Power Law Deviation measures how far Bitcoin's current price sits above or below its long-term power-law regression line, expressed as a log-scale distance. Deep negative readings (below -0.5) have marked major bear-market lows; high positive readings (above 0.8) have marked cycle tops.
What Is Power Law Deviation?
Power Law Deviation takes Bitcoin's long-term power-law growth curve — the same underlying model behind the Rainbow Chart — and expresses today's distance from that curve as a single, precise number, rather than a colour band. It answers the question: on a log scale, how far has price strayed from its long-term mathematical trend, right now?
The Power-Law Model, Refresher
Bitcoin's price history, plotted on a logarithmic scale against time since its genesis block, has tracked a smooth power-law curve reasonably well despite extreme short-term volatility. This kind of growth pattern — roughly linear on a log-log scale — is common in networks that grow through adoption, which is part of why the model has proven useful for a network-effect-driven asset like Bitcoin.
The Formula
Taking the natural log of the ratio between actual price and the model's fair-value estimate produces a symmetric, easy-to-compare number: positive values mean price is above the curve, negative values mean it's below, and the further from zero, the greater the deviation. Using a log rather than a simple percentage keeps the scale consistent whether price is far above or far below the trend.
Reading the Zones
| Power Law Deviation | Zone | Historical Interpretation |
|---|---|---|
| ≤ −0.5 | Deep Value | More than ~39% below fair value — near major bear-market lows, some of the strongest accumulation windows historically |
| −0.5 to −0.2 | Undervalued | Below fair value but not extreme — late bear markets, early recovery phases |
| −0.2 to +0.4 | Fair Value | Near the long-term trend — the historical equilibrium zone |
| +0.4 to +0.8 | Elevated | Running above fair value — consistent with an active bull-market phase |
| ≥ +0.8 | High Risk | Significantly above fair value — historically near cycle tops |
See today's live reading on our Power Law Deviation indicator page.
How It Relates to AHR999 and the Rainbow Chart
Power Law Deviation, AHR999, and the Rainbow Chart all share the same underlying power-law fair-value calculation — they just present it differently. The Rainbow Chart turns it into an intuitive colour band. AHR999 combines it with a separate 200-day trend ratio for a DCA-focused blended signal. Power Law Deviation isolates the power-law comparison on its own, as a clean, precise number with no blending — useful when you specifically want the pure power-law read without any additional smoothing.
Limitations
It's a single-model view. Because it isolates just the power-law comparison, it doesn't benefit from AHR999's additional 200-day trend blending — it can react a bit more sharply to short-term price moves as a result.
The curve is a simplification. As with any power-law-based tool, a smooth mathematical fit across 15+ years of data is a useful approximation of Bitcoin's growth, not a guaranteed law it must continue to follow.
Zone boundaries are historically calibrated. The specific thresholds reflect where past extremes have landed — a useful reference, not a certainty for future cycles.
How to Use It
Power Law Deviation is most useful when you want the cleanest possible read on Bitcoin's position relative to its long-term growth trend, without additional blending. Cross-check it against AHR999 for a second, medium-term-adjusted view of the same underlying model, or the Rainbow Chart if you prefer the visual version.
It's also one of the 21 inputs to our Cycle Compass composite score.
For a broader tour of the other major indicators worth knowing, see our guide to 10 On-Chain Bitcoin Indicators Every Investor Should Know.