A mathematical model describing Bitcoin's price as a function of time. On a log-log scale, Bitcoin's price history forms a straight line, producing support and resistance bands useful for identifying long-term value zones.
A mathematical model describing Bitcoin's price as a function of time. On a log-log scale, Bitcoin's price history forms a straight line, producing support and resistance bands useful for identifying long-term value zones.
The Bitcoin Power Law model describes the relationship between Bitcoin's price and time using a power function: Price = A x Days^n, where Days is the number of days since the genesis block. When plotted on a log-log chart (logarithmic axes for both price and time), Bitcoin's entire price history forms a remarkably straight line, indicating that the data follows a power law distribution.
The model generates three bands: a support band (lower boundary), a fair value line (the regression), and a resistance band (upper boundary). Price touching the support band has historically coincided with the best buying opportunities — the depths of bear markets when fear is greatest. Price reaching the resistance band has coincided with cycle peaks — the heights of euphoria when risk is greatest. The fair value line represents the model's expected price at any given time based on the mathematical relationship.
What makes the Power Law model compelling is its longevity. The linear relationship on a log-log scale has held for over 15 years of data across four complete market cycles. No other financial asset exhibits this precise a time-based relationship over such a long period. Critics argue the model is over-fitted to past data and must eventually break down as Bitcoin matures, while proponents argue the power law reflects fundamental adoption dynamics (network effects growing as a function of time) that will persist for decades.
Explore real-time data and interactive charts related to Power Law on Bitcoin Horizon.
View Live ToolThe Power Law model plots Bitcoin's price against time (days since genesis block) on a log-log scale. On this scale, the data forms a straight line — the signature of a power law relationship. A regression line through this data gives the "fair value" at any point in time, while parallel bands above and below create resistance and support zones. The key insight is that Bitcoin's growth decelerates over time in a mathematically predictable way, following the formula Price = A x Days^n.
When Bitcoin's price touches or drops below the Power Law support band, the model suggests it is historically undervalued relative to its time-based growth trend. These have been the best accumulation periods in Bitcoin's history — occurring during deep bear markets (2015, 2019, late 2022). It does not guarantee the exact bottom, but buying in this zone has produced the strongest long-term returns across all four cycles.
The model assumes the mathematical relationship that has held since 2009 will continue. If Bitcoin's adoption curve fundamentally changes — accelerating due to nation-state adoption or decelerating due to competition or regulation — the model would need recalibration. The bands also widen in dollar terms as price grows, meaning the buy and sell zones represent larger ranges. Most analysts use it as one tool among many rather than relying on it exclusively.