Research · Network Economics
Price against a power law in time since the genesis block, fitted live in your browser, with the exponent's sensitivity, its decomposition into adoption and Metcalfe scaling, out-of-sample validation, and the conditions that would falsify it.
Fetching daily price and address history from Blockchain.com.
Log deviation of price from the fitted model level, in dex (log10 units), placed on the fit window's own residual distribution. Cuts are the 10th, 30th, 70th and 90th percentiles.
| Origin | Fit from | β | R² | σ dex | Model-implied level |
|---|
| Start, dex | 90d | 180d | 365d | Days |
|---|
Descriptive, overlapping windows, in-sample. Not a forecast.
| Refit at | Days in fit | β | Next-year RMSE, dex | Bias, dex | Model-implied level today implied then |
|---|
| Source | Published finding | This page, live | Status |
|---|
"Power law" also names a different regularity in this literature: heavy, power-law tails in the distribution of Bitcoin returns (Begušić et al., 2018). That concerns the size of daily moves, not the level of price in time, and is not tested here.
With the daily snapshot the adoption series is the count of addresses with a non-zero balance (Coin Metrics), the same series the paper uses; without it the page falls back to cumulative addresses used and the test is indicative only. The adoption series in use is stated in the first row.
| Date | Model-implied level | −1σ | +1σ | Range across last five refits |
|---|
| Source | Value | As of |
|---|
| Series | First | Last | Days | Min | Max | Latest |
|---|
The model is log10 P = a + β · log10 t, with t the number of days since the chosen origin, fitted by ordinary least squares on daily closes from the chosen start. The published specification (Santostasi and Perrenod, 2026) uses the genesis block as origin and begins at day 560; on their sample they report β = 5.69 ± 0.05, R² = 0.961 and a residual σ of 0.302 dex. The default here is the same specification on the live feed. The feed begins on day 592, so the first month of their sample is absent; that and the later end date account for a difference of a few hundredths in β, inside their stated uncertainty.
The exponent is not a constant to the second decimal. It depends on the origin, the start of the fit, the end of the fit and the price source for 2010. The sensitivity table shows the same fit under the other defensible choices; the origin matters most, and the law is stated relative to the genesis block for that reason.
The paper's contribution is mechanistic: the exponent decomposes as adoption growth N ∝ t^βA (about 3, an epidemic saturation wave on a scale-free network) composed with generalised Metcalfe scaling P ∝ N^βM (about 1.84), whose product reproduces the direct exponent. The decomposition panel repeats that test with the public address stock as the adoption proxy. The Metcalfe half of the identity is the subject of the companion Bitcoin Metcalfe Value Monitor.
Validation follows the same protocol as the Metcalfe monitor: fit through each 31 December, predict the following year, repeat, and report the error, the exponent each refit produced and the value each implied for today. Early refits are unstable and the page shows that rather than hiding it. The falsifiability monitor applies the paper's own breakdown conditions to the live data: the rolling exponent leaving its historical range, the residual staying beyond two standard deviations for an extended period, or a secular drift appearing in the residuals.
Descriptive: price has followed a power-law relationship with time over the stated sample, with the fit and residual dispersion reported. The page also tests one-year-ahead performance out of sample and reports the resulting error. Not claimed: that time causes price, or that the model-implied level is a target. Not claimed: that time causes price, or that the model-implied level is a target. Time is a proxy for the adoption process the decomposition describes, and the extrapolation table is an extension of a fitted line under the assumption that the process continues, shown with its dispersion. A critique in the literature (arXiv 2605.21316, 2026) shows that scale-invariance tests of this kind can be passed by stacked sigmoids that eventually saturate; the falsifiability monitor exists because that objection is legitimate.
Daily price and unique-address history from the Blockchain.com Charts API. Spot price from Coinbase, refreshed every minute while the page is open. Data is cached in this browser for six hours.
G. Santostasi and S. Perrenod, "A mechanistic derivation of the Bitcoin price power law: network adoption dynamics and generalised Metcalfe scaling," Nonlinear Science, 2026, ScienceDirect. The critique: "Bitcoin's Power Law: Weak Structure, Strong Forecasts," arXiv 2605.21316. Also: "Bitcoin valuation through power law analysis: evidence for long-term mean reversion and short-term momentum," Journal of Business Economics and Finance, 2025; Wheatley, Sornette, Huber, Reppen and Gantner, "Are Bitcoin bubbles predictable? Combining a generalized Metcalfe's law and the LPPLS model," Royal Society Open Science, 2019; Peterson, 2018, and Alabi, 2017, on Metcalfe scaling; Begušić, Kostanjčar, Stanley and Podobnik, "Scaling properties of extreme price fluctuations in Bitcoin markets," Physica A, 2018, on power-law return tails; the survey "Bitcoin price prediction: peer-reviewed evidence and social media discourse," arXiv 2606.00071, 2026. Origin of the idea: Santostasi's 2014 and 2018 posts; corridor visualisation: Burger, 2019.
Nothing here is investment advice. The model-implied level is an estimate with a stated dispersion of about 0.30 dex, meaning price has spent a third of its history more than a factor of two away from it.