What this shows
The power-law model says that Bitcoin's price has grown roughly as a power of its age: plotted on log-log axes, with the logarithm of price against the logarithm of days since the genesis block (January 3, 2009), the history falls close to a straight line. The idea was popularized by physicist Giovanni Santostasi and others.
We fit that line ourselves on every daily Bitstamp close since September 2011 and update it daily. The fair value is where the line is today. The support and resistance bands are drawn so that 90% of daily prices in history fell between them (the 5th and 95th percentiles of the distance from the line).
The historical percentile tells you how cheap or expensive today's price is compared with the model: 15% would mean the price was further below the line on only 15% of past days.
What the model gets right
- Bitcoin has followed a remarkably steady long-term growth curve for over 15 years, and a power law has fit it better than a simple exponential, which would have predicted far higher prices by now.
- The bands have contained most cycle lows and highs, which is why the model is popular for long-term valuation.
What to be careful about
- It is a curve fit, not a law of nature. There is no guarantee adoption keeps following the same curve. The fit describes the past.
- The numbers depend on the choices made. Fitting only data since 2015 gives a steeper exponent and a fair value roughly 6% higher than our full-history fit. Published versions of the model use slightly different data and so show different targets.
- The R² looks better than the evidence behind it. Prices on consecutive days are not independent observations, so a high R² on log prices overstates how precisely the curve is known.
- The projections are not forecasts. The table shows where the model lines would be if the past relationship continues, nothing more.
How to use it
Use the ratio to fair value and the percentile as a long-term valuation gauge: buying in the lower part of the band has historically worked out better over several years than buying near resistance. For timing, look at it together with the 200-week moving average and the Pi Cycle Top indicator.
FAQ
What is the Bitcoin power-law fair value today? It is shown in the headline and the first card above, updated daily from our own fit to Bitcoin's price history since 2011.
What does the power-law model predict for Bitcoin? The table above lists the model's fair value and band for the next few years if the historical relationship continues. These are model outputs, not forecasts: the curve describes the past and could stop fitting at any time.
Who created the Bitcoin power-law model? The idea that Bitcoin's price follows a power law of time was popularized by physicist Giovanni Santostasi, with versions also published by other analysts. The parameters on this page come from our own fit.
Is Bitcoin undervalued according to the power law? When the price is below the fair-value line, the model counts Bitcoin as cheap compared with its long-term trend. The ratio and historical percentile above show by how much. Whether that matters for the next months is a different question the model doesn't answer.