Power-law Growth Curves

What are Power-law Growth Curves?

Power-law growth curves model an asset's long-run price as a power function of time: price proportional to elapsed time (measured from some origin, such as Bitcoin's genesis block) raised to a fixed exponent. On log-log axes, where both price and time are logarithmic, a power law plots as a straight line, so the model is fitted as a simple linear regression of log price on log time. Parallel rails offset above and below the fit form a growth corridor. The best-known application is the Bitcoin power law, a fit popularized by quantitative analysts studying its multi-year price history.

Read strictly, the model claims growth decelerates in a specific way: each doubling of the asset's age multiplies price by a constant factor. Its appeal is that price has so far stayed inside a corridor around one fitted line across several cycles. Its weakness is the same as any curve fit: the sample is one asset's short history, the exponent depends on the chosen origin date and fitting window, and nothing enforces future adherence. It is a descriptive fit, not a law of nature, despite the name.

How traders use it

• As long-horizon valuation context: distance from the fitted line, or position within the corridor's bands, frames current price as historically cheap or expensive on a multi-year scale, in the same spirit as other crypto cycle models.
• As cycle framing: past bull-market peaks appeared as temporary deviations toward the corridor's upper rail and bear lows near the lower rail, so some traders use band touches as regime markers rather than trade signals.
• As a check on extrapolation: because small parameter changes compound over years, projections are treated as scenario ranges, and refitting as new data arrives can shift the entire corridor.