A specter is haunting bitcoin – the specter of Metcalfe’s Law. In a new report from Goldman Sachs, analysts in the bank’s global investment research division suggested that bitcoin’s price may be undervalued relative to the size of the network. Bitcoin has grown, but the price apparently hasn’t kept pace. 

Goldman analysts Zach Pandl and Isabella Rosenberg draw upon a framework popular in computer science, but relatively unexplored in economics – Metcalfe’s Law, named after the founder of Ethernet – that states the value of a network grows along with the number of possible connections. In particular, a network’s value is proportional to the square of all connected devices. 

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Network effects have been crucial for understanding the development and adoption of the internet and social media. Likewise for cryptocurrencies. But it’s worth stepping back to ask what type of network Bitcoin is and why these interpretive frameworks might fall short. “Metcalfe’s Law is a simple statistical rule-of-thumb for thinking about the value of network technologies, and not a complete description of these assets’ fundamentals,” Pandl said in an email. Yet, it’s often been cited to presage a surge in the price of Bitcoin or even predict its collapse.

Looking at data provided by Coin Metrics, Pandl and Rosenberg found that the number of blockchain addresses for eight different digital assets – BTC, ETH, XRP, LTC, BCH, DASH, ZEC and ETC – is often correlated with price. But, in many cases, you’d expect such developed networks to have more societal value (at least as measured by market cap).

Taken together, they found that these assets had a “Metcalfe coefficient” of about 1.5, whereas Metcalfe himself would expect a two – a squared relationship. (A Metcalfe coefficient measures the relationship between network capitalization and users – a coefficient of one suggests a one-to-one relationship.)

A variation of Metcalfe’s Law has often been applied to social media giants. Facebook’s valuation, especially before going public, was derived from looking at monthly active users (MAUs). If just Mark Zuckerberg was on the blue page, it wouldn’t be a very useful social platform. The same could be said for Bitcoin – it wouldn’t be the same if it was just Satoshi and his node. 

What separates cryptocurrencies from other information networks commonly measured by Metcalfe’s Law is that the asset being valued is also the technology being adopted. A Bitcoin user is a stakeholder in the system.

Last November, bitcoin-native upstart NYDIG published “The Power of Bitcoin’s Network Effect,” which was nominally a look at Metcalfe’s Law but which also included a look at how the use of bitcoin has changed as it is adopted.

The number of daily active addresses was shooting up at the time, the company noted, as was the number of addresses that held BTC without moving it for at least a year. This latter statistic played into NYDIG’s argument that Bitcoin’s adoption is driven by its qualities as a store of value. 

Bitcoin’s hard-capped supply of 21 million coins coupled with a growing user base means the price is due to increase over time, NYDIG argued. It provided a chart showing potential five-year price levels, if the annual address growth was 5%, Bitcoin might reach $20,905. If 25%, then $118,544. That’s not just Metcalfe’s Law: it’s “pumpanomics.” 

Others have looked to Metcalfe’s Law to explain the messy way crypto bubbles burst. In 2018, Spencer Wheatley from the Swiss university Zurich ETH and colleagues found that bitcoin grows at an exponential rate with a Metcalfe coefficient of 1.69 (they used a slightly different way to generalize what counts as an “address” than Goldman). 

With that in mind, the researchers were able to look back at periods where Bitcoin’s price surged past its level of uptake and crashed – like the downturns of 2012, 2013 and 2017 – to come up with a generalized rule. Put simply, when the growth rate itself is growing, you’re in trouble. 

So does Metcalfe’s Law help us predict the future value of bitcoin or its periodic crashes? According to Pandl and Rosenberg, Metcalfe’s Law is likely a misnomer – less of a law than a mental model. “This research report was [to] explain the basic statistical relationships for some of the oldest crypto assets for our clients,” Pandl said. 

In fact, of all the assets the Goldman analysts looked at, bitcoin was the closest to meeting the expectations of Metcalfe’s Law – with a coefficient of 1.9. But Pandl was wary of saying the asset “behaved in line with expectations.” A number of factors could influence this: most notably bitcoin’s use as a speculative asset, which is hardly sustainable, he said. 

“Bitcoin’s market cap has risen almost two times more than measures of network size over this period – similar to the rate implied by Metcalfe’s Law – whereas the average token has risen about one and a half times more than measures of network size,” he said.