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 -45 % below trend: measured against the trend that is higher than on 20% of all days so far, i.e. "Undervalued". This describes the past; a power law is neither a law of nature nor a forecast.

Price now
$77,232
Trend (fair value)
$140,164
15-year power law
Deviation from trend
-45 %
20% of days lower
Valuation zone
Undervalued
20% of the time

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$1M$10M201020122014201620182020202220242026OVERHEATEDEXPENSIVEFAIRCHEAPDEEP VALUENOW
Hover the chart for date, price, trend & valuation zone.
Deep value10% of the timeUndervalued20% of the time← nowFair · on trend40% of the timeExpensive20% of the timeOverheated10% of the time

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; the exponent comes out at b=5.65, 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 of the size-sorted deviations. The fit runs over the whole history including today and shifts as new data arrive. It is a reading and 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 5.6. 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 -45 % below it. On 20% of all days so far the price sat lower against the trend than it does today, which puts it in the "Undervalued" zone. It is a reading relative to its own history and not a price forecast.

03How are the five valuation zones defined?

For every day since 2010 we measure how far the price sat above or below the trend line, then sort all those deviations by size. The zone boundaries are positions in that sorted list: the 10% of days with the smallest deviation make up "deep value", the next 20% "cheap", the middle 40% "fair", and mirrored above that "expensive" and "overheated". Positions like these are called percentiles. Because every boundary falls out of the data itself, it shifts a little with each new day.

04Is 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, so they are reproducible from the data.

05Can 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, but not where it is going. Past patterns need not repeat.

06Is this financial advice?

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