Bitcoin Power Law

Popularized by Giovanni Santostasi (a physicist) and further developed by analyst Harold Christopher Burger, the Bitcoin Power Law plots Bitcoin's price on a log-log scale against time since the genesis block. On this scale, Bitcoin's price history forms a remarkably straight line, suggesting a power law relationship: Price = A × (Days since genesis)ⁿ, where the exponent n determines the growth rate.

Unlike exponential models (like Stock-to-Flow), power law growth decelerates over time. This means each halving cycle produces diminishing percentage returns but still significant dollar gains. The model produces a support floor, a fair value line, and a ceiling that has contained virtually all of Bitcoin's price history.

According to Santostasi's analysis (2024), the power law model has an R-squared value of approximately 0.95 on Bitcoin's entire price history (2009–2024) on a log-log scale — an exceptionally tight fit for a financial asset. The model's support floor has never been definitively broken, including during the March 2020 COVID crash and the November 2022 FTX collapse.

Critics note that power laws are common in nature but their application to financial assets is debated in academic finance. Past fit does not guarantee future adherence. The model suggests Bitcoin will never reach $1 million in today's dollars within this century due to the decelerating growth rate, which contradicts more bullish projections. Regardless, the model provides useful long-term context for determining whether Bitcoin is relatively cheap or expensive within its historical growth trajectory.