What the power law model is
Plot Bitcoin's price against its age with both axes on log scales, and fourteen years of chaos collapse toward a straight line. That is the power law: price growing roughly as age raised to a constant power. We fit the line by ordinary least squares over every daily close since 2011 and draw the corridor that contained 95% of history around it — trend, upper edge, lower edge, all from one regression.
The methodology, in full
ln(price) = a + b·ln(days since 2009-01-03), fitted by OLS; corridor edges at the 2.5th and 97.5th percentiles of residuals. The fit is recomputed as new data arrives, so the exponent you see is measured, not asserted. Anyone can reproduce it from public daily closes in a few lines of code — that transparency is the point.
How to read it
The trend is gravity, not prophecy. Price has spent years above the line and years below it — those excursions are the cycles you can see aligned on the cycle comparison. Historically, touches of the upper corridor edge coincided with euphoric tops (check the risk score at those moments) and rides along the lower edge with deep bear markets. The deviation number in the title is simply how far price sits from trend today.
An honest caveat
A power law describes the past; it does not owe us a future. The fit is dominated by early explosive growth, and a maturing asset can leave any historical curve. We publish it because it is useful context with the error bars shown — not because the line knows where price goes next.
FAQ
What is the Bitcoin power law?
The observation that Bitcoin's price has grown roughly as a power of its age: on a chart where both price and days-since-genesis are on log scales, the whole history clusters around a straight line. We fit that line by ordinary least squares and draw a corridor holding 95% of history around it.
How is the trend line fitted?
Ordinary least-squares regression of ln(price) on ln(days since 2009-01-03), using every daily close since 2011. The corridor edges are the 2.5th and 97.5th percentiles of the residuals. The fit refreshes with the data — no hand-drawn lines.
Is the power law a price prediction?
No. It is a curve that has described the past well. Extrapolating it assumes the next decade behaves like the last one — a strong assumption. We show where price sits relative to the historical trend and let you draw conclusions.
How is this different from the stock-to-flow model?
Stock-to-flow models price from supply scarcity and made specific forecasts that missed badly in 2021–2022. The power law makes no supply argument: it is a descriptive fit of price against time, with an honest error band.
What does the current deviation mean?
Deviation above the trend has historically clustered around cycle tops, deviation near the lower corridor edge around bear-market bottoms. It is context for position sizing, not a signal by itself.
Related: Drawdown from ATH · Risk levels · Position sizing