Bitcoin valuation models compared: which one should you actually use?

Mechanism

Each model answers a different question. Power-Law Corridor: log10(P) = a + n·log10(d), d = days since genesis, with ±kσ residual envelopes — answers "where is price relative to a decelerating long-term trend?" 200-week moving average: mean of the last 200 weekly closes — answers "where is the historical cycle floor?" MVRV: market cap ÷ realized cap — answers "is the average holder in profit?" Stock-to-Flow: log(P) = a + b·log(stock/flow) — answers nothing causal, because stock/flow is fixed by protocol and known years in advance. Rainbow Chart: log(P) = a + b·t with hand-placed color bands — answers "does this feel hot or cold?"

Detail

The log-log power law model fits price as a function of network age after taking logs on both axes. Its core assumption is that Bitcoin can keep growing, but that the rate of growth decelerates as the network gets older and larger. That assumption is economically plausible because early adoption can compound from a small base, while later adoption faces deeper liquidity, broader ownership, and more macro competition. The model breaks when time is treated as the main causal variable. Time does not buy coins, set leverage, change regulation, or force liquidity. A power law can describe a long historical curve while still failing around regime changes.

Residual envelopes start with a fitted valuation curve, then measure how far price sits above or below that curve. Bands drawn from residual dispersion can help describe historical overextension and undervaluation. They should not be read as clean probability intervals. Bitcoin residuals are autocorrelated, meaning errors cluster through time rather than arriving as independent observations. A market can remain above trend or below trend for extended periods. That persistence weakens the usual interpretation of sigma-style bands. The envelope is useful as a regime map, not as a timer. It shows where price is stretched relative to model history, but it does not say reversal is due.

The Rainbow Chart uses a log-linear style framework with valuation bands placed around a long-term growth path. Its implicit assumption is that Bitcoin can continue compounding at a broadly constant annual multiple, even as the asset matures. The bands are partly descriptive and partly hand-placed, which makes the chart easy to read but less formal than a statistical model. It can summarize sentiment regimes, but its weakness is that the band structure is not derived from a stable economic law. If long-term growth slows faster than assumed, upper bands become too generous. If adoption reaccelerates, lower bands can look too conservative.

Stock-to-Flow links valuation to scarcity, using issuance schedule as the main explanatory variable. The problem is that the regressor is largely deterministic. Bitcoin halvings are known in advance, so the model tends to convert a pre-set calendar into a price path. That creates strong visual fit in earlier history without proving causal power. Its failed 2021 forecasts showed the limitation clearly. Scarcity matters, but scarcity alone did not force the market to the model's projected levels. Demand, leverage, liquidity, regulation, custody, and macro conditions all moved independently of issuance. Stock-to-Flow is best treated as a scarcity narrative, not a valuation engine.

MVRV compares market value with realized value. Realized cap values coins at the price at which they last moved, so MVRV approximates whether the aggregate holder base is in profit or loss relative to on-chain cost basis. When MVRV is high, the market contains more unrealized profit and therefore more potential supply from holders taking gains. When it is low, stress or capitulation may be closer. The measure does not tell you who must sell, who is hedged, or whether dormant coins are economically active. It also ignores off-chain leverage and exchange balances. Average holder profit is useful context, not a full valuation model.

The 200-week moving average is an empirical floor model. It smooths long-term price history and asks whether major bear markets have tended to hold near that moving baseline. The appeal is practical: it is simple, transparent, and tied to observed market behavior rather than a complex theory. The assumption is that past long-cycle support behavior remains relevant. That is also the weakness. The sample is small, the asset survived every prior break, and the rule is selected after observing history. Survivorship bias matters. If market structure changes, or if a future bear market is driven by different constraints, the moving average can stop acting like support.

Bootstrap confidence intervals on btccalcs.com are built by taking the model's historical errors and resampling them to estimate a range of possible outcomes around the fitted path. This avoids assuming that residuals are normally distributed, but it still inherits the dataset's limits. If the future contains regimes not present in the sampled history, the interval will be too narrow or miscentered. The best use is comparative. A decision stack can combine power-law location, residual envelopes, MVRV, moving-average support, and cycle position. Agreement across models strengthens a risk read. Disagreement should reduce confidence, not invite curve-fitting until one chart gives the desired answer.

Sources

1. Santostasi, G. — The Bitcoin Power Law Theory2024-03
2. Coin Metrics — realized capitalization and MVRV definitions2026-09
3. Bitbo Rainbow Chart (reference implementation)2026-09
4. btccalcs.com Power-Law Corridor methodology2026-09

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