BFV Model Methodology
A transparent account of the power-law regression model underlying the Bitcoin Fair Value Index, including mathematical formulation, data sources, calibration procedure, and explicit limitations.
1. Overview
The BFV Index applies a log-linear power-law regression to model Bitcoin's long-term price trajectory as a function of time elapsed since the Genesis Block (January 3, 2009). The core hypothesis — supported by empirical observation across Bitcoin's history — is that Bitcoin price follows a power-law growth curve in log-log space when plotted against days since genesis.
This approach was pioneered in academic and independent research contexts (notably by Harold Christopher Burger and Giovanni Santostasi) and provides a baseline "fair value" that abstracts away short-term volatility cycles. The BFV Score is a percentile rank of the current price deviation relative to the historical distribution of deviations, providing a normalized 0–100 signal.
2. Mathematical Formulation
// Log-linear regression in log₁₀-log₁₀ space:
log₁₀(Price) = α + β · log₁₀(Days Since Genesis)
// Equivalent power-law in price space:
Price = 10^α · Days^β
// BFV deviation:
Deviation = (Current Price / Fair Value) − 1
// BFV Score (percentile rank over historical window):
Score = rank(Deviation) / N × 100
The regression is performed in log₁₀-log₁₀ space using Ordinary Least Squares (OLS). The intercept term α and slope β are estimated from the available price history. The resulting power-law curve represents the model's estimate of Bitcoin's baseline value at any point in time, independent of market sentiment.
3. Live Model Parameters
The model is periodically re-fitted as new price data becomes available. Current calibrated parameters and model health:
R² Fit Quality
0.8700
Data Points
3,653
Alpha (α)
-16.3518
Beta (β)
5.6443
R² reflects in-sample statistical fit only. It does not imply predictive certainty or guarantee future accuracy.
Alpha (α) — Intercept
Log₁₀-space intercept of the regression line
Beta (β) — Slope
Power-law exponent; rate of price growth per log-day
R² (Coefficient of Determination)
Proportion of log-price variance explained by the model in-sample
Data Points Used
Number of daily price observations in the regression
Fit Date Range
Temporal range of training data
Last Calibrated
4. BFV Score Bands
The BFV Score is a 0–100 percentile rank of the current price deviation from fair value, computed over the available historical window. The following thresholds define risk bands:
| Score Range | Band |
|---|---|
| 0 – 19 | Deep Undervaluation |
| 20 – 39 | Accumulation Zone |
| 40 – 59 | Fair Value Zone |
| 60 – 79 | Elevated Risk |
| 80 – 100 | Euphoria Zone |
5. Data Sources
CoinGecko API
Daily and current Bitcoin price data (USD)
Bitcoin Genesis Block
Reference date: January 3, 2009 (days-since-genesis calculation)
6. Caching & Refresh
CoinGecko API responses are cached server-side to respect rate limits and ensure consistent data quality. The current price is refreshed approximately every 5 minutes. Historical price data (used for model fitting and chart rendering) is cached for up to 6 hours. The model regression is re-fitted periodically as new data accumulates; the last calibration date is shown in Section 3 above.
7. Limitations & Assumptions
Not investment advice
The BFV model is a quantitative analytical tool, not a financial advisory service. It does not account for individual risk tolerance, tax considerations, portfolio context, or macroeconomic factors. Nothing on this platform constitutes investment advice.
Model assumes power-law continuation
The regression assumes Bitcoin's price will continue to follow a power-law growth trajectory. This assumption may break down due to regulatory events, technological disruption, loss of network effect, or other structural changes. The model has no mechanism to detect or account for such regime changes.
In-sample fit does not guarantee out-of-sample accuracy
High R² values in-sample do not guarantee predictive accuracy out-of-sample. The model is calibrated on past data; future deviations from the fitted curve may be larger or more persistent than historical deviations. R² is reported for transparency, not as a performance guarantee.
Single-factor model
The BFV model uses only time (days since genesis) as a predictor. It does not incorporate on-chain metrics (active addresses, hash rate, UTXO age), macroeconomic variables (interest rates, M2 money supply), or market microstructure data. Multi-factor models may provide superior explanatory power.
Percentile rank is window-dependent
The BFV Score is computed over the available historical window. The interpretation of a given score depends on the composition of that window; scores computed over different windows will differ. Extreme events outside the window are not reflected in the score.
8. References
- Burger, H.C. (2019). "Bitcoin's natural long-term power-law corridor of growth." Medium.
- Santostasi, G. (2024). "Bitcoin Power Law Theory." Independent research.
- Nakamoto, S. (2008). "Bitcoin: A Peer-to-Peer Electronic Cash System." bitcoin.org.