*This is the first part of a four part series of blog posts on viral marketing. In part 2, I present a better mathematical model of viral marketing. In part 3, I show the weird dynamics of viral marketing in a growing market. In part 4, I'll discuss the effects of returning customers.*

Viral marketing is arguably the most sought after engine of growth due to it’s potential to drive explosive increases in the number of customers at little or no cost. There has been tremendous interest in understanding virality in marketing and product development, particularly with the advent of the social web. Unfortunately, efforts to build mathematical models for the business community have not been successful in reflecting reality and offering insights into which factors matter most in achieving viral growth.

In The Lean Startup, Eric Ries defines the viral coefficient as “how many new customers will use the product as a consequence of each new customer who signs up” and declares that a viral coefficient greater than 1 will lead to exponential growth while a viral coefficient less than 1 leads to little growth at all. However, his treatment of the viral coefficient makes no mention of a timescale. Is it the number of new customers an existing customer brings in immediately upon signing up? Or within a day? Or within the entire time that they are using the product?

At ForEntrepreneurs.com, David Skok introduces the concept of a “cycle time” -- the total time it takes to try a product and share it with friends. In doing so, he correctly notes the importance of a timescale as a factor in achieving viral growth. In fact, he declares it to be even more important than the viral coefficient. He first models the accumulation of users in a spreadsheet and then, with help from Kevin Lawler, derives a formula for viral growth:

[latex]C(t)=C(0) (K^{1+t/c_t} - 1) / (K-1)[/latex]

where [latex]C(t)[/latex] represents the number of customers at time [latex]t[/latex], [latex]K[/latex] represents the viral coefficient, and [latex]c_t[/latex] represents the cycle time.

This model depends on the following assumptions, which I’ll address in turn:

- The market is infinite.
- There is no churn in the customer base -- once a customer, always a customer.
- Customers send invites shortly after trying the product, if at all, and never again.
- Every customer has the same cycle time and the cycles all happen in unison.

**Infinite Market Size:**

Since viral growth can be so explosive, the market for a product can become saturated very quickly. As the market becomes saturated, fewer potential customers will respond to invitations, effectively reducing the “viral coefficient” (as it is defined by Ries and Skok). Since market saturation could occur in a matter of days or weeks, we cannot ignore the effect of a finite market size.

**Customer Churn:**

Neither Ries’ nor Skok’s models account for churn in customers -- the rate at which customers stop using the product. Eric Ries treats the concept of churn in his discussion of another engine of growth which he calls “Sticky Marketing” and suggests that startups concentrate on only one engine of growth at a time. While the advice for startups to focus on one engine of growth at a time may be sound, it does not justify leaving this very real effect out of the equations.

**When Customers Send Invites:**

Skok’s model depends on the assumption that each new customer sends invitations shortly after trying the product and then never again. While this may be true for some products, it’s likely that the pattern of sharing depends on the nature of the product and often occurs long after the user has had a chance to try the product and grow to love it.

**Customer Cycle Times:**

How users beget more users via invitations, leading to a compounding user base, is the essence of viral growth. In Skok’s model, users receive invites, try the product, love the product, and invite a batch of new users in synchronous cycles. These uniform cycles correlate conveniently to the columns of a spreadsheet. But in reality, different users take different amounts of time to progress from trying a new product to inviting their friends. The number of users of a product doesn't compound at finite, regular intervals like bank interest. Instead, it ramps up customer by customer. The customers have a distribution of cycle times which are not synchronous, but staggered randomly.

By modeling viral growth as batches of invitations that happen in tandem, Skok effectively conflates the timescale of “try it, love it, share it” with a compounding interval. That is, Skok’s concept of a “cycle time” represents two unrelated timescales:

- The total time between trying a product for the first time and inviting a batch of friends to try it.
- The finite intervals at which the user base compounds.

The reason Skok’s “cycle time” has such a large effect is because it represents a compounding interval, not because it represents how quickly users go from trying a product to sharing it with friends. Furthermore, this compounding interval is an artifact of the assumption that current users invite new users in synchronous cycles. *Thus, the conclusion that “cycle time” is the most important factor in achieving viral growth is an artifact of the faulty "synchronous cycle" assumption in this model.*

The assumption that the number of users compound at finite, regular intervals is further muddled by the derivation of a continuous formula. If current users only invite new users in a batch at the end of each cycle, then how can the number of users ramp up continuously during the cycle? A continuous, as opposed to stepwise, viral growth in usership is only possible if sharing is happening constantly, at an average rate. To model this, we need a totally new definition of a viral coefficient that includes a timescale in the denominator -- the average number of invitations per unit time.

**How this Model Breaks Down:**

Some real world examples contradict the models developed by Ries and Skok. A post at TechCrunch regarding the growth of Pinterest shows that a customer base can grow even with a smallish viral coefficient as long as the churn rate is low. This post from Mashable compares the half life of various sharing methods, showing that even the content shared via methods that have longer half lives get very little traffic once everyone has seen it a few times.

So how can the business community build a more realistic model of viral marketing? In part 2, I present a better mathematical model for viral marketing that uses a better definition of viral coefficient and takes into account churn, finite market size, and continuous sharing.

**TLDR: **Skok's conclusion that "cycle time" is the most important factor in viral marketing is an artifact of faulty assumptions. A better model of viral marketing requires redefining the "viral coefficient".