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Understanding Power Laws

Essentially, a power law shows how the size of an event or entity relates to its rank. Large occurrences are rare and small ones are common.

The distribution follows a predictable pattern where the frequency of an event decreases rapidly as its size or effect increases. This predictable pattern is found in many natural and social phenomena.

For instance, consider how city populations often follow a predictable pattern: a few cities are extremely large while many are relatively small. This distribution can be captured by a power law.

Considerations for the Bitcoin Power Law Model

The Bitcoin Power Law theory aims to make sense of the market chaos by applying the power law distribution to Bitcoin’s historical price data.

Theorist Giovanni Santostasi provided the following overview of Bitcoin’s feedback loop, which contributes to Bitcoin’s price following a Power Law model:

• Initial Adoption: Bitcoin was initially adopted by the Satoshi circle, paving the way for its acceptance.

• Metcalfe's Law Confirmation: The price of bitcoin increases roughly with the square of its user base, confirming Metcalfe's Law.

• Impact of Price Increase: Increased price attracts more resources, particularly mining power, influencing the difficulty adjustment and hash rate.

• Hash Rate and Security: Higher hash rates enhance system security, indirectly attracting more users concerned with Bitcoin's security.

• Power Law of Adoption: Bitcoin adoption follows a power law of three over time, contrasting with typical S-curve adoption models seen in other technologies.

• Cycle of Growth: This adoption pattern, combined with other observed power laws (addresses, price, hash rate), perpetuates Bitcoin's growth cycle indefinitely.

Is the Power Law model useful for predicting the price of Bitcoin? Read the full post here to find out more.

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