Log Regression Deviation

What is it?

Logarithmic Regression models Bitcoin's price as a log-linear function of time elapsed since the genesis block. The formula is log(price) = a × log(days) + b, where coefficients a and b are fixed at the Santostasi & Perrenod 2026 calibration (a = -16.509, b = 5.690); deviation from this curve is expressed as a z-score computed over the entire prior history, with a one-year minimum warm-up. The model produces a central trend curve (estimated fair value) and standard-deviation (σ) reference marks around this trend. The underlying assumption is that Bitcoin adoption follows an S-curve, whose log-linear phase is still ongoing.

How to read

Price oscillates around the central curve with decreasing amplitude each cycle. Crossing +2σ marks the extreme exuberance zone: on the delivered series, only 2013 and 2017 produced it. The -2σ band has never been reached: the series' lowest point is -1.30, on 14 January 2015. The slope of the central curve represents the implied long-term growth rate, which progressively decreases.

Key zones

On the delivered series, the +2σ band was crossed only in 2013 and 2017, and the April 2021 top capped at +1.53. The -2σ band has never been reached; the documented troughs stand at -0.84 (November 2011), -1.30 (January 2015), -0.71 (December 2018) and -1.23 (November 2022). The zone between -1σ and +1σ (85% of the time) is the 'fair value' zone. The progressive convergence of the bands reflects market maturation - excesses become less extreme each cycle.

What to observe

Identify which zone price currently occupies: undervalued below -1σ, fair value between -1σ and +1σ, or exuberance above +2σ. Transitions between zones provide invaluable cycle context. Also monitor whether price 'respects' the lower zone as secular support - a sustained break below the 2015 floor (-1.3σ) would challenge the model's validity.

Historical context

Logarithmic regression on Bitcoin was popularised by Trolololo (Bitcointalk, 2014) and developed by analysts like Dave the Wave. The model has survived 4 cycles with remarkable consistency, unusual for such a simple statistical fit. The convergence between this model, Giovanni Santostasi's Power Law, and PlanB's Stock-to-Flow (despite very different methodologies) suggests a fundamental property of Bitcoin's growth.

Expert notes

Logarithmic regression is a curve-fitting exercise on a single asset with ~15 years of history. Despite its historical robustness, the model is vulnerable to regime change (S-curve adoption flattening, major regulation, or competitor). Regression parameters shift slightly with each new data point, meaning bands 'move' - the model is retrospective and projects nothing. Using it on a log scale masks absolute variance which remains considerable.

Common mistakes to avoid

Using the regression as a precise price prediction tool is a fundamental error. The model provides a valuation envelope, not a price target. Claiming 'Bitcoin will be at $X in 2030 according to log regression' ignores the confidence interval spanning a 10x factor between high and low bands. Also, the underlying S-curve will eventually flatten, but nobody knows when - which would structurally invalidate the model.

Programmatic access

REST API

curl -sS \
  'https://api.trinityinsights.io/api/v1/onchain/metrics/logarithmic-regression/data?timeframe=90d' \
  -H 'X-API-Key: $TRINITY_API_KEY'

MCP server

{
  "tool": "get_chart_value",
  "metric_id": "logarithmic-regression",
  "timeframe": "1y"
}

Required tier: pro. See the pricing grid for the tier list and the MCP documentation for multi-client configuration.

Related metrics

• power-law-corridor
• bitcoin-rainbow
• stock-to-flow
• mayer-multiple

Institutional disclaimer

Trinity Insights is an educational and analytical tool. The metric above does not constitute investment advice. Trinity Insights is not a Crypto-Asset Service Provider (CASP) registered under MiCA Regulation (EU) 2023/1114. See the full disclaimer.