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.
Price Distribution: How Often Is Bitcoin This Cheap?
Based on 5,674 daily closes since July 2010. Each bar shows how many days per year Bitcoin typically trades at that multiplier of the power law trend. Today's position uses the live price. Inspired by PlanC's quantile analysis.
Reading This Chart
Each bar shows how much of Bitcoin's history was spent at that price level relative to the power law trend. The green zone on the left marks periods when Bitcoin was significantly cheaper than trend — historically great buying opportunities. The red zone on the right marks periods when Bitcoin was significantly more expensive than trend — prices always came back down from these levels. The orange line shows where we are today.
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 |
Loading weekly data...
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).