Bitcoin Sigma Bands Explained: Reading the Power Law Chart
The Bitcoin Power Law chart uses sigma (σ) bands to express price uncertainty around the central regression. If you've used traditional technical analysis, think of them as dynamic Bollinger Bands — except they operate on a logarithmic scale and are derived from a 15-year regression rather than a moving average.
What Is a Sigma Band?
In statistics, sigma refers to the standard deviation of a distribution. In the Power Law model, sigma is measured in dex (decades, i.e., powers of 10), which is natural for a log-scale regression.
For the Bitcoin Power Law (Santostasi 2026), sigma ≈ 0.302 dex. This means:
- +1σ band: the regression median × 10^0.302 ≈ 2.0× the median price
- −1σ band: the regression median × 10^−0.302 ≈ 0.5× the median price
- +2σ band: median × 10^0.604 ≈ 4.0× the median
- −2σ band: median × 10^−0.604 ≈ 0.25× the median
In plain terms: 68% of historical Bitcoin prices fell within the ±1σ channel, and 95% within the ±2σ channel.
Color Coding on the Chart
| Zone | Position | Historical Interpretation |
|---|---|---|
| Dark band (±2σ outer) | Beyond ±1σ | Extreme overvaluation or capitulation |
| Mid band (±1σ inner) | Around median | Normal trading range |
| Median line | Center | Long-run fair value |
When price is above +1σ: historically preceded by significant corrections (2013 peak, 2017 peak, 2021 peak). When price is below −1σ: historically represented generational buying opportunities (2015, 2018–19, 2022).
Practical Use Cases
1. Identifying Overvalued / Undervalued Periods
The RangeBar on the right side of the chart shows exactly where the current price sits relative to the model bands in real time. A reading near +2σ suggests caution; a reading near −2σ historically rewarded long-term buyers.
2. Setting Long-Term Price Targets
Because the median shifts upward over time following the power law, a "fair value" target for any future date is simply the median projection for that year. The ±1σ range provides a realistic bracket.
3. Comparing Models
The four models on this site (Power Law, Stock-to-Flow, Early Fit, Exponential) all produce different sigma values and different band widths. Cross-referencing them can reveal consensus zones where multiple models agree.
Limitations
Sigma bands assume stationarity of volatility in log-space. If Bitcoin's log-volatility decreases over time — as some on-chain data suggests — the bands may be too wide for future projections. Conversely, an unexpected shock could take prices well outside historical sigma ranges.
If you use charts or data from this site in research or media, please link to bitcoin-power-law.com and cite the source.
Not financial advice.