Glossary
Technical terms used in Bitcoin price modelling, on-chain analysis, and statistics. All definitions are in the context of the models shown on Bitcoin Power Law.
Power Law
A mathematical relationship of the form y = a · xᵇ. On a log-log chart it appears as a straight line. Bitcoin's price fits a power law as a function of its age (days since genesis), with an exponent of ~5.69 and R² = 0.961, meaning the relationship explains 96% of the variance in log price over 15+ years.
Stock-to-Flow (S2F)(S2F)
A scarcity model developed by PlanB (2019). It relates Bitcoin's market capitalization to its stock-to-flow ratio — the existing supply divided by annual new issuance. After each halving the S2F ratio doubles, and the model projects the price rises accordingly. Formula: ln(MktCap) = 14.62 + 3.32 × ln(SF).
Sigma (σ)(σ)
Standard deviation. In the Bitcoin Power Law context, sigma is measured in dex (decades, i.e., powers of 10) and represents the typical log-scale deviation of price from the regression median. For the Power Law model σ ≈ 0.302 dex, meaning the ±1σ band spans roughly 0.5× to 2× the median. About 68% of historical prices fell inside ±1σ.
Sigma Bands
Channels drawn ±1σ and ±2σ around the regression median line on the chart. They serve as dynamic over/undervaluation indicators. Historically, price touching +2σ preceded major corrections (2013, 2017, 2021 peaks); price touching −1σ or below represented generational buying opportunities (2015, 2018, 2022).
MAE
Mean Absolute Error. In this context it measures the average absolute deviation of actual log prices from the model prediction, expressed in sigma units. A MAE of 0.3 means predictions are typically off by 0.3σ. Lower MAE = better historical fit. Used to rank models in the selector.
R²
Coefficient of determination. A statistical measure of how well a regression model fits observed data. R² = 1.0 = perfect fit; R² = 0 = no explanatory power. The Bitcoin Power Law achieves R² = 0.961, meaning 96.1% of the variance in log Bitcoin price is explained by log time since genesis.
Halving
A scheduled event in Bitcoin's protocol that cuts the block subsidy (new BTC issued per block) in half, occurring every 210,000 blocks (~4 years). Halvings reduce supply issuance and historically precede major bull runs. Past halvings: H1 Nov 2012, H2 Jul 2016, H3 May 2020, H4 Apr 2024. Next (H5) expected Apr 2028.
Genesis Block
The first block of the Bitcoin blockchain, mined by Satoshi Nakamoto on January 3, 2009 (block 0). In the Power Law model, "days since genesis" is calculated from this date. It is the starting point (t = 0) for all time-based price regressions.
Log Scale(Log)
Logarithmic scale: a scale where equal vertical distances represent equal percentage changes (e.g., 10× growth), rather than equal absolute changes. On a log scale, Bitcoin's entire 15-year price history from $0.001 to $100,000+ is visible and meaningful. The Power Law is linear on a log-log chart (both axes log).
Dex
Short for "decade" in log-space — a unit of measure equal to one order of magnitude (10×). When sigma = 0.302 dex, the ±1σ band spans 10^0.302 ≈ 2.0× above and below the median. Used instead of percentage to describe log-scale deviations consistently across all price levels.
Block Reward
The amount of BTC awarded to miners for successfully adding a block to the blockchain. Started at 50 BTC, halved to 25 (2012), 12.5 (2016), 6.25 (2020), 3.125 (2024). After all 32 halvings (~2140), the block reward reaches zero and miners will be compensated solely by transaction fees.
Regression
A statistical technique for fitting a mathematical function to observed data to minimize prediction error. Both the Power Law and S2F models use Ordinary Least Squares (OLS) regression on log-transformed data. The resulting formula can then be used to extrapolate (forecast) values outside the training range.
Fair Value
In the context of these models, "fair value" means the model's median prediction at the current date — the price at which Bitcoin is neither overvalued nor undervalued relative to the long-run trend. The RangeBar on the right shows whether the live price is above, at, or below fair value.
OLS
Ordinary Least Squares — the standard linear regression method that minimizes the sum of squared residuals between observed and predicted values. All four models on this site use OLS regression on log-transformed price and time data.
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