Metcalfe’s Law and Bitcoin’s Value

3 min readJun 10, 2020

This article was additionally published by Coinmotion, the leading digital asset exchange in Nordics.

Metcalfe’s Law was originally presented in 1980 by Robert Metcalfe, describing “compatible communicating devices”. The theory was later refined in 1993 by George Gilder, referring to Ethernet. In its basic form, Metcalfe’s Law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system (n²), or n(n − 1)/2, where n equals to number of nodes. n(n − 1)/2 is proportional to n² asymptotically.

Metcalfe’s Law has been successfully used for evaluating valuations of FAANG technology-related stocks and internet usage in general. Metcalfe’s Law can be divided into original and generalized formulas:

A. Original Metcalfe’s Law: NV ~ n².

B. Generalized Metcalfe’s Law: NV ~ n^1,5.

Metcalfe and UTXO

As mentioned above, Metcalfe’s Law states that the value of a network is proportional to the square of the number of participants in the network. The following chart exploits a variant of the law with BTCUSD divided by n log n of the number of unspent transaction outputs (UTXO). Values are also scaled by 106.

Metcalfe UTXO indicates close correlation between BTCUSD and network value during 2017 retail-based rally. However during 2014 upstream the indicator was decoupled from BTCUSD and thus significantly higher compared with price. During 2019–2020 Metcalfe UTXO would indicate BTCUSD being somewhat overpriced, however the two have been more correlated towards 2020.

Metcalfe Ratio

The following chart mirrors Metcalfe Ratio, the amount of active addresses of network (squared n²), and bitcoin’s price (BTCUSD).