Across its entire history, Bitcoin's price has loosely followed one smooth long-term
trend — a pattern called a power law. This page draws that trend and shades the
space around it: green when Bitcoin is historically cheap (trading
below the trend) and red when it's historically expensive (above it).
The colored box just below gives you the one-line answer for today.
What am I looking at?
The orange line is Bitcoin's long-term trend — a rough "fair value" for each date.
Green zones (below the line) mean Bitcoin is cheaper than its trend; red zones (above) mean it's pricier than its trend.
The bands are measured in standard deviations (σ) — a way of asking "how unusual is this?". The inner band (±1σ) is the everyday range Bitcoin sits in about 68% of the time; the outer band (±2σ) is the wider range it stays inside about 95% of the time. Poking outside the outer band is rare and extreme.
The "σ from trend over time" strip below the main chart shows how cheap or expensive Bitcoin has been through every cycle — notice each peak reaching less extreme than the last.
How do I use the controls?
a and b are the two numbers that shape the trend line. Drag their sliders and every chart updates instantly — a good way to see how sensitive "fair value" is to the model.
Best fit lets the math choose the trend line that hugs real prices most closely.
The Display checkboxes turn the bands, the log-log view, and the σ history strip on and off.
Reset to defaults returns everything to the standard values.
A power-law fit is a heuristic that has held so far, not a guarantee — past
structure need not continue. This is an educational tool, not financial advice.
a = b = R² (log) = σ = best-fit: a=, b=
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Price (log) vs time
σ from trend over time — how cheap / expensive vs the model