ON-CHAIN METRIC
Power Law
How far is Bitcoin's price from a specified power-law fit—and how sensitive is that fit to its assumptions?
Open the Market Cycles dashboard
A Bitcoin power-law model fits price as a power of network age, commonly through a linear regression of log price on log time since a chosen origin date. On log-log axes, the fitted relationship appears as a straight line.
The historical fit can be visually striking. It remains an in-sample statistical model, not a protocol rule or a guaranteed price path.
What the model describes
The fitted exponent describes how price has scaled with time inside the selected dataset. Upper and lower bands then show historical departures from that fitted path.
Results depend on the start date, price source, sampling frequency, fitting method and band construction. “The Bitcoin Power Law” is therefore not one universal formula unless the chart publishes those choices.
Why the model is contested
Price and time both trend, which can produce high regression fit statistics even when forecasting power is weak. Residuals can also be autocorrelated and their variance can change through time.
A good fit to Bitcoin’s available history does not prove the same exponent will govern a different future market. In-sample fit should be separated from out-of-sample testing.
How to use it carefully
Use the model as a long-horizon reference for how far price sits above or below one specified historical fit. Avoid presenting future values as targets the protocol must reach.
Compare several specifications and publish the exact formula. If small modelling changes produce large future differences, the uncertainty is part of the result.
How to read it
Far above the fitted path. Price is high relative to this model’s historical trend and bands.
Above the path. Price is ahead of the fitted central line.
Near the path. Price is close to the model estimate.
Below the path. Price is beneath the fitted central line.
Far below the path. Price is low relative to this model’s historical bands.
The Power Law sits inside the Market Cycles & Structure dashboard. The chart should publish its origin date, fit and band method.
Common questions
Is the Bitcoin Power Law a prediction?
It becomes a prediction only when the fitted relationship is extended beyond the sample. That extension assumes the relationship continues.
Why do analysts disagree?
They disagree about whether the relationship is structural or a trend-fitting artefact, and about the correct statistical tests.
What is it useful for?
It offers a consistent long-run scale for comparing price with one published model, provided its assumptions remain visible.
Why do power-law charts differ?
They can use different start dates, price data, regressions and bands. Those choices matter.
Should it set a price target?
No single fitted curve should. Treat future values as model scenarios with uncertainty, not deadlines.
ON-CHAIN METRIC
Power Law
How far is Bitcoin's price from a specified power-law fit—and how sensitive is that fit to its assumptions?
Open the Market Cycles dashboard
A Bitcoin power-law model fits price as a power of network age, commonly through a linear regression of log price on log time since a chosen origin date. On log-log axes, the fitted relationship appears as a straight line.
The historical fit can be visually striking. It remains an in-sample statistical model, not a protocol rule or a guaranteed price path.
What the model describes
The fitted exponent describes how price has scaled with time inside the selected dataset. Upper and lower bands then show historical departures from that fitted path.
Results depend on the start date, price source, sampling frequency, fitting method and band construction. “The Bitcoin Power Law” is therefore not one universal formula unless the chart publishes those choices.
Why the model is contested
Price and time both trend, which can produce high regression fit statistics even when forecasting power is weak. Residuals can also be autocorrelated and their variance can change through time.
A good fit to Bitcoin’s available history does not prove the same exponent will govern a different future market. In-sample fit should be separated from out-of-sample testing.
How to use it carefully
Use the model as a long-horizon reference for how far price sits above or below one specified historical fit. Avoid presenting future values as targets the protocol must reach.
Compare several specifications and publish the exact formula. If small modelling changes produce large future differences, the uncertainty is part of the result.
How to read it
Far above the fitted path. Price is high relative to this model’s historical trend and bands.
Above the path. Price is ahead of the fitted central line.
Near the path. Price is close to the model estimate.
Below the path. Price is beneath the fitted central line.
Far below the path. Price is low relative to this model’s historical bands.
The Power Law sits inside the Market Cycles & Structure dashboard. The chart should publish its origin date, fit and band method.
Common questions
Is the Bitcoin Power Law a prediction?
It becomes a prediction only when the fitted relationship is extended beyond the sample. That extension assumes the relationship continues.
Why do analysts disagree?
They disagree about whether the relationship is structural or a trend-fitting artefact, and about the correct statistical tests.
What is it useful for?
It offers a consistent long-run scale for comparing price with one published model, provided its assumptions remain visible.
Why do power-law charts differ?
They can use different start dates, price data, regressions and bands. Those choices matter.
Should it set a price target?
No single fitted curve should. Treat future values as model scenarios with uncertainty, not deadlines.