Statistics · Cycles & signals

Bitcoin Power-Law Corridor

On a log scale Bitcoin's price has tracked a power-law straight line remarkably closely for 15 years (R²=0.96). Around that trend we build a corridor from the historical deviations: green below (historically cheap), red above (expensive). Right now price sits -53 % below trend - in the 10th percentile of history, i.e. "Deep value". This describes the past; a power law is neither a law of nature nor a forecast.

Price now
$64,213
Trend (fair value)
$136,121
15-year power law
Deviation from trend
-53 %
10th percentile
Valuation zone
Deep value
bottom 10%

Price, trend & valuation corridor

Black line = price, dashed = the fitted trend (fair value). The bands are the historical deviations: greener means price was cheaper relative to trend; redder means more expensive.

$1$10$100$1k$10k$100k$1M201020122014201620182020202220242026NOW
Hover the chart for date, price, trend & valuation zone.
Deep valuebottom 10%← nowUndervalued10th-30th pctFair · on trend30th-70th pctExpensive70th-90th pctOverheatedtop 10%

Methodology & data

Daily closes from our own price database (last price of each UTC day, USD historically real, since 2010). We fit ln(price) = a + b·ln(days since genesis) by linear regression - exponent b=5.66, R²=0.96. The corridor is the quantiles of the deviations (residuals) from the trend: the bands sit at the 1st/10th/30th/50th/70th/90th/99th percentiles. The fit runs over the whole history including today and shifts as new data arrive - it is a reading, not a forecast. Euro at the ECB daily rate. Not financial advice.

Frequently asked questions

01What is the Bitcoin power law?

Plot Bitcoin's price and its age since the genesis block both logarithmically and 15 years form nearly a straight line - a power law: price grows roughly with time to the power of 5.7. We fit that line by regression on our own daily price series; the fit quality is R²=0.96.

02Is Bitcoin cheap or expensive right now?

Against the 15-year trend, price currently sits -53 % below it - the 10th percentile of all historical deviations, zone "Deep value". That's a reading relative to its own history, not a price forecast.

03Is this the same as the "rainbow chart"?

Related, but computed more cleanly. Popular rainbow charts often draw the bands by hand. Here the bands are the actual quantiles of the deviations from the regressed trend - reproducible from the data.

04Can it predict the price?

No. The corridor is fit over the whole history including today and shifts with every new day. It shows where price sits relative to its own long-term trend - not where it is going. Past patterns need not repeat.

05Is this financial advice?

No. This page only shows historical price statistics from our own database. Not a recommendation.