Calculating Critical Mass

You’ve probably heard the term “critical mass” tossed around when discussing new social media products. The term is usually either used in the form of “we reached critical mass and then things just took off” or “we don’t have critical mass and we can’t grow…” But what is critical mass? How do you calculate it? And what is therefore the number of users that these products need in order to have it? Critical mass is different from “product/market fit,” another loosely defined term, in that there is a number we seek, even if no one admits to knowing what it is. With product/market fit there is no minimum number — your business just ends up growing faster than you can handle.

First off, the term critical mass does not originally come from social products or startups. It comes from physicists studying nuclear fission. Basic introductory definition: “A critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction.” Read at least the Wikipedia article and try out the equations.

Many things impact critical mass in nuclear fission. From Wikipedia again, the following can change the point of criticality: Varying the amount of fuel, Changing the shape, Changing the temperature, Varying the density of the mass, Use of a neutron reflector, and Use of a tamper.

In other words, in fission, the critical mass is not static. It changes depending on those other factors. Here’s the nuclear fission critical mass formula.

Where M is the total mass, m is the nuclear mass, s is 1 + the number of scattering events per fission event, ẟ is the total interaction cross section, ⍴ is density, and f actually is a fudge factor (their words, not mine) that accounts for geometrical and other effects. If the value is 1 or greater, the fissile material with go into a critical mass chain reaction.

Once I saw that fudge factor, I stopped feeling so bad about only trying to come within an order of magnitude when it came to critical mass for a social product.

The above ways to change the point of criticality of fissile material are each pretty instructive too.

• Varying the amount of fuel. The most direct way to think about a minimum amount of stuff needed to attain the critical mass chain reaction.
• Changing the shape. That is, a thin layer of fissile material will not reach critical mass, where the same amount rolled into a ball may achieve it.
• Changing the temperature. This is mostly related to expansion.
• Varying the density of the mass. Less dense: more needed to become critical, if it can become critical at all.
• Use of a neutron reflector. Sending escaped neutrons back at the fissile material to get another chance at causing a chain reaction.
• Use of a tamper, another way to send escaping neutrons back at the core.

You might even start to see some similarities in how we could look at critical mass in a social product.

But of course, the above equation isn’t completely relevant for social products. Humans are different from atoms. But it is a starting place. But when a term doesn’t have a clear definition people start to apply it loosely, so I’m going to rewrite the critical mass formula, with human users in mind rather than molecules.

First, how do we define critical mass for a social product without relying on “you know it when you have it, because then everything goes well” type of circular reasoning? My critical mass definition is the minimum number of users you need to sustain user value in the product with no other product changes. This is product critical mass, not business critical mass. Business critical mass (when your customers make the business sustainable) will almost always be much higher.

Even if we disagree on how to calculate critical mass, we can say that we don’t have it if a product becomes less valuable in aggregate for its users over time when there is no other change to the product itself. (There are many products that barely changed over years but where value remained, Twitter being a modern example.) So, not having critical mass should result in less action per user over time, even if the total number of active users stays the same. Having critical mass should mean that we maintain our users and most likely grow them — churn will be low and more people are likely to want to join.

Estimating critical mass for a social product

The purpose is to answer these questions:

1. Do we have critical mass at the current number of users? If not and if all else about the product and usage remains the same, what number of additional users needs to be added?
2. Do we have critical mass at the current number of users? If not, what do we need to change about usage in order to have critical mass at the current number of users?

For now, my inputs are these (and I am very open to changing these):

• Unaccountables. Time, place, UI / UX, subpopulation peculiarities, and other issues that act unpredictably. If the physicists used a fudge factor, I will too. This is also why I’m happy estimating this within a factor of 10x for now.
• Percent of users active in time period. We can imagine two different products, one with a high percentage of active users (could be because of recency or other factors that keep people engaged) the other with a low percentage of active users (low need to log in). A higher percentage of active users can sustain a smaller overall population of users. So critical mass would be lower if active user percentage is higher.
• Necessity and expectation of frequency. Some social products (like a microblogging service) only make sense when there are frequent new contributions from many users. Messaging apps or SMS, can have critical mass with smaller engaged populations (the extreme being just two people to send messages back and forth). Other services have much lower, or different, requirements (like a time-based app where users aggregate at specified times of day). Overall, a larger critical mass will be needed when a population is spread around every time zone. A smaller critical mass will be needed when a population is concentrated around a smaller number of time zones. That is, if there is a natural busy hour for activity shared by the user population, fewer people will be needed to attain critical mass.
• Activity per user. Do users browse the content of others or do they also contribute?
• User activity needed to cause a reaction from another user.
• Percent of users who take an action in time period. Features such as the “like” makes it easy to take an action with a single tap.
• Impact of messages received on messages sent percentage. This is similar to the probability that a fission event creates other fission events.
• Other users’ impact on retention or churn. Likelihood to remain active if user receives action from another in time period
• Amount of value from single-player mode or other way to get value without user interaction. This enables the product to attain critical mass with a smaller number of users.

I’m not going to write a formula now, because I’m still thinking through the variables and am figuring out how to weight them. What I’d really like is some more data to test against. Want to contribute? Please get in touch here.

But in general, I’m expecting something like these variations:

Messaging app like texting: two people minimum in the extreme example. This is the one that will cause the most disbelief. Remember, we’re not looking for what sustains the business financially. Depending on your revenue model, those numbers can be dramatically different anyway. Instead, we’re talking about what sustains the product. In this extreme case, just two people could sustain usage and get value from the product and then go on to invite others in.

Messaging app like Slack: 10x the above for one group. That’s enough for value from the small crowd, info from the group leader, plus enough people you want to talk directly to for one-to-one messages.

Broadcast / microblogging service like Twitter: 1,000x the above. That’s enough for value from the crowd plus enough people you want to message directly.

The above are the best case scenarios (lowest critical mass numbers), given the variables. In most cases, where the product needs work, the numbers will be much higher.

But I’m making the assumption that there is some predictability here that leads to better understanding users and systems. I might be wrong and there typically is not enough that can be predicted. But if we can improve our guesses, then talking about critical mass will shift away from being a loose concept and could carry more value as something at quantifiable, at least within bounds. I’d love to look at actual data of social products at their critical mass tipping points. If you have anonymized data you’d like to share, please contact me so we can refine the theory alongside actual results. Thanks!

This is a draft. I’m posting this in unfinished form to seek feedback.