Study · re-run every night · updated Oct 15, 2026

Does Bitcoin follow a power law? The line as each day could have drawn it, tested

Bitcoin closed at $81,682 on Oct 14, 0.66 times its power-law line of $123,662: half to 1 times the line. The line is fitted on every close up to that day, 6,493 days after the genesis block, and grows with time to the power 5.33. Drawn through every close on file today, the line had Bitcoin as low as 0.46 times it (Mar 12, 2020); as each day could have drawn it, the lowest reading since 2017 was 0.39 (Nov 9, 2022). Bitcoin bought at a close 0.50 to 0.99 times the line did +170.2% over the next year on average, against +19.3% after the other days. No band is clear of luck (a luck test of 3 with both halves of the days agreeing): the stretches far from the line are few, and a year's hold shares most of its days with the next. Past patterns, not financial advice.

Today

0.66×

half to 1 times the line

The line

$123,662

Bitcoin closed $81,682

Slope

5.33

time's power on a log-log chart

Every day

+77.7%

Bitcoin, the next year

First written Oct 15, 2026 · 1 revision

§ 01 · Today

Today

as of Oct 15, 2026 · Bitcoin's daily closes, Dec 30, 2017 to Oct 14, 2026

"Bitcoin follows a power law", the saying goes: on a chart with both axes in logs - the price against the days since the genesis block of January 3, 2009 - its closes fall around a straight line, and the line is drawn as its fair price, a floor under it and a ceiling over it. Drawn today through every close, any line looks good: it was fitted to the very closes it is checked on. So here the line is drawn each day anew, by least squares through the closes up to that day alone, and each close is set against the line it could have known - under half of it, half to 1 times it, 1 to 2 times it, twice it or more - and every day is a buy of Bitcoin at that close, held 90 days, 180 days or a year, against all the other days.

Oct 14, 2026, 6,493 days after the genesis block: Bitcoin closed at $81,682, 0.66 times its power-law line of $123,662: half to 1 times the line. Today's line grows with time to the power 5.33. Drawn through every close on file, it had Bitcoin as low as 0.46 times it on Mar 12, 2020 and as high as 5.17 times it on Jan 6, 2018; as each day could have drawn it, the lowest reading was 0.39 (Nov 9, 2022) and the highest 9.10 (Jan 5, 2018).

Bitcoin (a log scale)the line as each day drew itthe line drawn todaycloses under the day's line

§ 02 · After it

What came after it

as of Oct 15, 2026 · Bitcoin, from the reading day's close

Bitcoin's average next yearevery day's averageunder each bar: its days

Against the line	Days	Stretches	Next 90 days	Next 180 days	Next year
Far under it under 0.50×	107	4	+29.4%	+57.6%	+111.0%
Under it 0.50 to 0.99×	1,348	16	+26.6%	+69.8%	+170.2%
Over it 1.00 to 1.99×	1,271	12	+5.8%	+8.1%	+28.8%
Far over it 2.00 or more×	395	6	−11.3%	−20.0%	−35.5%
every day	3,121	—	+13.4%	+31.8%	+77.7%

Days and stretches count the days with 90 days after them; a stretch ends after 7 days out of its band. Today's band is marked. Each band against all the other days over the same hold, with its luck test under it (✓ past the bar, both halves of the days agreeing; the halves on hover):

Against the line	Next 90 days	Next 180 days	Next year
under 0.50×	too few	too few	too few
0.50 to 0.99×	+23.2% t 1.7	+65.0% t 2.0	+150.9% t 2.0
1.00 to 1.99×	−12.8% t −1.0	−40.8% t −1.5	−86.8% t −1.5
2.00 or more×	−28.3% t −1.5	−59.5% t −1.7	too few

Half to once the line (0.50 to 0.99 times the line) came on 1,102 days in 15 separate stretches, the last on Oct 14, 2026. Bitcoin bought at the close of one of those days rose over the next 365 days 96% of the time (+122.9% in the middle case, +170.2% on average): +150.9% against the other days, +247.0% in the older half of the days and +91.6% in the newer. A luck test of 2.0, not past the bar of 3.0: 5 holds that share no day, and a few long stretches decide the average.

§ 03 · How it is tested

How it is tested

as of Oct 15, 2026 · methodology

A luck test (t) says how far a result sits from zero, in units of its own noise: about 2 is rarely luck for one test, but many tests at once need more, which is what the first cut is for.

Each day's line is the least-squares fit of the base-10 log of every close up to that day against the log of its days since Jan 3, 2009, the genesis block; it needs 1,460 closes on file, about four years, so the first reading comes Dec 30, 2017. No close is read against a line drawn with later ones. Neighbouring days share most of their 90, 180 or 365 days, so the luck test does not count them as fresh evidence: each calendar day weighs in by how many of the band's holds, and of the other days', cover it, so a band counts as the holds that share no day, and each band is set against all the other days over the same hold. With 8 tests, a result needs a luck test of 3.0 or more and both halves of the days on its side.

Our closes miss Bitcoin's first five years, whose prices the usual power-law charts lean on; their line, fitted on 2010's closes on, is steeper and sits elsewhere. The bands were set before any number here was read: half the line, the line, twice it. Moves are Bitcoin's own price, before trading costs.

§ 04 · Revisions1 dated

Revisions

as of Oct 15, 2026 · every change to its headline numbers, dated

This study is re-run every night on the whole history. It was first written on Oct 15, 2026; its numbers last moved on Oct 15, 2026. Each night its headline numbers moved is listed here, newest first.

Oct 15, 2026Bitcoin over the next year against the other days: after closes under half its power-law line 0% · twice it or more 0%

§ 05 · More

More research

as of Oct 15, 2026