Bitcoin power law

How to read it

Plotted with both axes logarithmic — price against time since the genesis block — Bitcoin's history flattens into something close to a straight line. A straight line on log-log axes is a power law: price growing as a fixed power of age, rather than at a fixed percentage per year. The dashed centre line is the fitted trend; support and resistance are the envelope past prices have stayed inside, extended a few years forward.

How it's calculated

An ordinary least-squares fit of log price against log days since genesis, over the full daily history available. The result takes the form log₁₀(price) = a + b · log₁₀(days), with the exponent b landing near 5.8. Support and resistance are that line offset by fixed amounts in log space, chosen to contain the historical range.

The fit is re-estimated on every daily build, so both the exponent and the band levels move as new data arrives. Two screenshots of this page taken a year apart are not quite the same model.

What it did in past cycles

The model's practical record over the last two cycles is one of drift. The rainbow bands, which are this same fit with labels attached, show it numerically: price closed above the top band on 151 of 4,345 days, and the last of those was 2021-05-11. At the October 2025 peak, price reached only 38% of the level the top band had drifted to.

That is what a model calibrated on steep early growth does when growth flattens. It keeps extrapolating the old slope, and the market moves further below it every year without anything being 'wrong' in the fit's own terms.

The support side has held up better, which is the usual fate of lower bounds on a rising series — but it too has drifted upward faster than price since 2021.

What it doesn't tell you

A power law fitted to a series that has only ever gone up will find that the series goes up. There is no mechanism here — no theory of why an exponent near 5.8 should hold — only a curve that has fitted well so far, on a single asset, over a single fifteen-year run.

The projection is where it becomes least useful. Extended forward a few years, the envelope this page draws spans from roughly $170,000 to $2.8 million. A band that wide is compatible with almost any outcome, which is another way of saying it forecasts nothing.

Fitting in log-log space also weights the earliest data enormously. Bitcoin's first thousand days, when price moved from cents to dollars, occupy as much horizontal room in the fit as the last decade — so the model is anchored on a period whose dynamics have no modern equivalent.

Reading it with other metrics

The power-law rainbow is this fit with bands and conventional labels; this page is the underlying model without them.

The 200-week moving average is the instructive contrast — a trailing average that adapts to what the market does, against an extrapolation that does not. Over the last two cycles the adaptive one tracked price and the extrapolated one did not. AVIV Z-Score answers the same 'is this expensive?' question from cost basis instead of from time.