Bitcoin Long-Term Price Models: Power Law, S2F, Early Fit, Exponential Compared
Four mathematical frameworks dominate serious Bitcoin long-term analysis. Each takes a different approach to modeling price, with different assumptions about what drives Bitcoin's value. Here's a structured comparison.
1. Bitcoin Power Law (Santostasi 2026)
Formula: log₁₀(P) = −16.509 + 5.690 × log₁₀(t)
Variables: t = days since genesis (Jan 3, 2009)
R²: 0.961
Sigma: 0.302 dex
Core thesis: Bitcoin's price follows a power law as a function of network age — similar to how other adoption-driven technologies (internet, mobile, etc.) scale. The model is time-only: it does not use supply data, market cap, or external variables.
Strengths:
- Highest R² of the four models
- Simple, parsimonious (one variable)
- Naturally accounts for halving-driven deceleration
- Testable out-of-sample
Weaknesses:
- No mechanism — purely empirical
- Does not account for potential regime changes
- Very long-range projections ($1T+ per coin) are extrapolation
2. Stock-to-Flow (PlanB 2019)
Formula: ln(MktCap) = 14.6227 + 3.3182 × ln(SF)
Variables: SF = stock-to-flow ratio (circulating supply / annual new supply)
R²: ~0.947 (on log market cap)
Core thesis: Bitcoin's value derives primarily from its scarcity, quantified as the stock-to-flow ratio. As the ratio increases with each halving, the model price rises sharply.
Strengths:
- Grounded in monetary theory (scarcity → value)
- Correctly predicted post-2020 halving bull run direction
- Widely cited and understood by institutional investors
Weaknesses:
- Stock-to-flow will approach infinity after ~2140 (last halving) — model breaks down
- Significant deviations in 2022–2023 challenged its reliability
- Criticized for non-stationarity in the regression
3. Power Law (Early Fit)
This variant fits the Power Law regression using only the early period (pre-2017) to reduce survivorship bias. It tends to produce a slightly steeper slope, giving higher projections for long-range years.
R²: 0.978 (higher in-sample fit, lower out-of-sample due to overfitting early data)
Useful as an upper bound reference alongside the standard Power Law.
4. Exponential Model
The simplest model: exponential regression on Bitcoin price as a function of time.
log₁₀(P) = a + b × t
Strengths: Works well for short windows (3–5 years). Weaknesses: Exponential growth is physically unsustainable. At constant exponential rates, Bitcoin would exceed global GDP within decades. This model should be used only for near-term reference.
Side-by-Side Forecast Comparison (Median)
| Year | Power Law | S2F | Early Fit | Exponential |
|---|---|---|---|---|
| 2026 | ~$150k | ~$200k | ~$180k | ~$300k |
| 2028 | ~$540k | ~$600k | ~$680k | ~$2M |
| 2030 | ~$1.2M | ~$1.1M | ~$1.5M | ~$10M |
| 2040 | ~$8M | ~$4M | ~$12M | far too high |
Approximate values — use the live chart for current model outputs.
Which Model Should You Trust?
No model should be trusted unconditionally. The Power Law has the best long-term fit and the most defensible mathematical framework. S2F remains useful for cycle-timing analysis. Early Fit and Exponential are best as short-range references or upper-bound estimates.
Comparing all four on the same chart — as you can do at bitcoin-power-law.com — gives a richer picture than any single model alone.
Please cite Santostasi (2026) and PlanB (2019) when using model data. Link: bitcoin-power-law.com
Not financial advice.