Rethinking Metcalfe's Law

- startups

The value of a network is the number of users times the revenue per user.

We must empirically look at the value of networks as they scale and then fit a curve.

If the average revenue per user (ARPU) stays constant as the user base grows, then the value of the network grows proportionally to the number of users.

If the ARPU grows proportionally to the number of users on the network, then the value of the network grows proportionally to the number of users squared. This would validate Metcalfe’s law.

If the ARPU grows modestly as the network grows, then the relation is superlinear but sub-quadratic. It could be something like:


Conventional startup wisdom tells us that metcalfe’s law is correct. It asserts that social networks become proportionally more valuable as they grow for each individual user. It follows then that if (a) the total value delivered is the number of users times the value per user, and (b) the value per user is a constant multiple of the number of users then (c) the total value delivered is the number of users squared.

The law however makes a very big error and a poor assumption.

In reality, the value we derive from a social network does not increase with the number of users.

In practice, the value we derive is based on either (a) the quality of our feed or (b) the percentage of our close friends who are on the social network.

If we focus on the percentage of close friends framing, we quickly realize that metcalfes law cannot be right.

That’s because social networks grow in clusters. They hit certain social circles and cities and walks of life and expand very quickly within them.

Facebook dominated the Harvard campus before it expanded anywhere else.

Think back to the value you derived from Facebook over time.

Many people will say that they got the most value from it in the first few years they used it.

That’s because they joined Facebook around when all of their other close friends joined, so the value derived to them was extremely high.

Now we can look at this phenomenon from another angle.

The value you derive from facebook is tied to the quality of the content in your feed. Maybe it’s the quantity of the desirable content times the average positive-value of that content minus the quantity of the undesirable content times the average negative-value of that content.

And we should keep in mind that negative-value content can also be addictive and keep you on facebook and actually make you less content. So we shouldn’t use time spent on the app as a proxy.

Another part of this is the value driven to the company, which is different from the value driven to the user. This is measured easily in revenue. And oftentimes average revenue to the company per user doesn’t correlate to average value driven to each user. Sometimes they grow together and sometimes they are at odds. A great example of this is how more ads can increase ARPU but diminish the experience and the value driven to the user.

Now back to the feed angle for measuring value driven to the user.

Think back to the various years you’ve used Facebook. What were the years where you had the most positive experiences and when did you have the most negative experiences?

Many people will say the first few years they used Facebook were their best.

Why is this?

The obvious reason is that in the early years there were no ads to very few ads, whereas now ads are all over the place.

Another reason is because content on Facebook has become much more text based and political and around the resharing of viral links. And that isn’t nearly as satisfying as the early days when it was in large part photos and heartfelt original content by your friends.

Yet a third reason is because in the early years people tended to have their list of friends be confined to their close friends, whereas over time they friended more people who they weren’t as close to, and their feed started to get worse.

A fourth reason is likely because real meaningful engagement on Facebook has actually declined. Active users for Facebook are really high but that doesn’t tell the whole story.

Think back to times you’ve just gone on Facebook to check a notification and then hopped right off. Or checked a message on messenger. These are not meaningful engagements and they don’t drive value to the rest of your friends.

Now imagine a large percentage of your friends are just like you and are doing the same thing.

Do you have any idea what percentage of your friends have posted in the last month?

If this is indeed the case, that would mean that the value driven to each user could actually have gone down with the larger user base. Despite stable monthly active user numbers. Because the problem is deeper than that.

A network with lots of “passive active users” is a zombie network with no good content.

It’s a network where your feed is filled with junk because that’s all that Facebook can put in there.

It’s the few friends you know who are still posting plus ads plus articles that are surfaced to you because one of your friends liked the article or follows the author.

What we’re describing here is something drastically different from metcalfes law.

If the average surplus per user (ASPU) is actually decreasing as the number of users increases, then the value of the network is growing *sub-linearly* compared to the growth of the user base. At least for the early users.

The value per user might fall from something like 100% to something like 50% or 25%.

Thus metcalfe’s law could be quite wrong.

The value per user could be something like:

y = 0.5*(N-2)/(N-1)

Multiple that by N for the number of users growing over time and you get a moderately sublinear function (linear by order of magnitude).

If we step back and simplify everything for a second and say the value per user stays constant over time, then we’re back to linear.

And if we’re generous and say the value increases modestly over time, then we are back to:


That means that on approximation the value of a social network is proportional to the number of users.

Marc Andreessen has famously said that network effects are overrated because they can be quite easily overcome.

We are led to believe that networks grow quadratically with the size of the network because it’s an excellent story.

And because it makes breaking into networks and outcompeting existing networks sound that much harder.

And it is hard, but for other reasons.

One of the important takeaways from this should be that when thinking about value in networks, you should look at it from one of three ways: (1) the average percentage of close friends on the network for each user times the number of users (2) the net satisfaction per user times the number of users (3) the average revenue per user times the number of users.

This should lead to a few lessons if you’re building a social network.

First, you can make something value and competitive if you can pick a niche and initial target user base such that the average percentage of close friends on the network is very high. And only allow users to use the platform if you know they will have a high number of friends on the platform and active. One network that did this well in the early days was Snapchat.

Second, you can make something valuable and competitive if you can design a network that has a feed that ensures the average feed for every user is very rich and drives a high net satisfaction to the user. One network that comes to mind that does this well is HQ.

Third, you can make something very valuable and competitive if you can choose a market and problem such that you can ensure your ARPU is high even if you have a network that is less than one one-thousandth the size of Facebook. Be careful with this one, though, because the revenue you can drive is really due to the unique draw of the network.