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Power-Law Trend

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In plain English

If you plot bitcoin’s age on a log scale and its price on a log scale, the history looks roughly like a straight line. That fitted line is the “power-law trend.”

The band around it is how far price has usually wandered. The lower pane is simpler: how many percent price sits above that lower edge. Near 0% means it is hugging the historical floor. A huge number means it is stretched above that floor.

Math and metrics

OLS power law in log-log time. Fallback pins if the fit cannot run: Santostasi / bitcoinpower.law a≈−16.493, b≈5.68, σ≈0.3.

log10(P) = a + b·log10(d), d = max(1, days since 2009-01-03).

trend = 10^(a+b log10 d). r_i = log10(P_i)−pred_i. σ = √mean((r−r̄)²) (population).

floor k=−1.15, ceiling k=+2. band = trend·10^(kσ). osc% = (spot/floor − 1)·100.