Metcalfe’s law 101

A simple explanation of the “law” of network effects

The tldr explanation of Metcalfe’s law is that as networks grow bigger, they grow in value much bigger and faster than the user base. I want to go one level deeper and provide an explanation using some simple math.

First of all, it helps to think of Metcalfe’s Law as a framework for how to think about the value of a network. Just like how in Econ 101, you learn about supply and demand under perfect competition (nothing is perfect), you should treat this as a model to think about network value and not an equation that you can use straight out of the box in real life.

Here are a few basic assumptions to simplify the model:

• Think about this example as a communications network (e.g. phones or fax machines)
• The value of the network is simply measured by the number of connections you can make
• The value of each connection is the same

Let’s use the example of fax machines. The simple idea is that if more of my friends have fax machines, we can all fax each other stuff and we all get value from that.

Next, let’s tally the number of possible connections in between the fax machines:

Here are illustrative examples:

Two fax machines create a value of one

Three fax machines create a value of three

Four fax machines create a value of six

If you keep repeating this, you end up with a table like this:

I could’ve kept going but stopped at 15 because it’s clear that the number of possible connections is growing much faster than the number of fax machines. The relationship between the number in column 1 and column 2 turns out to be:

So if we test this by using 15 from the table above, we should get 105:

So how do you go from the equation above to “n^2”? Well, the law states that the value of the network is “proportional to n ^2”. The easiest way to think about this is that as n gets bigger, there’s not much difference between [n x n] and [n x (n-1)].

So that’s really it.

Once you understand the framework, we can then start to tear it apart :P

“What if I own one of two fax machines in the world and the other is owned by my archenemy and I get no value from that connection?”

“What if the more people that join the network, the more polluted my communications system seems to get?”

“If I use this framework to try and figure out the monetizable value (or enterprise value) of a network, am I conflating two very different things?”

“How does this model hold up when I apply it to social networks and not fax machines?”