Zipf’s Law - The Network Effect

As a peer to peer distributed network, bitcoin benefits from network effects - the positive relationship between the number of users on the network, or Daily Active Users (DAUs), and the utility of the network.


The network effect was first modelled by Robert Metcalfe as v = n^2, where v represents value and n is the number of users. A number of variations on the relationship between n and v have been proposed. We have modelled a number of variations to identify the most relevant for bitcoin’s specific use case, settling on Zipf’s law, which states v = n^1.5.


We have modelled the network effect for bitcoin over the past 6 years with some success. Our findings indicate periods where bitcoin was considered undervalued, which coincide with the bear market, and overvalued, which coincide with the later stages of the bull market.

Data: Coinmetrics; Analysis: Bitassist Research & Analytics

We can identify three points in the past 24 months where the bitcoin price matched the price extrapolated using Zipf’s law. Firstly, during initial run up to the Dec’17 peak, and then in the first major correction in early Feb’18 at $6,8k. The most recent point of parity is also the most interesting. From Dec’18 to Mar’19, the market price of bitcoin was within 20% of the price modelled on Zipf’s law – with the two being equal on 14th Dec’18 at $3,2k. With this in mind, we believe user growth has historically been a good proxy for the relative network value.

The bitcoin price temporarily found support at the Zipf price in Dec’18, before the two prices began to diverge. The near parabolic increase in price since Mar’19 is yet to be matched by a relative increase in daily active user growth. The difference in price between market price and Zipf price is currently +116%.


We view the price modelled on the network effect as a price floor for the bitcoin network. The sharp divergence since March does however suggest that we are overvalued in the short run. We expect active users to increase before a considerable continuation of a move upwards.


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