A16Z describes three different network effect formulae in their deck. https://a16z.com/2016/03/07/all-about-network-effects/ Ever wondered how the formulae came to be without looking it up? It’s actually simple.
Well, the value formula is a way of quantitatively assessing how many connections can be formed within the network.
In Yahoo
If there are n users, they all connect to Yahoo and have no connections to each other. So value is proportional to number of users. V ∝ n.
In Facebook
Users are connected to each other. How many connections can you form between 2 users from a pool of n users?
nC2 = n*(n-1)/2
So that’s like roughly saying V ∝ n².
In WhatsApp
Users can form many groups and share unique connections within the groups too.
How many groups can we form with n users?
nC2 + nC3 + .. + … nCn
Guess what that equates to?
= 2^n-nC1- nC0
We are subtracting nC1 = n because a group requires 2 people.
We are subtracting nC0 = 1 is because groups cannot have 0 people.
But yeah, for brevity V ∝ 2^n.
But why should value be measured in connections at all?
Because, as a company, you want to have as many ways to reach a particular user as possible to deliver your product.
And the graph
https://redcatco.com/communication/metcalfes-law-really-useful-not/