Physicist explains how his ‘Power Law’ model got to $10M Bitcoin by 2045

The price of Bitcoin could increase by 6300% in the next 15 years, according to Giovanni Santostasi’s power law model.

Former physics professor Giovanni Santostasi has shed new light on his “power law” model for predicting the price of Bitcoin (BTC) — which tips arrived at a prediction of $10 million per individual BTC by the year 2045. 

A power law is a mathematical relationship where one value is proportional to a fixed power of another value. The power law has been observed throughout a wide range of naturally occurring phenomena, from the frequency of earthquakes to the dynamics of stock market changes.

Santostasi first shared the power law model in the r/Bitcoin subreddit in 2018. However, it witnessed a resurgence in January of this year after finance YouTuber Andrei Jeikh mentioned it in a video to his 2.3 million subscribers.

Santostasi said the model predicted that Bitcoin could reach a peak of $210,000 in January 2026 and then fall as low as $60,000 afterward. 

In a March 2 discussion with mathematician and Bitcoin investor Fred Krueger, Santostasi said a power law model displays a more easily understood and predictable model of Bitcoin price action over long time periods.

First cut from my 90 min deep dive with @Giovann35084111

This is the chart that you "can't unsee".
Non-intuitive aspects of the power law
In the next 15 years of Bitcoin, we expect the price
to go up not by 2, but by 64! pic.twitter.com/K1RiQSPt1M

— Fred Krueger (@dotkrueger) March 2, 2024

In contrast, the majority of short-term Bitcoin price charts used in mainstream media tend to show a “messy” and inaccurate view of Bitcoin’s price action.

“The linear chart that they usually show in TV — what [Jim] Cramer is talking about — looks messy.”

“But when do you the log of the y-axis, and you start to see some regularity there, it doesn’t look that messy, it looks like a very nice pattern,” he explained.

Santostasi said that, unlike the now widely-criticized stock-to-flow model, the power law is logarithmic instead of exponential.

This means Bitcoin’s price doesn’t have to increase constantly over time and significant fluctuations in price — witnessed most recently between 2020 and 2023 — can still be accounted for under the model.

Related: Bitcoin daily withdrawals challenge records as $2B leaves exchanges

In a follow-up post to X on March 3, Krueger outlined further mathematical modeling of the power law when applied to Bitcoin, which predicted that Bitcoin would reach a price of $100,000 within the next two years.

Hyperbitcoinization timeline and the meaning of 5.8
——————————————————-

I have done a lot of thinking over the last 24 hours on the meaning of power laws, and the implication for future Bitcoin prices.

But as i asked @Giovann35084111 the… pic.twitter.com/4iSP0IQMse

— Fred Krueger (@dotkrueger) March 2, 2024

Krueger added that if Bitcoin adheres to the power law model, its market cap would overtake that of gold by the year 2033 at which point Bitcoin would be worth $1 million per token.

Despite Santostasi’s and Krueger’s belief in the power law model, critics say that any mathematical model can be prone to substantial errors and does not account for random events that could have a serious impact on price.