Having said this, while we see a risk of correction, we stay bullish on Bitcoin price in the long run.

Metcalfe’s Law: how it all began

Cryptoassets are networks of users connected in digital space. Users can interact with each other by exchanging information and engaging in transactions. Due to the fact that these networks are digital, always online, and published on the the blockchain, network usage data is more readily available than for other types of networks (telephone, fax, messengers, and social media). Transaction data availability combined with public crypto markets create a unique opportunity to analyze and value these networks in real time.

Nearly four decades ago, Xerox Palo Alto Research Center (PARC) employee Robert Metcalfe proposed a relationship between the value of a network and its size (Metcalfe, 2013). He stated that the value of the network is proportional to the square of the network nodes (users). This relationship is based on the so-called “network effect”: a positive effect described in economics and business that an additional user of a product or service increases its value to others. The original Metcalfe’s Law has the following form:

The logic behind this formula is the following: the number of unique connections in a network with n nodes can be expressed as n(n − 1)/2, which is proportional to n² asymptotically.

Over time, some variations of this law were proposed. For example, Andrew Odlyzko et al. noticed that Metcalfe’s Law estimates a number of potential connections between users of the network, while, in fact, there are certain limitations to how many useful connections one user can have. He proposed to use n * log n instead of n² for network value estimation for large n. There were multiple other modifications to the original law. Some researchers have successfully applied the law to describe Facebook and Tencent user growth and financial metrics.

Usage in cryptoasset valuation

Over the past year, a lot of research has been done on the topic of valuing cryptoassets using Metcalfe’s Law. Cryptolab Capital research on Metcalfe’s Law was initially inspired by Thomas Lee of Fundstrat, who has stated back in November 2017 that 94% of Bitcoin price movement can be explained by Metcalfe’s Law.

We decided to dig deeper and have found an earlier paper on the topic published by Ken Alabi in June 2017. In all these articles the number of network users is usually approximated by the number of Daily Active Addresses (DAA). For internet companies with strong network effects, the analogous Daily Active Users (DAU) indicator is one of the most important performance and valuation metrics.

One of the recent articles on the topic by the Clearblocks team explored in detail how well different versions of Metcalfe’s Law describe Bitcoin price. Their research revealed 3 candidates for the title of “the most predictive model”:

Original Metcalfe’s Law: NV ~ n² Generalized Metcalfe’s Law: NV ~ n^1.5 Odlyzko Law (also called Zipf’s Law): NV ~ n • log n

They calculated Pearson correlations for all three of these laws over the period between 2010 and 2018, and based on this analysis chose law #2. They then used it to define Price-to-Metcalfe Ratio by dividing actual Network Value by the one predicted by the law:

where n is Daily Active Addresses (DAA), and 30 day MA is 30 day moving average.

There is an issue here, however: it is very hard to objectively choose between these three laws, and the Clearblocks team admits it in the article themselves:

All formulas show near perfect correlation with BTC’s USD price, particularly on a natural log scale. In any other field, such a correlation would be considered witchcraft… The differences in correlations are so small they can effectively be considered equal

At the same time the value of the ratio (and hence the results of PMR analysis) depends greatly on which law you choose for denominator. Different values in denominator give you contradicting results when it comes to predicting December 2017 bubble and to describing current BTC price.

Different laws — contradicting results

If you define the PMR denominator using Odlyzko Law (NV ~ n log n), you will get the following formula:

where n is DAA. If you then plot the resulting Odlyzko PMR against Bitcoin price, you will get the graph below. Based on this graph, PMR is at its all-time high level of around 5, and we are still in the middle of the worst bubble in Bitcoin history. Corrections in Q1 2018 didn’t help much — even at around $6k in February 2018 Bitcoin was still presumably significantly overvalued according to this analysis.