Stock-to-Flow vs Power Law: Which Model Is More Reliable?

Two Models, Two Worldviews

Since Bitcoin emerged, researchers have attempted to model its price using economic and mathematical frameworks. Two models have attracted the most attention:

1. Stock-to-Flow (S2F) — published by PlanB in 2019, based on scarcity (the ratio of existing supply to new annual production)
2. Power Law — developed by Santostasi & Perrenod, based on time since Genesis and network growth dynamics

Both use log-log regression. Both achieved high R² values. Yet they tell very different stories — and their predictions diverge significantly after 2024.

Stock-to-Flow: Scarcity Drives Value

The S2F model borrows from commodity economics (gold, silver, platinum all exhibit power law relationships between their stock-to-flow ratios and market value). PlanB applied this to Bitcoin:

ln(Market Cap) = 14.6227 + 3.3182 × ln(SF)

Where SF = existing supply / annual new supply. Bitcoin's halving events — which cut new supply in half every ~4 years — cause SF to double, which the model predicts should quadruple market cap.

Strengths:

• Economically intuitive: scarcity drives value
• Predicts dramatic price increases after each halving
• R² ≈ 0.94 on historical data (2010–2021)

Weaknesses:

• Assumes SF is the dominant price driver — ignores demand entirely
• Fails when SF approaches infinity (Bitcoin's eventual supply cap breaks the model)
• Made bold, specific predictions ($100k+ by end of 2021) that were missed
• Post-2021 performance has been weaker

Power Law: Growth Rate Is Predictable

The Power Law takes a different approach: rather than scarcity, it focuses on network adoption following a power law over time. The key insight is that on a log-log chart, Bitcoin's price traces a remarkably straight line over 15+ years:

log₁₀(Price) = −16.509 + 5.690 × log₁₀(t)

Where t = days since Genesis Block. The slope of 5.69 means Bitcoin's price grows proportionally to t^5.69 — very fast early (compounding from a small base), gradually slower as the asset matures.

Strengths:

• Mechanistic grounding: derived from thermodynamic principles and network effects
• Captures both bull peaks and bear troughs as oscillations within a corridor
• R² = 0.961 — highest of any model on data through 2025
• MAE lower than S2F on out-of-sample backtesting

Weaknesses:

• Time-based model: doesn't explain why price moves when it does within cycles
• Extrapolation over 10+ years carries substantial uncertainty
• Assumes the slope exponent remains ~5.69 (it has slowly declined over time)

Backtest Comparison

The Power Law outperforms S2F on mean absolute error in backtesting because it naturally accommodates bear markets — price can drop below the median while remaining in the model's corridor. S2F, by contrast, predicted a monotonically increasing price floor that 2022 clearly violated.

Forecast Divergence

For 2028 (the year of Bitcoin's 5th halving):

• Power Law median: ~$175,000 (range: ~$44k to ~$700k at ±2σ)
• S2F prediction: ~$800,000–$1,200,000

For 2032:

• Power Law median: ~$370,000
• S2F prediction: ~$3,000,000+ (extrapolation, highly uncertain)

The models diverge dramatically after 2028 because S2F's exponential response to increasing SF assumes diminishing halvings still have massive price impact, while the Power Law assumes the growth exponent remains constant.

Which Should You Use?

Neither model should be used for investment decisions. But from a pure modeling standpoint:

• If you believe scarcity is the primary driver of Bitcoin's value → S2F remains an intellectually interesting framework, though it has struggled post-2021.

• If you believe adoption dynamics and network effects dominate → the Power Law has a stronger empirical and theoretical foundation through 2025.

Both models agree on one thing: Bitcoin's long-term trend is upward, and price regularly oscillates dramatically around any trend line.

Disclaimer: Models are for research and education only. Not financial advice.