Concepts: Metcalfe’s Law

Metcalfe’s Law is a way of describing the usefulness of networks. Roughly put, Metcalfe’s Law states that the more users a network has, the more valuable it is to each individual user.

Gunnar Jaerv   Gunnar Jaerv · Published on 11 March 2021

Obvious examples from the past include the postal service and the telephone. If only a handful of telephones exist, getting one doesn’t benefit you much. If everyone but you has one, you more or less have to get a phone.

The situation is now the same with regard to internet-connected devices. In the late 70s, the whole internet was hosted on a server under the desk of an American academic, who periodically kicked it by accident and turned off the whole thing.

Gaining access to the internet then meant you’d get some academic gossip and some important intellectual work a bit sooner than others.

Now, internet access is essential. You can shop — because all the shops are online. You can pay taxes, apply for university courses, book hotel rooms, airplane flights and theater tickets, order clothes and groceries — because all those institutions are online.

They’re there because you’re there. You’re there because they’re there. Metcalfe’s Law in action.

Metcalfe’s Law in the original

Stated more precisely, Metcalfe’s Law is:

The effect of a telecommunications network is proportional to the square of the number of connected users of the system (n2).

It’s a kind of simplification of a law originally posited by Robert Metcalfe, among other things the inventor of Ethernet (and the person who persuaded Xerox to give up their copyright over the name and technology so it could become a standard).

The systemic effect would be 4 if there were 2 users (2 x 2), 9 if there are 3 users (3 x 3), and so on; user numbers grow linearly (1, 2, 3, 4) but systemic effect grows nonlinearly (2, 4, 9, 16). Metcalfe addresses the actual outcome of this using an uptake curve that doesn’t quite match systemic effect; it lags at first, then accelerates to meet the systemic effect line at the Critical Mass Crossover.

Critical Mass Crossover


This is a copy of Metcalfe’s original slide from his circa. 1980 presentation at which he proposed what became Metcalfe’s Law. His original analysis is more sophisticated than either of the two versions of his Law stated above. We can see prices in dollars are considered; and the crucial number isn’t how many individuals are connected, but how many devices.

That’s a big difference. More importantly, Metcalfe described these devices in more detail: they don’t have to just be connected. They have to be compatibly communicating.

Metcalfe’s Law and digital assets

Metcalfe was thinking of the LAN networks he was instrumental in creating, in which multiple devices could discover and communicate with each other easily. He wasn’t thinking of the internet; while the general, broad-brush concept holds good, more or less, the Law doesn’t really apply to big networks filled with non discoverable devices that never communicate with each other. When Metcalfe says “devices”, he’s really talking about nodes.

However, there are currently networks on which large numbers of users are discoverable and compatibly communicating: blockchains, markets, digital asset exchanges all meet that description.

Interestingly, so do social media networks. Both social media and digital assets have something in common that makes them uniquely “Metcalfe-susceptible”: their value derives from their systemic effect. The more people are using them the more value a new user stands to derive from them — like the phones example we gave at the start of this piece. So if Metcalfe’s Law holds good, we should expect to see adoption curves for digital assets and for Facebook looking pretty similar.

Digital assets and Facebook


That looks a lot like the Metcalfe curve, albeit a little straighter than we would expect. How about digital assets?

Digital Assets


Even more similar to what Metcalfe predicted.

For businesses that are involved in the digital assets space, there’s a lesson here. We would look at these adoption rates and expect that Facebook’s profits would mirror the Metcalfe curve. Here’s their revenue and net income:

Facebook Revenue and Net Income


Net income is depressed by expenditures, but the shape of both looks pretty similar to the systemic effect curve Metcalfe predicted. The crucial difference is that the acceleration is even more exponential than that predicted by Metcalfe.

What about Bitcoin pricing?

Bitcoin Pricing


At first glance it doesn’t look much like Metcalfe has much to do with it. But BTC has a high opportunity cost. It was seen as risky and was relatively difficult to invest in. That depressed the initial uptake. The high potential profits and its function as a perceived store of value elevated uptake later. Draw a line through the 2013 start price and the 2014, 2018 and 2021 peaks, though, and what do you see? You can draw a similar line through BTC price ignoring its spikes. The shape comes out the same — a Metcalfe parabolic curve. This curve is driven by new users or increasing network usage; increasing numbers of transactions, more active accounts, wallets, and nodes, and decreased hash rates all contribute to higher pricing. This is directly in line with Metcalfe’s prediction.

What explains the sharp deviations from this parabola? These are usually referred to as “non-economic factors” and they include deliberate price manipulation as well as traditional price bubbles. These factors can include wash trading, falsified trade volumes (referred to as “painting the tape”), and other activities.

However, Metcalfe’s predictions aren’t the only ones relevant here. Facebook is a network, but it’s also an application, an interface and — for many of its users — a technology. It’s often the real “front page of the internet” for older or app-dependent users. So its revenue curve looks a little Metcalfian, and a little like the growth curve of a fast-growing business, and a little like the classic tech adoption curve:

Classic Tech Adoption Curve


Revenue curves compound adoption in that early adopters are still contributing revenue as new adopters add to the stream. That Facebook income curve makes more sense now.

Bitcoin is in a similar position: it’s a network, so Metcalfe’s Law should apply — and as we’ve seen, with caveats, it does; but it’s also a market, subject to the cyclical nature of markets; a technology; and an application (arguably it’s also a currency, though it’s primarily viewed as a store of value now). Adoption rate of the technology and the interface, and flows of money across the wider market, affect price. You wouldn’t expect a perfect Metcalfe curve.

Making BTC price predictions can be a risky business, particularly in the short term. How many wrong predictions have you read? We should all approach with caution. And it’s always had a choppy price history replete with bubbles and crashes. But Metcalfe’s curve might be a useful tool to illustrate where it’s likely to move to in the medium term.


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