Bitcoin power law

Plotted with both axes on logarithmic scales, price against days since January 2009, bitcoin's history forms a band around a nearly straight line. That pattern corresponds to a power law: price grows in proportion to time raised to a fixed exponent, estimated at around 5 to 6. Physicist Giovanni Santostasi and others popularised the model, and variants add upper and lower corridors that have contained most of the price history.

Supporters argue the fit reflects network growth and adoption dynamics, making it more robust than models tied to halvings. It implies continued but slowing percentage growth, so it projects much more modest returns than the stock-to-flow model did. Analysts use it to discuss fair value and to describe where the price sits relative to the long-term trend.

Critics note that many curves can fit a short, noisy history, that the model has no causal mechanism linking time to value, and that log-log charts compress large deviations visually. A regime change, such as different adoption dynamics or a major failure, would break the fit. As with similar models, it should not be used as a price forecast.