Bitcoin's current price is 0.58× its power-law fit (October 18, 2026 close): $82,116 against a fitted $140,559, inside the band of $56,744 to $742,423 that has held 95% of days.
Plot bitcoin’s price on a log scale against the number of days since the genesis block, also on a log scale, and the whole history of daily closes falls around a straight line. That line is the power law. We fit it to our own price data and refit it every day. Using daily closes up to 18 Oct 2026, the fitted exponent is 5.60. That day the close stood at 0.58 times the fitted value ($140,559), and the lower band, which 2.5% of all days in the history fell below, was at $56,744. It is a fit to what has already happened, not a forecast.
“Bitcoin power law: price at $82,116 is 0.58× its fitted value of $140,559, 18 Oct 2026 close.” NodeWitness, https://nodewitness.com/en/charts/bitcoin-power-law-chart/
Picture a parent walking a long trail while their kid rides alongside on a bike. The parent is the fitted line: always moving forward, but covering proportionally less ground each year. On the fit through 17 Oct 2026, the line rose 271% in the twelve months to 17 Oct 2013 and 38% in the twelve months to 17 Oct 2026. The kid is the price, racing far ahead at times and dawdling behind at others. Each burst ahead has been shorter than the last: at its cycle peaks, price reached 16.51 times the line in 2011, 10.92 in 2013, 6.40 in 2017, 3.61 in 2021 and 1.39 in 2024. The lags, by contrast, have barely changed, between 0.37 and 0.59 times the line at every low since 2015. Two caveats. The parent’s route, and the bands showing how far the kid strays on 95% of days, weren’t mapped before the walk; we drew them at the end, from where the kid had been. And nothing ties the two together. The kid has always come back so far, but that is a pattern in the data, not a law.
The top panel shows price in grey, the fit in orange and the two dashed bands, with price on a log scale. Time, though, runs on an ordinary date axis, which is why the line looks curved: steep at first, flatter and flatter after that. In the model itself time is logged too, and there it really is a straight line.
The bottom panel divides price by the fit. A reading of 1 means price is sitting on the line, 0.5 means half of it and 2 means double. That strips out the long-run growth and leaves only the distance, which makes different eras easy to compare. The table lists each year’s highest and lowest reading.
Two traps to avoid. One is treating the line as where price “should” be: it is an average of the history, and price spends a lot of time under it (56% of days up to 18 Oct 2026). The other is treating the bands as a guaranteed floor and ceiling. They are set so that 95% of past days fit between them, so of course the history sits inside.
The roots go back to 2014, when a BitcoinTalk user going by Trolololo posted a log regression that, rewritten, is a power law [4]. The physicist Giovanni Santostasi was the one who framed it that way: in September 2018 he posted on Reddit a chart of price against days since the genesis block with both axes logged [2], and in January 2024 he put the exponent at 5.83 [4]. Harold Christopher Burger popularised the idea in 2019 with a corridor between two power-law lines and an exponent of 5.845 [5]. Santostasi argues it comes from network growth: more users lift the price, a higher price draws in more mining and security, and that security draws in more users [3]. That is his reading; the fit by itself doesn’t prove it.
On our data, the exponent moves depending on where the history stops. On closes through 31 Dec 2013 it was 6.44; through 31 Dec 2017, 5.63; through 31 Dec 2021, 5.84; and through 31 Dec 2025, 5.66. On closes through 18 Oct 2026 it is 5.60. Other researchers report values between 5.6 and 5.9, depending on the period and method [6].
On the ratio, each cycle has peaked lower than the last. Using the fit through 17 Oct 2026, the daily high was 16.51 in June 2011, 10.92 in November 2013, 6.40 in December 2017, 3.61 in March 2021 and 1.39 in December 2024, and the highest close in our series, $124,777 on 6 Oct 2025, came with the ratio at 1.24. The lows have moved far less: 0.37 in August 2015, 0.59 in December 2018, 0.46 in March 2020, 0.45 in November 2022 and 0.46 on 30 Jun 2026. Price hasn’t closed above the upper band since 6 Jan 2018, or below the lower band since 15 Oct 2015.
Highest and lowest daily ratio in each calendar year, most recent first. They come from the fit through yesterday’s close, so they can shift slightly from one day to the next.
We take every daily USD close from 17 Aug 2010 to yesterday [1] and, for each one, the number of days since the genesis block was mined on 3 Jan 2009. An ordinary least-squares line is fitted between the log of price and the log of those days, which is the same as price = A × days^b. A sets the height of the line; b, the exponent, sets how steep it is: multiply the number of days by some factor and the fit is multiplied by that factor raised to the power b. For example, 17 Oct 2026 was day 6,496 since genesis, twice the 3,248 days reached on 25 Nov 2017, and on the fit through that date the line stands a little over 48 times higher than it did then, because 2 to the power 5.6 is just over 48.
The bands are the same line moved up and down. We measure each close’s distance from the line in log terms and take the 2.5th and 97.5th percentiles of those distances, so 95% of days sit between the bands by construction. Everything is refitted daily over the full history, and neither the line nor the bands are extended past the latest close.
Using closes up to 11 Oct 2026, our lower band for that day comes out at $56,516. Jurrien Timmer’s chart at Fidelity, on weekly data as of the same date, put the lower line of his power law at $56,488 [7]. He doesn’t publish his method, so a 0.05% match may be partly luck. Other public models land on different fitted values and bands because they pick a different period, price series or measure of spread.
The line is fitted over the full history, so its value on any past date uses prices that came later; it isn’t what the model “said” at the time. Each new year of data moves the exponent and the bands, as the history above shows. A high R², 0.96 on closes through 17 Oct 2026, doesn’t prove much on its own either: two series that both grow over time nearly always fit a line well, and the days aren’t independent, since today’s price is a lot like yesterday’s. Price having stayed between the bands says nothing about what it does next. This page describes the series; it is not investment advice.
How Fidelity reads bitcoin through a power law, set against Mike McGlone’s $10,000 call, is in our McGlone vs Fidelity analysis. Short definitions of log scale and overfitting are in the glossary, and where other price-based cycle indicators stand today, each against its own history, is on Bitcoin top and bottom indicators today.
A model linking price to time: price = A × days^b, with days counted from the genesis block on 3 Jan 2009. Put both on a log scale and that relationship is a straight line with slope b. It uses no on-chain data at all, just price and the calendar.
On our daily closes through 18 Oct 2026, 5.60. Santostasi published 5.83 in 2024 and Burger 5.845 in 2019; the gap comes from the period, the price series and the fitting method. On our data it has gone from 6.44 on closes through 2013 to 5.63 through 2017 and 5.84 through 2021. Every new year of data shifts it.
No. It is a fit to past prices. A line matching more than fifteen years of history well doesn’t bind price to it, and the exponent changes every time data is added. That is why we don’t extend it past the latest close. This is not investment advice.
Because only price is on a log scale; time runs on a normal date axis. The power law is a straight line when both axes are logged, and on a normal time axis the same line bends. On the fit through 17 Oct 2026, its value rose 271% in the twelve months to 17 Oct 2013, 116% in the twelve months to 17 Oct 2016 and 38% in the twelve months to 17 Oct 2026.
Because the bands capture the spread of the whole history, and most of that spread comes from the early years: the 2011, 2013 and 2017 bubbles ran far above the line. Price hasn’t closed above the upper band since 6 Jan 2018. With milder cycles, the band is drifting closer to the line: on closes through 31 Dec 2013 it sat at 8.44 times the fit, and on closes through 31 Dec 2025, at 5.44.
The rest of the cycle metrics are on Cycle & Score.