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Statistical · fitted

Power Law Corridor

A log-log regression of price against Bitcoin's age, with corridor bands at the 2nd and 98th percentile of residuals. This is the rigorous cousin of the Rainbow Chart — fitted, refit on every load, and labeled as such.

Data: PriceUSD · Coin Metrics community API · computed live in your browser, nothing uploaded

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What this chart shows

Plot Bitcoin's price on a log axis against the log of its age in days, and the eleven-year scatter is remarkably straight. This page fits that line by ordinary least squares on the full history — recomputed every time you load it — and draws corridor bands at the 2nd and 98th percentile of the residuals.

log₁₀(Price) = a + b · log₁₀(days since genesis)

How to read it

The gauge shows where today's price sits within the historical residual distribution: near the floor has historically meant late-bear conditions, near the ceiling late-bull. The fitted exponent b (shown in the legend) implies price has grown as a power of time rather than exponentially — i.e., growth that decelerates.

Limitations — this model is in the same family as the Rainbow Chart

Be clear-eyed: this is curve fitting on price alone, exactly the technique behind the Rainbow Chart, just executed with standard statistics instead of hand-drawn bands. The high R² is largely an artifact of regressing a trending series and says nothing about out-of-sample predictive power. Because the fit is recomputed on every load, the corridor quietly shifts as new data arrives — the same “repainting” problem that makes such models unfalsifiable. We publish the fit parameters and date on every load so you can at least see it move.

Use it as a compressed visual summary of history. Do not use it to project price targets; the dashed extension exists to show what the model asserts, not what will happen.

Further reading

Bitcoin Power Law Explained: Why a Straight Line on a Log-Log Chart Is Controversial

FAQ

Is the Bitcoin power law scientifically valid?
It is a good descriptive fit and a poor scientific model. It has no causal mechanism, its parameters shift as data arrives, and a high R² on a trending time series is expected, not impressive. Physicists and statisticians have criticized it on exactly these grounds.
How is this different from the Rainbow Chart?
Same family — a regression of log price on log time. The differences are procedural: the fit method is standard OLS, the bands are residual quantiles rather than hand-tuned colors, and the parameters plus refit date are displayed instead of hidden.
Why does the corridor change slightly between visits?
Because the regression is recomputed on the full dataset at load time. That transparency is deliberate: fitted models drift, and hiding the drift is how the Rainbow Chart lost credibility.