In this post, I will discuss features of freemium products, which I work with mainly, and introduce the complex parameter F-Growth, which is useful both for internal and external assessments of freemium products, especially from the viewpoint of investing in and marketing them. 

The business model based on the freemium principles (this term was coined of the words “free” and “premium”) involves maximum propagation of the product in the related market, and capture and retention of the maximum possible number of users. 

As a rule, there two business approaches to creating freemium products are used: 

1. Purchase and other paid-for attraction of users (traffic). Partial monetization of the traffic by selling additional paid-for functionality. New users are attracted by using the earned profit.
   Within this approach, the key factor is cash: it is necessary to have a successful monetization model, involve a significant percentage of users in paid-for mechanisms, and maintain the balance of the incomes from the existing users against the costs of attracting new users. It should be remembered that the costs of attracting new users can be significant, and there is a risk of being unable to meet them using the monetization income.
   The advantages of the approach are that first money starts to be earned fast, and the virality K-factor can be less than unity. 
2. Involvements of users in product promotion: Virality. One should ensure that the virality coefficient (K factor) is significant, which is complicated and, for some products, unachievable. In the framework of this approach, the user base grows exponentially up to saturation. 

In what follows, I will be talking about the second case, which I call “virality-based freemium approach”, since it is most interesting for me. 

Freemium products are characterized by the following models of interaction with the user base: 

1. in-app cycle — the core cycle of the application, the basic function, which corresponds to a user’s choice of the application (in our case, studying a foreign language with a help from a native speaker); 
2. monetization cycle (the smaller circle labeled “$” in the Figure) — supplementary cycle involving the most venturous and loyal users and providing them with additional functionality. This cycle is smaller, since not all users get involved (this is a feature of the freemium business model); 
3. Retention cycle — withdrawal of users from the system and their consequent return to the system. Successful return and retention is ensured by a set of actions, starting from e-mailing and sending messages via social networks and other communication channels to remind users about events taking place in their absence, and ending at gamification. 
4. Viral cycle — existing users invite new users from external environment (e-mail, social networks, blogs, forums, personal sites, applications, and other communication channels), accommodation of new users included. 

David Skok, a successful venture capitalist, in his paper The Power of Free, The Entrepreneurs (December 2009) mentions the following important aspects of freemium products aimed at viral growth: 

“..in a typical business the single biggest expense is sales and marketing, and recognize that offering a free product/service is an extremely smart way to acquire customers at a low cost that can then be monetized in a different way.”  “Another powerful effect of using the free strategy is that it usually results in a far larger customer base using the free products, who become proponents for your company. This expanded footprint or market share can have a huge effect on the price that acquirers or investors are willing to pay for your company, as they recognize that even though these customers have yet to be monetized, they represent a great potential for future monetization. Twitter and Facebook are two perfect examples of this.”


For practical purposes, I calculate the local k-factor as the ratio between the number of users attracted by viral methods within a conventional period and the calculation base, which can be the number of only new users (dNU), all users within the period (dU) or only those users which stayed active within the period:

local K-Factor = dIU / dAU

the term “k-factor” is borrowed from epidemiology, where a virus having a k-factor of 1 is in a "steady" state of neither growth nor decline, while a k-factor greater than 1 indicates exponential growth and a k-factor less than 1 indicates exponential decline.

The k-factor, which is commonly called the viral coefficient in literature, can be calculated as the number of invitations sent by each user, which is multiplied by the ratio of conversion of each invitation to a user. For example, if the average number of invitations is equal to 5, and the invitation conversion ratio is 20%, then the k-factor is k × 0.2 = 1 (the k-factor with no allowance for the period is called the “global k-factor”). 

IPi =  IU / i  
(Ratio of invited users and the number of invitations, where IU is the total number of the invited users, and I is the total number of invitations)

AiPU= i / U  
(Average number of invitations per user, where I is the total number of invitations,
and U is the total number of users)

K-Factor = AiPU* IPi  
(Global k-factor)

The dynamics of the k-factor reflects changes in users’ behavior, the way they react to appearance, activation, or deactivation of various viral mechanisms, which involve them in inviting new users, and how well these mechanisms are apprehended. 

Thus, for practical purposes the authors use the local k-factor calculated daily on the basis dAU, i.e., the active user base. 

It is important to understand here that if the k-factor is less than 1 (e.g., 30%), then in the absence of retention (i.e., when the loyalty of the existing users is zero), the growth of the system dies out. At best, this viral mechanism counterbalances partially the loss of users which results from the normal loyalty drop in the retention cycle. This k-factor increases the efficiency of paid-for user attraction. For example, 100 paid-for users take part in the operation of the viral mechanism and invite 30 users more. This reduces the averaged involvement cost and cuts budget expenses. 
If the k-factor exceeds 1, the user base grows exponentially. 

Interconnectedness of Virality, Retention, and Monetization

All three parameters (Virality, Retention, and Monetization) are interconnected. Higher-loyalty users are more likely to participate in the viral mechanisms and get involved in Monetization. 

Despite the fact that they compete in attracting user’s attention, these mechanisms can spur each other, and various techniques, such as gamification, can serve both Monetization and Virality. 

I wrote about that in the article called “PARADOXICAL MOTIVATION”

For example, if virality is strong, and retention is weak, the growth of the user base due to successful virality will be counterbalanced by the losses in this base to low loyalty of the users. And contrariwise, weak virality and perfect retention will make the product and its user base stagnant and, in the long run, result in a loss in the competition. 

The coefficient of inherent growth of the product user base (F-growth) can be expressed as a sum of the viral coefficient (k-factor) and the retention coefficient (k-retention): 

F-Growth =  K-Factor + K-Retention 

In my opinion, this is the main formula for the growth of a virality-based freemium product. One can see that it does not allow for alternative methods of client involvement, such as paid users, organic users, i.e., those who come in via search engines, world-of-mouth, or high brand awareness. 

K-retention is always less than unity in long time intervals, since there is no product capable of retaining 100% of its user base at all times. 

Local K-retention  =  (dAU - dNU) / dAU-1  

where dU is the user base on a given day, dU-1 is the user base on a previous day, and dNU is the amount of new user in this period. For calculation, it is convenient to allow for the active user base only. 

For example, if the viral coefficient is equal to 20%, and the retention coefficient is k-retention = 90%. i.e., 9 of 10 clients use the service on the next day, then F-growth will be equal to 0.2+0.9 = 1.1. Such a system will grow independently, day after day adding 10% of its user base per day (or any other calculation period). 

F of inherent growth can be represented as: 

F-Growth = (dAU – dNU + dIU) / dAU-1, 

i.e., it is the ratio of the user base of the following period with no allowance for new users, but allowing for those invited by using viral methods, and the user base of the previous period. 

If dNU and dIU are equal, i.e., all new users are attracted due only to viral methods (there is no paid-for or organic traffic), then F-Growth =  dAU / dAU-1 .

Conclusions:
If the growth coefficient (F-Growth) is less than 1, the product cannot grow and loses its user base with all that it implies for the project. 

On the other hand, if one achieves the value of the growth coefficient exceeding 1, the product starts growing exponentially. This is the absolute target, when the product team achieves non-paid user base growth. This is necessary for project capitalization which exceeds investments in buying of the user base. 

Thus, when creating a freemium product, it is reasonable to market it and check the virality- and retention-related mechanisms using small volumes of the paid-for or attracted in any other way user base, more so since these mechanisms can be assessed statistically and analyzed. Having achieved a positive value of F-Growth, one can mobilize a round of venture investments and advance the product to a major market. In the opposite case, if the project is incapable of increasing its user base, i.e., F-growth < 1, the raised money will be wasted.

I start with this Wikipedia ” entry about k-factor on purpose. Certainly, in theory it is all right. However, this is just a high-brow theory. In real life, this k-factor should be calculated during the entire lifetime of a project, from the launch till the closure. This formula corresponds to the “global” k-factor, which nobody really needs, aside from the security service of a venture capital fund who try to find out why this or that startup has gone dead. 

In real life, what we are interested in is the “local” k-factor (the term is borrowed from “Freemium Economics” by Eric B. Seufert), i.e., the value calculated during a certain period of time. For example, within my approach, I use weekly factors, thus using the “weekly k-factor”. Moreover, in our case the statement that the project grows or collapses exponentially, if the value of the k-factor exceeds or falls short of unity, respectively, is wrong!

However, Richard Fond, the author of the Bliss Drive blog, and the Wikipedia entry, and even Harry Harrison in his story called “The K-factor” fail to allow for many factors. Borrowing the term blindly from nucleonics and epidemiology, they assume that merely “infecting” a newcomer is sufficient to expand the user database. In reality, how a project retains existing users is more important than how fast it grows. And the ways, which are used to retain users, should also enter the formula. 

K-factors of actual projects rarely exceed unity, for long periods of time, anyway. A normal current value of the K-factor for a successful and growing project at any given time moment is equal to 10%, 20%, or 30%, and the project is thriving at that, despite the fact that it should collapse, according to the classical formula. But why? Because it is not a nuclear explosion or a plague in a population of mice, where the death rate is 100% of the infected animals. The thing is that in the normal project, the “infected” users continue using the project and even attract new customers in the following time period. This can be regarded as a different factor, namely, k-retention being the ratio of the number of the users, who use the service repeatedly during the current period, as compared with the previous period. This parameter will be always less than unity, since some users will be lost anyway. Even in such environments as a prison or North Korea, this factor fails to reach unity due to release of inmates, mortality, and escapes. 

The real, “fundamental” coefficient, which shows the natural dynamics of the project, is the sum of the above-specified factors, specifically, k-factor and k-retention. If the total exceeds 1, the project grows, if it is less, the number of loyal users decreases. 

Additionally, I call for using only “active” users when calculating these factors, i.e., those who, rather than being just passive visitors, perform some purposeful actions typical of the project, game or service under consideration. For example, for a drawing service, it is creation and saving of a new sketch, for a game, playing through at least one level, etc. Only then we will obtain unbiased evaluations of our parameters. 

For instance, if we create a virtual prison, we should count only the prisoners who have real prison terms, rather than adding all their relatives, guards, controllers, investigators and lawyers. The latters are random factors in this game. 

Fair and equitable calculations will show that for a good project, the k-factor will equal to about 10% (if it is higher, accept my congratulations!), and the k-retention, to about 90%. The sum of these parameters will yield the sought-for value of 1, the stability level, when the project neither grows, nor withers away. The only thing to be done here would be to increase at least one of the parameters by 1% to make the project to increases by 1% daily or weekly. 

It is known that the daily growth rate of 1% yields a 37-fold increase per year. ☺

PS: I call the sum of the above-said two factors the “f-growth”

The figure shows a typical online application diagram. There are three pathways for the user to choose from, “A”, “B” and “C” (invite friends to earn minutes to learn, spend minutes by learning and teach to earn minutes). Plus we have added a case “D” – to just buy minutes for real. The result was not long coming. People did not buy anything, instead they have become more active to invite friends to participate in our edutainment as “teachers”. More specifically, virality growth increased 1.5 times and there became 8% more teachers than students.

As a result, the "F-growth" factor, which totally reflects these parameters, increased.

This situation resembles one study about the visitors of the bar, who drank significantly more beer when offered free spicy chips. You can draw your own conclusions. In my opinion the behavior of people is obvious, and thus predictable.

In fact, we certainly not invented it, but the idea of a double bonus works perfectly, encouraging people to cooperate. 
Great motivator for virality. 

Invite a friend, get a bonus, not only for yourself. Both participants get a bonus.