Why does bitcoin behave like a powerlaw in time?

By: The BitLog Team | Last update: Aug. 2025 | 3 min read

We don't know exactly.

However, an elegant suggestion was given by @giovanni, who is often credited with first observing the bitcoin powerlaw.

Giovanni pointed out that not only the bitcoin price, but also the number of users (owners of bitcoin), as well as the mining rate, all approximate powerlaws in time.

In order to estimate the number of users, we plot below the number of daily new active addresses. Other metrics, such as the daily transaction rate, or the number of nonzero addresses, can also be used as a proxy, yielding similar results.

Between 2011 and 2017, the trend above is well described by a powerlaw, observable as a straight line in a double logarithmic scale.

After around 2017, the number of daily new addresses no longer accurately represents the number of users, as ownership shifts to a few 3rd parties (websites/exchanges) that consolidate addresses. The effect this consolidation of addresses has on the network is unknown, though the continuing powerlaw in price may indicate that it is not significant.

We also plot below the total rate of cryptographic mining computations in the network ("hashrate" - in billions of hashes per second).

The fit to a powerlaw in this case is not perfect, but the fact that the hashrate has evolved over 100-billion fold, while maintaining approximate agreement with the trend makes it rather convincing (see the previous article on how convincing is the Bitcoin Powerlaw?).

Putting It All Together

Powerlaw behavior is uncommon in financial assets, and therefore it is difficult to explain the bitcoin price trend on its own, if an explanation is at all possible.

One possible explanation:
The bitcoin price grows like a powerlaw because the number of users grows like a powerlaw, or perhaps they (along with the hashrate) grow together inter-dependently. There is important precedent for such behavior in modern networks (see the next article on network growth).

This implies that the value of bitcoin as an asset lies in the fact that it's a network, and that network size is a primary driver of price (perhaps this is true for other currencies as well).

We note that while there is evidence for the above claims, these are not complete quantitative models that properly explain the mechanism connecting users and price. We also have not accounted for the peaks in price that deviate from powerlaw behavior, nor is it clear how the story presented above would fit with common financial reasoning (e.g. supply and demand).

In our last article, we examine some future implications of the claim that price is driven by user growth.