Valuation

Power-law valuation residual (z)

How many standard deviations today's price sits from the long-run trend that best describes Bitcoin's whole history.

Why it matters

It's the one valuation measure on this site that doesn't look inside the chain: it only compares price against itself across the years. On a log-log scale (log price against log days since the genesis block) Bitcoin's history looks fairly close to a straight line, and "how far price has drifted from that line" is a real valuation reading. Importantly, the project computes it with a fit that only ever uses data before each day — it never sees the future — so the 2015 reading is the one you'd have seen in 2015, not one reconstructed with today's knowledge.

Build it yourself

Drag the actual price and the trend price and watch the two stages: first the residual in logs, then its normalization.

z = ln(Actual price ÷ Trend price) ÷ 365d stdev
Residual (z)

Raw residual (in logs):

The −1 and +1 cuts are the ones the project's own /research page uses today as a descriptive reading, with no position rule attached.

Illustrative example numbers for practice — not real data.

How it's calculated, step by step

  1. For each day its age is computed: days elapsed since the genesis block (2009-01-03).
  2. A least-squares line of log(price) against log(age) is fitted using ONLY days before the one being scored — an expanding window, with a minimum of 730 training days and a refit every 90 days.
  3. Residual = log(actual price) − log(the price that line predicts). Positive = above trend; negative = below.
  4. The residual is z-scored over a rolling 365-day window (its own last-year mean subtracted, divided by its own last-year standard deviation), so the scale stays comparable across eras whose prices differ by orders of magnitude.
Descriptive. Descriptive, with a limitation worth understanding: the rolling 365-day window makes the z go strongly negative EARLY in a decline (when the fall is recent relative to the past year) and re-centre as the bear market drags on. As a "how far from trend are we" reading it's real information; as a buying rule it's precisely where it failed — see the next indicator.

Chart

This is real Bitcoin data, computed from the blockchain — not the illustrative example above.

Data last updated on 2026-09-09.

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