You've met the Power Law. This page looks at it through a single lens — price doublings — with three visuals that make its behavior tangible: where each doubling has landed, how far the market strays from the trend, and what the pattern is (and isn't) telling you.
This page builds directly on the doubling-cadence framing of Matthew Mezinskis (Porkopolis Economics · porkopolis.io/thechart), whose published table first laid the per-doubling progression out as a ladder. The underlying power-law theory it rests on originates with Dr. Giovanni Santostasi, and the earliest logarithmic-regression sketch of Bitcoin's price came from the pseudonymous Trolololo (BitcoinTalk, 2014). The reframing, the deviation analysis, and any errors here are this site's own.
Mezinskis spotted it first: laid out as a ladder, bitcoin's price doublings come at a steady cadence — each one takes about 12.8% more of bitcoin's life than the last. Not magic — arithmetic, as we'll show. What this page adds is a way to see it: where each doubling has actually landed, and how far the market strays from the line along the way.
Each 12.8% of additional age has doubled the price. That's the whole pattern — and it's a fact about the math, not a habit of the market.
The ~12.8%-per-doubling cadence isn't bitcoin keeping time. It is what any power law of exponent 5.76 must do, by algebra alone.
A fixed 12.8% of a growing age means each doubling takes longer in calendar time than the last: 128 days when the network was 1,000 days old, but 766 days when it was 6,000 days old. The cadence is constant in proportion and stretching in years. The ladder is the Power Law trend line, marked with a step at each price doubling — a record of past doublings, with the steps extrapolated forward. Not a schedule; a consequence of the curve.
If the ladder is “just algebra,” where is the genuinely remarkable part? Here: across more than fifteen years, the actual price has spent the whole time misbehaving — overshooting wildly in every mania, crashing far below in every bear market — and yet, averaged over its entire life, it sits almost exactly on the trendline.
The trend doesn't tick like a clock. It pulls like gravity. Price is always somewhere it shouldn't be, and always being dragged back — reversion to the mean.
Measure the distance from trend month by month — ln(actual ÷ trend) — and the record is anything but orderly. It is a series of enormous excursions: up to +2.5 in the 2011 and 2013 frenzies (roughly twelve times the trend), down past −0.9 in the deepest bear troughs (the wave plots ln(actual ÷ trend), so +2.5 means about 12× above the line; −0.9 means roughly 0.4×). But sum all 191 months and the mean log-deviation is +0.014 — just a whisker above the line. The median month sits slightly below trend; only about 41% of months close above it. The average is held near zero not by calm, but by a few violent overshoots balancing many quiet undershoots.
The ceiling is falling; the floor holds. Each mania has overshot the trend less than the last — about 9× in 2011, 4× in 2017, 3× in 2021 — while every bear has bottomed near 0.4× of trend. The wave is compressing from the top: bitcoin's overshoots are shrinking as the asset matures, even as its floor stays remarkably constant. The dashed green line fits the four cycle peaks; the dashed red line fits the four cycle troughs.
Four cycles is a small sample, and 2013 overshot more than 2011; read this as a tendency across recent cycles, not a guarantee the ceiling keeps falling.
The wave isn't just describing the past — it's been a rough map of where the risk sat. Two things stand out across fifteen years.
The swings are shrinking. The spread of price around the trend has compressed every few years — from enormous in the early cycles to a fraction of that lately. As bitcoin has grown, its overshoots and undershoots have both pulled in toward the line. (This is the maturing-asset story The Bitcoin Horizon makes in full: as a network gets adopted, its price stops behaving like a lottery ticket and starts behaving like an asset.)
Where you stood relative to the trend has mattered. Historically, the further below the line bitcoin sat, the stronger the years that followed; the further above, the weaker. In the record so far, periods that began well below trend went on to far outpace periods that began well above it. The line behaves like a center of gravity — stretched far from it, the pull back has tended to be strongest.
None of this is a signal to act on, and past patterns can break. But it reframes the deviation wave from a curiosity into something with a use: a sense of when the asymmetry has favored patience, and when it has favored caution. That's the discipline Disciplined Rebalancing turns into an explicit, rules-based method — sell into the highs, buy into the lows, by the channel rather than by feel.
The audit trail. Every figure on this page is reproducible from the daily Blockchain.info series and the stated coefficients. The deviation statistics below are recomputed in-browser from the embedded month-end series, so what you read is provably what the wave is drawn from.
| Doubling level | Trend reaches | Market first reached | Lead / lag |
|---|
The trend says when each level arrives on the line. Market history has always under- or over-shot it. Move the slider to see when the remaining doublings would occur on your own assumption. These are scenarios to explore — not a prediction of the schedule.
| Doubling level | Trend date | Your-scenario date |
|---|
The doubling cadence is arithmetic; the adherence to trend is the empirical claim. Only the second can fail, and it is the one worth exploring. The trend is an observed regularity across fifteen years, not a law of nature, and not any guarantee about the next fifteen. That said, the fit is strong — the trend has held a ~95% R² across fifteen years, and the channel floor tighter still — and the model's value is in projections, not promises. Being far below the trend, as bitcoin periodically is, has historically preceded a more favorable forward setup; being far above it, the reverse. The discipline is to read the ladder as a center of gravity to reason from, not a schedule to count on.
The exponent is sensitive to how you fit it. Using the canonical Porkopolis / Santostasi coefficients (a = 1.69×10−17, b = 5.763), an ordinary least-squares fit through end-2023 reproduces b ≈ 5.77. A naive fit over the entire series through 2026 instead yields b ≈ 5.63, because recent prices have run slightly under the steep early-fitted trend. The cadence shifts with the exponent: 12.8% per doubling at b = 5.76, about 13.1% at b = 5.63.
Future rungs — everything above today's price — are projections of the trend, not predictions of when the market will arrive. Past rungs show the market reaching levels years early or, occasionally, late; there is no reason the future will be tidier. Treat the upper ladder as a scenario to reason from, never a timetable.
The doubling-cadence framing and the per-doubling progression table this page is built around. The canonical coefficients used here are from his work.
Originator of the Bitcoin Power Law theory — the structural explanation for why price = a · dayb holds at all.
The earliest logarithmic-regression chart of Bitcoin's price, the seed of the later power-law work.
Full daily history since 2009. The ladder's first-crossing dates and the month-end deviation series are computed directly from it.
Every page on this site has been improved by someone pushing on it. Ask a question, flag an error, or suggest what’s missing — it goes straight to the author, never published.