What did the power law predict, and what happened?
Six years ago, using only the prices known then, the power law put today's trend at $161,084; two years ago it said $154,766. Today's price is $81,462. Every fit since 2017 placed today's trend between $130,306 and $202,522, so the trend line moved far less than the price did, and the price sits below all of them. Out of sample, the price stayed inside the 0.4×–3× bands on 88% of days since 2016.
The test, with no look-ahead
A model that is refitted every night can always look good in hindsight. The fair test is to go back to a date, fit the power law using only the closes that existed before it, and then compare what that fit implied with what followed. That is what this page does, from Coin Metrics daily closes: an ordinary least-squares line through log price against log days since the genesis block (3 January 2009), fitted at every 1 January since 2014 and at the dates exactly 2, 4 and 6 years ago.
What the fits of 2, 4 and 6 years ago said
Each column is a fit frozen on its date. The cells show the trend it implied on each later 1 January and today, with the actual price divided by that trend in brackets: 1.00× means exactly on trend, 0.40× is the lower band, 3.00× the upper band.
| 1 Jan | Actual | Fit of 20 October 2020 | Fit of 20 October 2022 | Fit of 20 October 2024 | Today's fit |
|---|---|---|---|---|---|
| 1 January 2021 | $29,381 | $16,779 (1.75×) | — | — | $15,554 |
| 1 January 2022 | $47,560 | $26,552 (1.79×) | — | — | $24,426 |
| 1 January 2023 | $16,607 | $40,611 (0.41×) | $47,026 (0.35×) | — | $37,095 |
| 1 January 2024 | $44,049 | $60,319 (0.73×) | $70,407 (0.63×) | — | $54,734 |
| 1 January 2025 | $94,456 | $87,418 (1.08×) | $102,806 (0.92×) | $84,330 (1.12×) | $78,834 |
| 1 January 2026 | $88,684 | $123,752 (0.72×) | $146,560 (0.61×) | $119,106 (0.74×) | $110,954 |
| Today | $81,462 | $161,084 (0.51×) | $191,792 (0.42×) | $154,766 (0.53×) | $143,791 |
The older fits are close to each other and close to today's fit. That is the real finding: once there were about eight years of data, the trend line stopped moving much. The price did not follow the line; it swung around it, as it always has.
Where it missed
Measured out of sample, against the fit made on 1 January of each year, the price closed below the lower band on 8.7% of days since 2016 and above the upper band on 3.1%. The worst low was 0.33× the trend on 22 May 2016, when the fit still carried the 2013 bubble and its exponent was too steep. The worst high was 7.15× on 16 December 2017, the peak of the 2017 bubble.
The bands are not a law either. Against today's fit, over the whole history, 90% of daily closes sit between 0.4× and 3×; 2.1% are below. A band that holds about nine days in ten is useful, but it is not a floor.
The exponent drifts
The exponent is a regression estimate, not a constant. Fitted at each 1 January since 2016 it ranged from 5.62 to 6.03; today it is 5.64. Bull runs pull it up, long bear markets pull it down, and the honest uncertainty is about ±0.4 because consecutive daily prices are not independent observations.
| Fit made on | Exponent | R² | Trend it implies for today | Price today ÷ that trend |
|---|---|---|---|---|
| 1 January 2014 | 6.54 | 0.860 | $670,413 | 0.12× |
| 1 January 2015 | 6.85 | 0.905 | $1,243,878 | 0.07× |
| 1 January 2016 | 6.03 | 0.885 | $272,080 | 0.30× |
| 1 January 2017 | 5.62 | 0.889 | $130,306 | 0.63× |
| 1 January 2018 | 5.73 | 0.909 | $157,051 | 0.52× |
| 1 January 2019 | 5.87 | 0.924 | $198,965 | 0.41× |
| 1 January 2020 | 5.80 | 0.934 | $179,270 | 0.45× |
| 1 January 2021 | 5.74 | 0.941 | $162,365 | 0.50× |
| 1 January 2022 | 5.89 | 0.948 | $202,522 | 0.40× |
| 1 January 2023 | 5.82 | 0.951 | $182,901 | 0.45× |
| 1 January 2024 | 5.71 | 0.952 | $158,374 | 0.51× |
| 1 January 2025 | 5.70 | 0.957 | $155,218 | 0.52× |
| 1 January 2026 | 5.70 | 0.961 | $155,275 | 0.52× |
| Today | 5.64 | 0.962 | $143,791 | 0.57× |
The 2014 and 2015 fits are the cautionary tale: with only four or five years of data, dominated by the 2013 bubble, they implied a trend for today several times higher than anything since. Early fits were wrong; later fits converged. Whether they keep converging is the open question, and this page will show it, because it is rebuilt every night.
Frequently asked questions
Has the Bitcoin power law been accurate?
Is this backtest free of look-ahead bias?
Why does the power law exponent change?
Does the power law predict the price?
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Numbers updated 20 October 2026 · Coin Metrics daily closes through 19 October 2026 · price $81,462 · trend $143,791