Log Regression Deviation
Z-score measuring how far Bitcoin's price deviates from its best-fit logarithmic growth curve. Positive = above trend, negative = below. Statistical extremes have marked every cycle top and bottom.
What is it?
Logarithmic Regression models Bitcoin's price as a log-linear function of time elapsed since the genesis block. The typical formula is log(price) = a × log(days) + b, where parameters a and b are fitted by regression over the full history. The model produces a central trend curve (estimated fair value) and ±1σ and ±2σ bands 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. When price touches the +2σ band, the market is in extreme exuberance (historically, cycle tops). When it reaches the -2σ band, it marks maximum capitulation (cycle troughs). The slope of the central curve represents the implied long-term growth rate, which progressively decreases.
Key zones
The +2σ band coincided with the 2011, 2013, 2017, and 2021 tops. The -2σ band coincided with the 2011, 2015, 2018, and 2022 troughs. The zone between -1σ and +1σ (approximately 70% of the time) is the 'fair value' zone. The progressive convergence of bands reflects market maturation - excesses become less extreme each cycle.
What to observe
Identify which band price currently occupies: undervalued (-1σ to -2σ), fair value (-1σ to +1σ), or overvalued (+1σ to +2σ). Transitions between bands provide invaluable cycle context. Also monitor whether price 'respects' the lower band as secular support - a sustained break below the -2σ band 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, not truly predictive. 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. Moreover, 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/logarithmic-regression/history?days=90' \
-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.
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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.