Bitcoin Power Law Explained: How it Works and How to Use it

The Bitcoin Power Law is a price model, created by Giovanni Santostasi and shared around 2018, that uses a mathematical equation to attempt to explain Bitcoin's price growth.

In this guide, we'll cover what the Bitcoin Power Law is, how it works including the formula, its limitations, and how to use it in your investment strategies.

What is the Bitcoin Power Law?

The Bitcoin Power Law is a mathematical model that describes the long-term relationship between Bitcoin’s price and the time elapsed since genesis (creation).

A power law is a mathematical relationship in which a change in one quantity produces a proportional relative change in another. The proportional rule remains consistent regardless of which number you start with.

When applied to Bitcoin, this formula uses historical data to estimate long-term trends in Bitcoin’s price.

How does the Bitcoin Power Law work?

The Bitcoin Power Law model compares Bitcoin’s age and historical price to find a mathematical relationship. The chart plots Bitcoin’s age in days since the genesis block (January 3, 2009) on the X-axis and its price in USD on the Y-axis. They use a logarithmic scale to produce a regression line (the center line) known as the fair value line.

The fair value is supported by two parallel bands known as the resistance line and support line which create the price corridor:

• Resistance line: The upper band of the price corridor that Bitcoin’s price is always meant to be equal to or below.

• Support line: The lower band of the price corridor that Bitcoin’s price is always meant to be equal to or above.

Bitcoin Power Law formula

The Bitcoin Power Law formula is:

Price = A × (days since genesis)^n

• Price: The estimated Bitcoin price

• A: Scaling constant that determines the position of the curve

• Days since genesis: Number of days since Bitcoin’s creation

• N: The exponent determining how the estimated price scales

A and n are determined by historical price, where A is approximately 10⁻¹⁷ and n is ~5.8 (depending on the dataset and methodology).

What does the Bitcoin Power Law chart show?

The Bitcoin Power Law chart uses a central trendline and two surrounding bands to show the historical, current, and potential price of Bitcoin.

The central line shows the estimated long-term relationship between Bitcoin’s age and price. The support and resistance bands follow the central curve and illustrate how far the price may go below and above the trend. Historically, Bitcoin’s spot price has often remained within the model’s price corridor, with bull markets sometimes pushing it toward or above the upper band and bear markets bringing it toward or below the lower band.

It is a useful chart for visualizing historical market behavior and Bitcoin’s potential, but it should not be treated as the be-all and end-all of Bitcoin’s price. Political, economic, and social factors can also influence Bitcoin’s price, and the formula cannot account for all of them.

Why is the Bitcoin Power Law chart used?

There are several reasons why investors choose to use the Bitcoin Power Law chart, including:

• Assess market cycle: Investors can compare Bitcoin’s price with the chart to assess whether it is trading relatively high or low.

• Drown out speculative noise: The chart is based on a mathematical model that does not react to emotional or speculative trading. Investors use this to ignore panic and assess whether Bitcoin is going through a normal cycle.

• Assess long-term trends: The chart uses historical Bitcoin prices to illustrate the asset’s long-term trajectory.

• Network effects: Seeing Bitcoin’s price grow can increase interest and interaction with the network; this results in more hashrate and drives up the price.

Is the Bitcoin Power Law accurate?

There are many arguments for and against the accuracy of the Bitcoin Power Law chart. Bitcoin’s price changes have fit within certain versions of the model’s corridor. However, historical fit alone does not establish projections will remain accurate and there are a few factors be cautious of:

• Short history: Compared to other established financial markets, Bitcoin has a relatively short history, which critics argue is not long enough to develop a permanent rule.

• Variations between models: Not all Power Law charts use the same methodology. Differences in starting dates, price sources, and trend-fitting techniques can produce different estimates.

• External factors: The chart does not explain every market movement; it cannot assess liquidity, regulatory changes, macroeconomic changes, impact from wars, and investor sentiment.

How to use the Bitcoin Power Law in your strategy

You can use the Bitcoin Power Law chart to assess whether Bitcoin is trading below or above its estimated long-term trend (for example, near the support or resistance band). However, the chart cannot predict the price of Bitcoin and should always be used with other technical analysis tools and off-chain context, such as macroeconomic movements or regulatory changes, to better understand price movements.

Don't forget the tax bill

If you’re buying, selling, or earning Bitcoin, you likely owe some tax. With a crypto tax calculator like Koinly, you can easily manage your portfolio, calculate your crypto taxes, and generate country-specific forms for filing.