Bitcoin Power Law & Stats Dashboard

Power-law corridor

Q50 is the fitted power law. Other bands are historical rich/cheap offsets around that line, compressed after the last data day — not separate forecasts.

RANGE

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BTC Price

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Power-Law Rank

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Model Q50

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Time Below

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Tap and drag on the chart for full details.

Year-end prices Same curves as the chart

Q50 is the trend at each 31 Dec; other columns are that corridor, not 10/25/75/90% outcome probabilities. Toggle bands on the chart.

Scenario explorer

Pick a year-end and a corridor line to see the implied price and CAGR from today's actual BTC price.

Target year-end

Corridor line

Implied price

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CAGR from today

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Total return

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vs Q50 that year

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Model-implied scenario only — not a forecast. CAGR is computed from today's actual price, not the Q50 trend.

Today

At a glance

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Daily closes since 2010. 200-week MA is a 1,400-day average.

Mayer Multiple Price ÷ 200-day SMA

The Mayer Multiple shows how far price is trading above or below its 200-day moving average over time. Values near or below 1.0 have often coincided with bear-market accumulation zones; 0.8 has been cited as a deep value / oversold zone in later analyses; readings well above 2.4 have historically preceded major corrections.

Current Mayer Multiple

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Independent of the power-law model. 200-day simple moving average.

Historical CAGR Annualized returns to the latest close

CAGR computed from actual daily close prices at the closest historical dates ~N years prior to the latest data point.

Period	CAGR	Start Price	Start Date
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Compound annual growth from the closest daily close about N years ago.

More analysis

When cheap, what happened next Historical, not a forecast

Median forward return after past days in each power-law regime.

Regime	n	+3 months	+6 months	+1 year	+2 years
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Each cell is the median historical return and episode count. Highlighted row is today’s regime. Not a forecast.

vs gold Model market cap vs gold growing at a set rate

BTC market cap = power law price × 21M supply. Gold market cap starts at ~$31T and compounds at a constant long-term historical rate. The chart and table show when the power law corridors cross gold under different gold growth assumptions.

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Assumptions: fixed 21M BTC supply (long-term); gold MC growth rate combines new above-ground supply (~1–2%/yr) + price appreciation; crossovers use yearly samples from the model to 2050. Q25/Q75 show the inner power law corridor. Long-horizon extrapolations have substantial uncertainty.

vs other assets Rolling daily return correlation

How closely Bitcoin daily returns have moved with stocks (SPY), gold (GLD), bonds (AGG), and US real estate (VNQ) over rolling windows.

Asset Class	30d	90d	180d	1y
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Correlations range from −1 (opposite moves) to +1 (lockstep). Computed on overlapping trading days from /correlations. Property proxy = VNQ (US REITs). Updates with scripts/update_data.py.

Fit over time Expanding-window OLS on log-log data

How the power-law relationship strengthens as more Bitcoin history accumulates. Each point refits log₁₀(price) ~ log₁₀(days since genesis) using all data up to that date.

Scale β (today)

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R² (today)

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Correlation

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Data points

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Line color by R²: < 0.85 0.85–0.92 ≥ 0.92

Top: scale coefficient β (how steep the log-log slope is). Bottom: OLS R² (share of log-price variance explained by log-time). Central trend on the main chart uses Q50 quantile regression; this card uses OLS for comparability with common analyst presentations. Series is precomputed at refit (~monthly samples) and served from /stats.

Is the fit still holding? Santostasi §10 falsifiability tests

A scientifically useful model must be falsifiable. Santostasi identifies five conditions under which the Bitcoin price power law would be expected to break down, with measurable precursors for each.

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ID	Test	Status	Live metric	Threshold
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Source: Santostasi & Perrenod — A Mechanistic Derivation of the Bitcoin Price Power Law: Network Adoption Dynamics and Generalised Metcalfe Scaling, Section 10 (with fit-quality methodology from §7). F1 floor (3σ below fit >1y), F3 β outside [5, 7] multi-year, and F5 cumulative R² < 0.80 for >2y are measured from price history via /stats. F5 uses expanding-window OLS R² (paper §7); naive trailing 3-year refits are cycle-dominated and shown only as a diagnostic. F2 (address-growth β_A) and F4 (Metcalfe R²) need on-chain address series and are not monitored here.

Futures

Power Law Monte Carlo Futures OU residuals around Q50

Educational simulation only — not a forecast, valuation, or investment recommendation. These paths are random draws from a simple mean-reverting model of the log₁₀ residual around the fitted Q50 power-law trend. They illustrate a range of trajectories consistent with that model, not probabilities of what Bitcoin will do. Past residual behavior does not predict the future.

Every path starts at today's price. The residual r = log₁₀(price) − log₁₀(Q50) then follows a daily Ornstein–Uhlenbeck step r ← r − κ(r − 0)Δt + σ√Δt · Z with κ = ln(2) / half-life. The deterministic power-law trend is projected forward and the residual path is added back.

Horizon

Mean-reversion half-life 10 mo

3–24 months κ = —

Volatility scale 1.00 × historical

1.0 = historical residual innovation σ

Paths

Advanced

Shock distribution

Floor reflects residuals below the historical mean − 2σ. Student's t uses 5 degrees of freedom, scaled to unit variance.

Median at horizon

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10–90% range

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Median vs Q50

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Median CAGR

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Fan shows simulated 10–90% and 25–75% quantiles of the ensemble, plus a light sample of individual paths. Calibration (current residual, historical σ, residual series) comes from /monte-carlo/calibration. Paths are generated in the browser so sliders stay responsive; the same OU engine is also available at POST /monte-carlo/simulate. Residual-bootstrap is a planned alternative to the OU shocks.