Historical Analysis
Bitcoin's price history plotted on a log-log scale reveals a remarkably consistent power law relationship. Deviations from the trend are dramatic but statistically ordinary.
How to read this chart
Linear + Linear shows the explosive recent growth in raw dollar terms — early years are flattened near zero.
Linear + Log (price) spreads out the early history so you can see every cycle clearly.
Log + Log is the classic power-law view: if BTC follows a power law, the trend becomes a straight line.
Log time + Linear price compresses the early quiet years while keeping dollar moves intuitive.
Trend is the power-law fair-value curve. The σ bands show one and two standard deviations above and below — historically price has always reverted back inside these bounds.
Understanding Mean Reversion
Think of the power law trend as a rubber band. Price can stretch far above or below the trend, but it always snaps back. This isn't magic; it's statistics. Extreme deviations are unsustainable by definition.
Volatility Eras: How Bitcoin's Price Corridor Is Narrowing
Five halving cycles show Bitcoin's volatility shrinking dramatically. Each curve shows how many days per year price traded at each multiplier of the power law trend.
Reading This Chart
Each curve represents one halving cycle. Earlier cycles show wide, flat distributions — price swung wildly around trend. With each successive cycle the corridor narrows. The vertical dashed line shows where today's price sits relative to trend. Note: Cycle 5 (dashed curve) is incomplete — it has not yet experienced a bull market, so its narrow shape reflects only accumulation-phase behaviour, not a full cycle.
Floor Distance Analysis
How far is BTC from the -2σ power law floor? Two perspectives: a fixed global floor (σ = 0.2) shows BTC pulling further from danger over time; a per-cycle adaptive floor shows normalized behavior within each volatility regime.
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Reading this chart
At 0σ, price touches the floor. At 2σ, price is exactly at the power law trend. The solid line uses a fixed reference floor — it trends upward as BTC matures, meaning each cycle's worst day is further from existential risk than the last. The dashed line adjusts the floor per cycle — it stays flatter because the ruler shrinks along with volatility. The growing gap between them is the volatility compression story.
Weekly Historical Data
Your primary sanity check: see every week's closing price, trend value, and deviation. Use this to judge current position in historical context.
Understanding Log Deviation
Log deviation = log₁₀(price ÷ trend). It measures distance from trend value on a logarithmic scale, which better captures Bitcoin's exponential nature.
| Log Dev | Meaning | Multiple | Action Signal |
|---|---|---|---|
| −0.30 | 50% below trend | 0.50× | Borrow fiat / Strong buy |
| −0.15 | ~30% below trend | 0.71× | Accumulate |
| 0.00 | Fair value (on trend) | 1.00× | Hold |
| +0.30 | ~100% above trend | 2.00× | Take profits |
| +0.60 | ~300% above trend | 4.00× | Sell / Bubble zone |
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Notable Deviations
| Event | Date | Peak Multiplier | Subsequent Drawdown | Time to Trend |
|---|---|---|---|---|
| 2011 Bubble | Jun 2011 | ~8× over trend | -94% | ~2 years |
| 2013 Double Top | Dec 2013 | ~4× over trend | -86% | ~3 years |
| 2017 Bull Run | Dec 2017 | ~4× over trend | -84% | ~3 years |
| 2021 Peak | Nov 2021 | ~2.5× over trend | -77% | ~2 years |
| 2022 Bottom | Nov 2022 | ~0.5× (under) | N/A (bottom) | Recovery began |
The Rubber Band Effect
Price stretches away from trend, then gravity pulls it back. Every cycle. Without fail (so far).