To master fission, you also have to learn how to build a viral growth model!

Recently, the "fission" gameplay has been the hottest thing in the Internet product industry. With NetEase Cloud Music 's "Your Jungian Psychological Archetype" once again going viral a few days ago, many products are relying on or hoping to rely on fission to achieve user growth .

But how do you analyze and predict the impact of this viral growth on user numbers? We need to build a growth model. Below I will use 5,000 words to guide you through building a growth model step by step.

This article is translated from Rahul Vohra’s series of articles “How to Model Viral Growth”. This series is the most thorough analysis of viral growth models that I have ever seen , so I recommend it to you and hope it can inspire you.

1. What is a viral product?

When we make a product, we need to acquire new users through various channels . But perhaps the most fascinating channel is existing users themselves.

Most of a viral product’s growth comes from existing users attracting new users, either through a simple recommendation (“Check out this product, it’s cool/useful/fun!”) or by attracting another user directly through using the product (“I want to send you money on PayPal!”).

One of the most famous examples of virality is YouTube .

Before it gained significant traffic , you were likely to find YouTube videos embedded on news sites or personal blogs. When you finish watching the video, you'll be invited to email it to your friends, and you'll also be given a code to embed the video on your website. If you don't want to share, YouTube will recommend other videos you might like.

Most likely, you will watch one of these and share it with your friends. Your friends will then watch the video and share it with their friends. Through this "viral loop", YouTube quickly acquired users.

So how do we predict the performance of viral products?

For example: How long does it take to get 1 million users? Can our product reach 10 million users?

To answer these questions, we need to build a viral model.

2. The simplest possible model

Assuming we have 5,000 initial users, how many new users will these initial users bring in?

The common situation is this: some users like our product, some users don’t; some users will invite many friends, some will not; some users may invite friends after one day, while some users may need a week...

If we eliminate all these uncertainties and assume that, on average, one in five users successfully brings in new users in the first month, our viral coefficient is 1/5 = 0.2. Our initial 5,000 users will attract 5,000 * 0.2 = 1,000 new users in the first month, and these 1,000 new users will attract another 1,000 * 0.2 = 200 new users in the second month, and then another 200 * 0.2 = 40 new users in the third month, and so on.

Based on the above calculations, as shown in the figure below: Our users will continue to grow until we have 6,250 users.

Figure 2-1

What happens if our viral coefficient is 0.4?

Figure 2-2

Likewise, we are acquiring users at an ever-decreasing rate. But this time, our growth will continue to around 8,300 users.

What happens if our viral coefficient is 1.2?

Figure 2-3

This time, we are acquiring users at an ever-increasing rate.

In fact, with some simple math, we can deduce the following:

Assuming the initial number of users is x and the viral coefficient v is less than 1, we will acquire users at a decreasing rate until we have x/(1-v) users.
Assuming the viral coefficient is greater than 1, we will acquire users at a significantly higher rate.

Seeing this, you might say, this is easy, we just need to make the virus coefficient greater than 1. But, not so fast...

First, there were a lot of problems with our model, such as: as we acquired more and more users, we would eventually run out of new users to acquire.
Second, true viral growth is extremely rare, and few products can achieve a viral coefficient above 1 for a period of time.

Through discussions with other entrepreneurs , investors , and growth hackers , I’ve come to this conclusion: For Internet products, a sustainable viral coefficient of 0.15 to 0.25 is good, 0.4 is excellent, and around 0.7 is great.

However, we’ve just demonstrated that when our viral coefficient is less than 1, we’ll acquire users at an ever-decreasing rate until we stop growing. This isn’t what we wanted, so what’s missing?

We ignore other channels through which users can be acquired: news, app stores , direct traffic, inbound marketing , paid advertising, SEO , celebrity endorsements, street advertising, etc.

Next, we take these factors into account in the model.

3. Hybrid Model

The hybrid model includes non-viral channels.

Some non-viral channels, such as news, will cause our user count to soar. But other channels, such as app stores, will contribute relatively continuously and steadily to user growth.

Our model needs to be as inclusive as possible and as simple as possible, so we will consider the following 3 non-viral channels:

News: A good press release is likely to attract 70,000 new users.
App store search traffic: App stores can deliver 40,000 downloads per month. But not all downloading users will run, register our app and have a good first-time user experience . Let’s assume that 60% of downloading users have a good first experience.
Direct traffic: Potential users will find our product directly due to word-of-mouth from our existing users, which may result in 10,000 downloads per month. Let’s assume again that 60% of downloaders have a great experience.

Finally, we assume that both app store search traffic and direct traffic will remain constant.

Let’s set the viral coefficient to 0 and see what user growth would look like if our product didn’t go viral at all.

Figure 3-1

By the end of this year we will have about 450,000 users, so let's go viral now.

Figure 3-2

In a good scenario, with a viral coefficient of 0.2, we would have around 550,000 users by the end of the year. With a viral coefficient of 0.4, we would have about 700,000 users by the end of the year. If our product is really great and has a viral coefficient of 0.7, we will have about 1.2 million users by the end of the year.

Amplification factor

The above graph illustrates what I think of as viral growth: it’s not about the viral coefficient v, but the amplification factor a = 1/(1-v). To calculate the total number of users, all we have to do is multiply the number of users acquired through non-viral channels by the amplification factor.

Figure 3-3

This graph shows the incredible potential of the viral coefficient, even when it is less than 1: As the viral coefficient increases, the amplification factor grows hyperbolicly. In other words, as long as we have a good viral coefficient, we can continuously accelerate and amplify the drainage effect of non-viral communication channels.

Problems with the model

Adding non-viral channels to the model is useful, but our model still has significant problems. For example: We assume that the acquired users will stay forever.

But the reality is cruel: users may deactivate, delete or forget a product at any time. Therefore, we need to further optimize the model.

4. Hybrid Model (including churn )

Let’s assume our viral coefficient is 0.2 and we have the following non-viral channels:

Published news, attracted 70,000 initial users
App store search traffic, attracting 24,000 new users per month
Direct traffic, bringing in 10,000 new users per month

In the model, let’s assume that there is a 15% churn per month, with the following data:

Figure 4-1

After an initial spike in users from our press release, our growth seemed to slow. In fact, even if our non-viral channels continue to bring in new users and our viral channels continue to exert their amplification effect, our growth may stop completely, as shown in the figure.

What exactly happened?

To make the effect more obvious, let’s set the viral coefficient to 0 and the monthly churn rate to 40%.

Figure 4-2

Table 4-2

After we released the news, our user growth rate quickly stabilized at 34,000 users per month. However, in the churn column, since we lose a certain percentage of users each month, our churn number will expand and shrink as our user pool expands and shrinks. In reality, our user pool will tend toward a fixed size because eventually churn will equal growth.

Carrying capacity

The growth and churn rates of users directly determine the number of end users, which is called carrying capacity in this model. Carrying capacity is defined as the number of users when the rate of losing users equals the rate of acquiring users. The formula is as follows:

U•l = g

U is the carrying capacity; l is the monthly churn rate (or the probability of losing any particular user in a month); and g is the monthly non-viral growth rate.

Therefore, the calculation formula for carrying capacity is:

U = g/l, where l≠0

To double the number of end users, we have two options:

Double your non-viral growth rate (i.e., spend more money on non-viral channels).
Cut churn in half (e.g. by improving the first-time user experience or focusing marketing channels on a more targeted user base).

Often we have both.

In our previous example, g is 34,000 users per month and l is 40% per month. This formula predicts that our final number of users U will be 34,000/0.4 = 85,000, as shown in Figure 4-2.

Carrying capacity with viral factors

Next, how do we modify the carrying capacity formula to account for virality?

As mentioned earlier, when our viral coefficient is less than 1, we can interpret it as the amplification factor a = 1/(1-v). Since the amplification factor applies to our non-viral growth rate g, we can just plug a into the formula:

U = a•g/l = g/(l•(1-v)) where l≠0 and v <1

Let's go back to our first example, where our growth rate is slowing down. Here, g is 34,000 users per month, l is 15% per month, and v is 0.2. This formula predicts that our final number of users U will be 34,000 / (0.15•(1-0.2)) = 283,000. This conclusion coincides with the development direction of Figure 4-1.

5. Retention Curve

Let’s say our product is amazing—people can’t live without it and keep it for months or even years after they start using it. Our previous churn model was too harsh for such a good product. As users continue to use our product, we will retain them better because of several self-reinforcing effects:

Users leave more data in our products, making it harder to switch to competitors (e.g., Dropbox and Evernote);
As users spend more time on our products, they develop habits (e.g. Uber);
Based on the above two situations, users establish an emotional connection with our product.

In reality, our users will show a retention curve, which reflects the probability that a user is still using our product at a given point in time.

The retention curve depends on the type and quality of the product, as well as our positioning of the marketing channels. For example: browser plug-ins. Through investigation, I learned that the retention curve of a good browser plug-in looks like this:

Figure 5-1

After one week, 80% of users can be retained. After one month, 65% of users can be retained. After two months, 55% of users can be retained. In the long run, about 40% of users will be retained, and the monthly decline rate will be very slow.

6. Viral spread curve

Before we add retention curves to our model, let’s first consider the impact of retention curves on virality.

So far, we have assumed that our users will only invite their close friends in the first month. However, if 40% of users use our product for a long time and continue to invite their friends, our user base will grow virally.

In other words, our users will also exhibit a virality curve, which shows how the viral coefficient of an average user changes over time.

Why does a user's viral coefficient change over time?

A lot depends on the product, but also consider the following scenarios:

At first, users were hesitant to invite their friends because they were still testing our product;
Once users fall in love with our product, they will quickly invite a group of friends to use it;
Soon, users will invite all the friends around them who can be invited;
Occasionally, users will invite new friends they have just met.

In this scenario, a user's viral coefficient would experience a short initial delay, then increase rapidly, and then quickly decrease to a steady but lower rate.

We can model every part of this curve, but we can focus on the main trend: the viral coefficient gets smaller over time as users run out of friends to invite.

Let’s model this with geometric decay: each month, the viral coefficient is half of the previous month. For example: the viral coefficient might be 0.2 in the first month, 0.1 in the second month, 0.05 in the third month, and so on:

Figure 6-1

If we add up all the viral coefficients over the user’s lifetime , we get the lifetime viral coefficient v’, which is 0.2 + 0.1 + 0.05 + … = 0.4.

Our previous intuition continues to apply:

For Internet products, a sustainable lifetime viral coefficient v' of 0.15 to 0.25 is good, 0.4 is excellent, and 0.7 is outstanding.
Our amplification factor a is now 1/(1-v').

7. Combination Model

As of now, we have upgraded our model by combining non-viral channels, retention curves, and virality curves. The formulas are more complicated than before, so let's make them more intuitive.

In addition to the user growth chart, we also made the following chart to compare various growth channels and their impact on user churn.

Figure 7-1

The best way to see how these factors interact is to play with the numbers and watch the graph change. When looking at growth channels versus churn, we can try the following:

(1) Improving the retention curve

Set the first month retention to 90%, the second month retention to 80%, and the sixth month retention to 60%.

Figure 7-2

We saw not only a decrease in churn, but also an increase in viral growth. Because when users stay longer, they will invite more friends.

（2）Improving the viral spread curve

Assuming the viral coefficient for the first month is 0.35, the lifetime viral coefficient will be about 0.7.

Figure 7-3

This had a huge impact on the viral growth channel, which increased from about 20,000 users per month to about 40,000 users per month. But it will not have much impact on the total number of users, because in the long run, we will still lose 40% of our users.

(3) Add another press release

Set the Release News for month 6 to 100,000.

Figure 7-4

We can clearly see the peak in the graph, which in turn leads to a peak in churn. After a while, you can see the viral growth spike quickly and then slowly decline because there are no more new users and our new users don’t have any more friends to invite.

8. Limitations

We should never settle for any model because they all have limitations, here are some areas where our model can be improved:

We assume that non-viral channels remain constant, which is not the case: platform growth, new competitors, and word-of-mouth all have a large impact.
We considered a limited number of channels, and in fact, we would have more non-viral channels and viral channels.
We assume that user churn stops after 6 months. Unfortunately, we lose users all the time, either naturally or through users switching to competitors. Fortunately, it was easy to model once we had the data: all we had to do was extend the retention curve beyond 6 months.
We conservatively assume that viral growth stops after 6 months. Again, it’s easy to model when we have the data: all that’s needed is to extend our virality curve.
We assume that the retention and virality curves do not change over time. This is not the case: as we continue to test and iterate on the product, our retention and virality curves will improve.

Finally, let’s review how the model in this article was optimized step by step: it started with the simplest possible model, then non-viral channels were introduced, iterated to a hybrid model, then user churn was further introduced, upgraded to a hybrid model, and finally the retention curve and viral spread curve were introduced to become a combined model.

Of course, as mentioned at the end of the article, each model has its limitations. I hope this article can help you clarify your modeling ideas and thus help and inspire your user growth.