Bitcoin Power Law Research
A comprehensive survey from Trolololo (2014) through Santostasi, Burger, Perrenod, and PlanC. The complete intellectual lineage of Bitcoin’s power law floor — every researcher, every paper, every exponent.
The Bitcoin Power Law Theory has generated a rich ecosystem of original research, academic validation, quantile refinements, and statistical critiques spanning 2014–2026. This survey catalogs every known researcher, paper, and analysis relevant to Bitcoin’s power law floor.
The power law exponent for Bitcoin’s price-vs-time relationship has been independently measured by at least ten researchers. Values cluster between 5.6 and 5.9. This convergence, using different data windows, time bases, and regression methods, is itself strong evidence of a real underlying phenomenon.
Origins: From Trolololo to Santostasi
The intellectual lineage begins on BitcoinTalk in October 2014, when pseudonymous user Trolololo posted a logarithmic regression formula. His mixed-base equation obscured the underlying power law. As Santostasi later showed, it’s algebraically equivalent to Price = A × daysn with n ≈ 5.83.
Giovanni Santostasi
PhD Astrophysics, Northwestern University. CEO and Director of Research, Quantonomy Fund. The originator of the Bitcoin Power Law Theory. His contributions span three phases:
The core derivation: Network adoption follows N ~ t³ (the Difficulty Adjustment converts logistic growth into power law growth). Value scales as V ~ N1.95 (near-Metcalfe). Combined: P ~ t5.85, matching the empirical slope. The model has only failed once: March 13, 2020 (COVID crash intraday).
The Power Law Corridor
Harold Christopher Burger
Entrepreneur and engineer. His September 2019 paper identified two power-law boundaries: a support line (floor) and a top line fitted through cycle peaks. Formula: price = 10−17.016 × d5.845, R² = 0.931. Used RANSAC to identify “normal mode” and “bull mode” — price spends ~50% of time in each.
Stephen Perrenod
Astrophysicist, OrionX affiliate. Produced the most statistically sophisticated treatment. His FGLS correction with AR(2) improved Durbin-Watson from 0.03 to 2.01. His three-layer decomposition (power law spine + log-periodic oscillations + noise decay) shows fat tails are structural artifacts. After all layers removed, innovations are approximately Gaussian.
Matthew Mezinskis
Operates Porkopolis Economics. His distinctive contribution: percentile band methodology. “Finance is not a bell curve. The bands are calculated as percentiles.” Red bands: 2.5th to 97.5th percentile. Blue bands: 16.5th to 83.5th. His “13% doubling rule”: for every ~13% increase in Bitcoin’s age in days, the trendline price doubles.
Quantile Regression: PlanC, Sina, and Sminston
PlanC built the most sophisticated quantile regression framework: 133,000+ data points, 1,500 lines of code, 999 quantile levels. Key floor claim (March 2026): 522 weekly fits over 10 years show “essentially zero change” in the 1st quantile slope. The floor doesn’t decay.
Sina developed the Volatility-Adjusted Power Law Index (VPLI) with a three-zone framework. Sminston With (PhD Materials Science) created the Bitcoin Decay Channel — PlanC credits Sminston as “by far the biggest influence” on the v2 hybrid approach.
“The floor doesn’t decay. The median does. OLS overestimates fair value at ~$118–130K when the true decay-adjusted fair value is ~$100–101K.” — PlanC, March 2026
Academic Papers on Metcalfe’s Law
The Metcalfe exponent — how network value scales with users — has been measured across multiple peer-reviewed studies:
| Study | Year | Beta | Venue |
|---|---|---|---|
| Santostasi | 2014/24 | ~1.95 | Non-academic |
| Alabi | 2017 | ~2.0 | Electronic Commerce Res. |
| Peterson | 2018 | 2.0 | Alt. Inv. Analyst Review |
| Wheatley/Sornette | 2019 | 1.69 | Royal Society Open Sci. |
| Shanaev et al. | 2019 | Rejects all | SSRN working paper |
Wheatley & Sornette (ETH Zurich, Swiss Finance Institute) provided the only peer-reviewed measurement: Beta = 1.69, forcing Beta = 2 was “robustly rejected on moving windows.” Shanaev et al. used instrumental variables and found “previously reported strong positive relationships are spurious” — formally unresolved in the literature.
Criticisms and Defenses
The strongest objection comes from the spurious regression critique: Marcel Burger (CIO, Amdax) and Tim Stolte argued ADF tests show non-stationarity, making the regression “logically and statistically invalid.”
The defenses are multiple and convergent:
Taleb (2021) argued that any non-zero probability of reaching zero gives Bitcoin an expected present value of exactly zero. Burger’s rebuttal: mining stopping temporarily is NOT an absorbing barrier; if applied to gold via DCF, Taleb would reach the same conclusion.
Exponent Convergence
The strongest evidence for the power law: independent researchers, using different methods, data windows, and time bases, converge on the same exponent.
| Researcher | Basis | Exponent n | R² |
|---|---|---|---|
| Trolololo (2014) | ln-log10 mixed | ~5.83 | N/A |
| Santostasi (2018/24) | Days from GB | 5.8 | 0.95 |
| Mezinskis (2018) | Days from GB | 5.77 | >0.95 |
| Burger (2019) | Days from Jan 1 2009 | 5.845 | 0.931 |
| Sigman/B1M (2025) | Years from GB | 5.616 | 0.957 |
| Perrenod QR (2024) | Block years | 5.83–5.865 | 0.94 |
| Perrenod FGLS (2024) | Weekly data | 5.68 | 0.999 |
| Observatory | Days from GB | 5.688 | 0.95+ |
Read the Paper
9 pages. 13 sections. 10+ researchers cataloged. The complete intellectual lineage from Trolololo (2014) through the Observatory. Every exponent, every critique, every defense.
The power law exponent converges. The researchers converge. The floor converges. The only question is whether you converge with them.