Facebook was ramping up the first few years, they knew how their engagement KPIs would convert to revenues (ad revenues)...  so they could actually model out LTV without focusing on revenues.

This "R+K" article is just focusing on the belief that even with a LTV/CAC view...  CAC could rise in a way you can't control.  CAC is a function of ad inventory and the market for that inventory.  So LTV/CAC at some point might be < 1.  If/when that happens, you don't have a business.  I.e. a LTV/CAC view of the business is a perspective that gives you insufficient control as to what happens to the business—From this perspective, whether the business is viable is, in part, outside your control.

At least an R+K perspective gives you control ...  Both R and K are functions of product design...  which you control.

Final Thoughts

We see more than a thousand businesses a year, and we are regularly surprised that startups don't track the key parameters required for predictable scaling. Founders need to be aware of the interrelationship between retention and virality and how crucial these are to business growth and profitability.

Ultimately there's no foolproof way of achieving R+K>1; however, by thinking empirically and embracing the spirit of experimentation, entrepreneurs can future-proof their businesses for success.

(2021-09-21 v2.0 added explanation of coefficient of virality.)
(2021-08-10 Deleted "Series A" from title. Fixed titles formatting.)


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