Z-Score Probability Waves.
Rolling 52-week log z-score. The asset's distance from its own mean, in standard deviations.Price is trading more than 2 standard deviations above its 52-week geometric mean — historically rare and often coincides with cycle peaks. Forward returns from this band are skewed negative across 3-12 month horizons.
Price has collapsed more than 2 standard deviations below its 52-week mean — a statistically extreme accumulation zone. Historical congruent states produce >75% positive forward returns over 12-24 month horizons.
For each weekly close, we take the trailing 52 weekly log prices, compute their mean μ and standard deviation σ, then express today's log price as a z-score: z = (log P − μ) ÷ σ. A z of zero means price equals its trailing mean. A z of +2 means price is two standard deviations above — statistically rare.
The chart shows two regimes selectable from the toggle. Long mode uses a 52-week window with an EMA smoothing pass over the z-series, surfacing macro cycle phase. Short mode uses an 8-week window with no smoothing, surfacing short-term mean-reversion swings for traders.
Once μ and σ are known, every z-band projects back to a concrete USD level via price(z) = exp(μ + z·σ). The snapshot row shows the ±0.5σ, ±1.5σ, and ±2.5σ price levels — they update each day as the rolling window advances.
Log space is essential for assets that span orders of magnitude. A 50% drop and a 50% rise have equal weight, which makes the z-score interpretable across full cycles rather than only the most recent regime.