BITCOINREVERSAL RESEARCH / Long-term valuation
Bitcoin Power Law
Bitcoin price, fitted long-term trend and deviation. Completed daily data, with the formula and its limits.
Bitcoin Power Law price and deviation chart
Daily calculations · Drag to pan · Pinch or scroll to zoom
Selected reference bands: $40,274 – $827,573.
Full-sample fit: historical values are recalculated. Bands are heuristic; projections are conditional.
Recreated by Simon · BitcoinReversal. Original concept: Giovanni Santostasi. Method & sources
Charting by TradingView Lightweight Charts™
How to interpret the Bitcoin Power Law chart
On Sep 19, 2026, Bitcoin closed at $81,255, 37.56% below the fitted Power Law reference of $130,130.
The gap compares price with this fitted reference. It does not tell you when price will move toward it, or whether it will.
What does a power law mean here?
A power law has the form P(t) = a × tb. This chart fits the logarithm of Bitcoin’s price against the logarithm of its age. Its price axis is logarithmic; the horizontal axis shows calendar time.
There is no universal Power Law “fair value”. Different prices, sample periods, anchors and band rules produce different charts.
Data delayed: the latest available completed observation is Sep 19, 2026. Refresh the page.
Put the long-term trend in context
Explore how BitcoinReversal combines defined cycle conditions into buy-side, sell-side and transitional research signals.
The fitting period changes the curve
A line fitted to all available history contains information from later years. To show the effect, these calculations stop the input at different dates, then evaluate each fitted curve on Sep 19, 2026.
Fitted reference on Sep 19, 2026
b = 5.3392
Fitted reference on Sep 19, 2026
b = 5.7017
Fitted reference on Sep 19, 2026
b = 5.5291
Fitted reference on Sep 19, 2026
b = 5.4877
All rows use today’s stored price history, truncated at the stated date. These are retrospective reconstructions, not archived live forecasts or a prospective backtest. The differences are not confidence intervals.
Inspect the calculation behind this comparison
| Fit through | Observations | ln(a) | Exponent b | Reference on Sep 19, 2026 |
|---|---|---|---|---|
| 2017-12-31 | 2,554 | -35.3306483636 | 5.33921649227 | $100,605 |
| 2021-12-31 | 4,015 | -37.9830354309 | 5.70170476046 | $170,633 |
| 2024-12-31 | 5,111 | -36.6918027435 | 5.52914902328 | $136,542 |
| 2026-09-19 | 5,738 | -36.3758906768 | 5.48766375381 | $130,130 |
Only the fitting cutoff changes. The UTC anchor, logarithms and regression rule stay the same. Inspect the dated calculation snapshot.
History is refitted
New completed observations can change earlier fitted values and both bands. The curve is a description using today’s sample.
Bands can break
The lower and upper bands follow custom residual rules. They are not statistical confidence intervals or guaranteed price boundaries.
Future curves are conditional
Dashed lines evaluate the current formula on future dates. They contain no observed Bitcoin prices and no demonstrated probability of success.
A predictive test would freeze the specification and fitting sample before measuring subsequent observations. This page does not claim that the displayed historical fit is such a test.
How this Power Law chart is calculated
Every available valid completed daily close enters a natural-log ordinary least squares regression. Bitcoin’s age starts on January 3, 2009.
t = max(30, calendar days since 2009-01-03) x = ln(t); y = ln(BTC daily close) b = [nΣ(xy) − ΣxΣy] / [nΣ(x²) − (Σx)²] α = mean(y) − b × mean(x) Fitted price = exp(α + b × ln(t)) Deviation (%) = 100 × (BTC close / fitted price − 1)
Current coefficients and exact reference-band rules
| ln(a) | -36.37589067684819 |
|---|---|
| a | 1.592763903242449e-16 |
| Exponent b | 5.487663753808274 |
| Residual RMSE σ | 0.67798232690732 |
| Lower residual offset | -1.172831993557097 |
| Upper residual base | 2.611033064512256 |
| Input SHA-256 | 57b63ac0478fbc479734668ea1831350cd6b09692e11fa1ea97ca105ff79f448 |
| Method SHA-256 | b08a4b1a5c764ef7d601a4bd924ef4bebcaab56ada57d38921bf4e3c6db42b8e |
For each historical observation, residual r = ln(price) − fitted ln(price). σ is the root mean squared residual across the full sample.
Lower band: fitted price × exp(rmin − 0.12σ)
Upper band: fitted price × exp[(rmax + 0.12σ) × (0.86 − d)]
Time adjustment d: min[0.055 × ln(1 + max(0, t / 365.25 − 3)), 0.16]
The 0.12, 0.86, 0.055 and 0.16 constants are BitcoinReversal’s inherited heuristic band choices. They are not probability estimates.
Data sources, UTC dates and missing observations
The historical import from January 4, 2011 through March 13, 2026 does not preserve the original vendor or closing cutoff. That part of the source history remains unverified.
From March 14, 2026, BitcoinReversal aggregates CoinGecko ticks and stores the final available tick in each UTC day. Canonical stored dates are represented at 00:00 UTC. The unfinished current day is excluded. Sampling and source revisions can affect prices.
Only valid positive closes enter the fit. Missing dates do not receive invented prices. This snapshot contains 0 missing calendar days between its first and last observation.
Weekly and monthly sampling, selected dates and future values
1D, 1W and 1M change display frequency, not the regression. Weekly buckets start on Monday in UTC. Monthly buckets follow the UTC calendar.
Each bucket retains its last observed daily value and that observation’s actual date. An unfinished period keeps its final real close; a projected day does not replace it. A future-only period contains the fitted reference and bands, with no Bitcoin price or deviation.
The date selector reads an exact daily calculation. When it differs from the sampled plotted point, both dates are stated below the graph. Solid lines show historical calculations; dashed lines show conditional projections.
Versions, snapshots and first-recorded publication history
Method v9.0 standardizes complete-day inputs and canonical calendar dates. Earlier versions included legacy timestamp offsets and an unfinished day. Presentation v16 improves the interface and verification without changing that regression or its band rules.
The page’s date, figures, sensitivity comparison and reference chart come from one calculation snapshot. Its compact display data includes daily closes and full-precision fitted coefficients; CSV and full JSON publish the calculated daily model values.
The publisher-maintained log begins with this release on September 8, 2026. It records the first available reading for each newly completed day, the coefficients and input checksum. Older dates are not backfilled; original records remain if the source history later changes. This is not independent timestamp certification.
Inspect first-recorded readings · Inspect the frozen method specification
A chart others can verify
Keep the observation date and method version with the chart. Credit this independent recreation and link to the canonical page.
A descriptive model reference is not a price target. Check applicable source terms before redistributing third-party raw prices.
Bitcoin Power Law questions
Is the fitted line Bitcoin’s fair value?
It is a mathematical reference fitted to the chosen historical sample. It does not establish intrinsic value, an expected return or a price the market must reach.
Does a negative deviation mean Bitcoin is cheap?
It means price is below this particular fitted curve. It does not establish undervaluation or tell you when to buy. Read it with the sample choice, source limitations and wider market context.
Why does another Power Law chart look different?
Prices, fitting periods, time anchors, coefficients and band definitions can differ. Compare the exact methods before comparing their displayed levels.
Can Bitcoin leave the bands?
Yes. The bands are custom historical reference rules. They do not bound future prices with a known confidence level.
Does the model update in real time?
The model uses completed UTC-day observations. The separately labeled latest BTC price is refreshed automatically and does not refit the model intraday. New completed data can change the regression and its past fitted values; each displayed snapshot states its data date.
Research presentation reviewed September 8, 2026 · Method v9.0 · Independent recreation by Simon · BitcoinReversal. Model and market risks · Report a data or calculation issue.