Does the Bitcoin power law work?
The power-law position at 95 or above. Mixed: 3 of 4 signals were on within 90 days of a cycle top, catching 3 of the 4 tops in its record; a year later the price had changed by a median −24.5%, against +72.6% for a typical day of the same cycles. With 3 independent signals, chance cannot be ruled out.
The power-law position below 5. Held up: 5 of 10 signals were on within 90 days of a cycle bottom, catching 3 of the 4 bottoms in its record, and a year later the price had changed by a median +274%, against +79.4% for a typical day of the same cycles.
- The power-law position at 95 or above: 4 signals; 3 of 4 decided were on within 90 days of a cycle top (1 false alarms); it caught 3 of the 4 cycle tops in its record.
- The power-law position below 5: 10 signals; 5 of 10 decided were on within 90 days of a cycle bottom (5 false alarms); it caught 3 of the 4 cycle bottoms in its record.
What followed the signals
The power-law position at 95 or above
| After | Signals | Median change | Mean change | Share up | All days: median | All days: share up | Same cycles: median |
|---|---|---|---|---|---|---|---|
| 7 days | 4 4 independent | +2.3% | +4.5% | 50% | +0.8% | 55% | +0.8% |
| 30 days | 4 4 independent | +28.7% | +31.9% | 50% | +3.3% | 58% | +3.1% |
| 90 days | 4 4 independent | +29.0% | +172% | 75% | +10.4% | 60% | +12.3% |
| 365 days | 4 3 independent | −24.5% | +1132% | 50% | +85.4% | 71% | +72.6% |
The power-law position below 5
| After | Signals | Median change | Mean change | Share up | All days: median | All days: share up | Same cycles: median |
|---|---|---|---|---|---|---|---|
| 7 days | 10 10 independent | +15.7% | +12.1% | 70% | +0.8% | 55% | +0.8% |
| 30 days | 10 10 independent | +16.1% | +17.3% | 70% | +3.3% | 58% | +3.1% |
| 90 days | 10 8 independent | +30.9% | +28.4% | 90% | +10.4% | 60% | +12.3% |
| 365 days | 8 5 independent | +274% | +361% | 100% | +85.4% | 71% | +79.4% |
Every signal
The power-law position at 95 or above
| First day | Reading | BTC close | 7 days | 30 days | 90 days | 365 days | Nearest cycle top | Near a turn |
|---|---|---|---|---|---|---|---|---|
| 29 Jan 2013 341 days in signal | 100.0 | $19.54 | +5.4% | +70.8% | +637% | +4637% | 309 days before the 2013 top (4 Dec 2013); price −98.4% from it | Hit |
| 25 Nov 2017 49 days in signal | 95.0 | $8,755 | +24.7% | +58.0% | +16.2% | −54.3% | 21 days before the 2017 top (16 Dec 2017); price −54.7% from it | Hit |
| 7 Jan 2021 101 days in signal | 95.0 | $39,479 | −0.8% | −0.5% | +41.7% | +5.2% | 305 days before the 2021 top (8 Nov 2021); price −41.6% from it | False alarm |
| 5 Sep 2021 58 days in signal | 95.1 | $51,784 | −11.1% | −0.5% | −4.9% | −61.8% | 64 days before the 2021 top (8 Nov 2021); price −23.3% from it | Hit |
| Cycle top | BTC close | Signal on within 90 days |
|---|---|---|
| 4 Dec 2013 | $1,238 | Yes: the signal from 29 Jan 2013, which began 309 days before it |
| 16 Dec 2017 | $19,345 | Yes: the signal from 25 Nov 2017, which began 21 days before it |
| 8 Nov 2021 | $67,549 | Yes: the signal from 5 Sep 2021, which began 64 days before it |
| 6 Oct 2025 | $124,766 | No signal on within 90 days |
The power-law position below 5
| First day | Reading | BTC close | 7 days | 30 days | 90 days | 365 days | Nearest cycle bottom | Near a turn |
|---|---|---|---|---|---|---|---|---|
| 16 Feb 2012 302 days in signal | 4.8 | $4.27 | +17.3% | +22.0% | +19.1% | +534% | 90 days after the 2011 bottom (18 Nov 2011); price +108% from it | Hit |
| 14 Jan 2015 308 days in signal | 0.0 | $164.92 | +38.4% | +43.2% | +32.2% | +160% | the same day the 2015 bottom (14 Jan 2015); price 0.0% from it | Hit |
| 22 May 2016 | 4.9 | $439.62 | +17.4% | +51.8% | +32.5% | +383% | 494 days after the 2015 bottom (14 Jan 2015); price +167% from it | False alarm |
| 2 Aug 2016 | 4.8 | $513.43 | +14.0% | +11.4% | +36.1% | +430% | 566 days after the 2015 bottom (14 Jan 2015); price +211% from it | False alarm |
| 12 Mar 2020 7 days in signal | 0.0 | $4,917 | +25.8% | +40.1% | +101% | +1065% | 453 days after the 2018 bottom (15 Dec 2018); price +52.1% from it | False alarm |
| 27 Aug 2022 156 days in signal | 4.4 | $20,038 | −1.0% | −4.0% | −17.6% | +30.2% | 86 days before the 2022 bottom (21 Nov 2022); price +27.1% from it | Hit |
| 14 Jun 2023 | 3.9 | $25,126 | +19.4% | +20.7% | +2.8% | +166% | 205 days after the 2022 bottom (21 Nov 2022); price +59.4% from it | False alarm |
| 17 Aug 2023 64 days in signal | 3.6 | $26,630 | −1.7% | −0.2% | +42.3% | +121% | 269 days after the 2022 bottom (21 Nov 2022); price +69.0% from it | False alarm |
| 5 Feb 2026 39 days in signal | 2.1 | $62,858 | +5.3% | +7.0% | +29.6% | – | 145 days before the current cycle's bottom so far (30 Jun 2026); price +7.4% from it | Hit |
| 27 May 2026 146 days in signal | 4.7 | $74,337 | −13.9% | −19.3% | +5.6% | – | 34 days before the current cycle's bottom so far (30 Jun 2026); price +27.0% from it | Hit |
| Cycle bottom | BTC close | Signal on within 90 days |
|---|---|---|
| 14 Jan 2015 | $164.92 | Yes: the signal from 14 Jan 2015, which began that day it |
| 15 Dec 2018 | $3,233 | No signal on within 90 days |
| 21 Nov 2022 | $15,760 | Yes: the signal from 27 Aug 2022, which began 86 days before it |
| 30 Jun 2026 | $58,532 | Yes: the signal from 27 May 2026, which began 34 days before it |
Method and sources
Signals. Top signal: the power-law position at 95 or above; Bottom signal: the power-law position below 5. The levels are the ones commonly quoted for this indicator, fixed before any result was looked at. A signal starts on the first day the condition holds after it has been off for at least 30 days, so a run of days counts once (the same rule as the signal lab).
Point in time. The published power-law lines are refitted every 1 January on every close up to the end of the year before and drawn over all history, so their past positions use prices that came later. Here each year is read against the 1-99% quantile lines it had that year (the same quantile regressions of log price on log days since 3 January 2009, from the same code), starting once a fit has a full year of closes. Daily readings are closed UTC days from 1 January 2012 to 26 October 2026; the open day is never used.
Outcomes. The change of the BTC daily close from the close of the signal's first day to the close 7, 30, 90 and 365 days later, against the same change from every day the indicator has a reading (the base rate). Signals whose windows overlap share the same price moves, so the tables also count independent signals: windows that do not overlap, counted from the first. Recent signals wait for their outcomes.
Cycle tops and bottoms. A cycle top is an all-time-high close followed by a fall of at least 75% before any higher close; the latest all-time high starts the current cycle. A cycle bottom is the lowest close between two tops; the current cycle's bottom is its lowest close so far, so it can still move. A signal is a hit when a turn of its kind came while it was on or within 90 days either side (from 90 days before its first day to 90 days after its last), and a false alarm otherwise; a signal still on, or ended less than 90 days ago, waits. The verdict compares each signal with the median change of every day in the same four-year halving cycle, so the outsized early years neither flatter nor penalise later signals.
Plans. The chart is Free, so every signal and today's reading are shown to everyone.
Sources. Our own Bitcoin node and BTC/USD price record, through the published chart linked below. Past signals describe what happened; they are not a forecast and nothing here is investment advice.
Questions
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How is this backtest calculated?
Each signal is the first day the power-law position meets its level after at least 30 days without it, using only data that existed that day. We measure the BTC price change 7, 30, 90 and 365 days later against the same change from every day and from the days of the same four-year cycle, and the distance to the nearest cycle top or bottom.
Open the Power law chartAll free tools
Signals and outcomes are calculated by CryptoKeyhole from our own Bitcoin node and price data, using only data that existed on each day. Past signals describe what happened; they are not a forecast, and nothing here is investment advice.