Debate rages over Bitcoin power law as critics label it a ‘magic trick’

The Bitcoin power law — a mathematical model that suggests continued growth in the price of Bitcoin over time — has become the subject of fierce debate, with critics slamming it as “deeply flawed” and saying it’s more like a “horoscope” than a predictive model for the cryptocurrency’s price. 

Consultant and Bitcoin advocate Adrian Morris told Cointelegraph that while the Bitcoin power law had been touted as a predictive model for the future price of Bitcoin (BTC), its legitimacy has been drastically overblown by its advocates.

On the other hand, Italian physicist Giovanni Santostasi — the man responsible for discovering the power law as it relates to Bitcoin — told Cointelegraph that the Bitcoin power law is undeniable and one only needs eyes to see it.

The Bitcoin power law works by plotting Bitcoin’s historical price data on a “log-log” scale — the log of price vs. the log of time along a line that best fits this data.

Advocates of the power law, who include Santostasi and his colleague, mathematician Fred Krueger, say the law shows that the price of Bitcoin should continue to grow at a relatively consistent rate well into the future.

Power laws are a common occurrence in nature and have been applied to various natural phenomena ranging from the growth of animal teeth and claws, the distribution of wealth in societies — the well-known Pareto principle — all the way to plotting the severity of earthquakes and tornados.

Santostasi told Cointelegraph that the power law isn’t just limited to Bitcoin’s price and can be found across a wide range of Bitcoin-related data, including the growth of the network’s hashrate and the rate of new Bitcoin wallet addresses over time.

Bitcoin power law: Statistics or physics?

But Morris, a non-believer of the power law, has a long list of criticisms.

He has accused Santostasi’s power law of “overfitting” mathematical data to try and explain what are fundamentally human systems.

Morris argues that any study of Bitcoin’s data falls into the realm of statistics, not physics, which is more concerned with the nature and properties of matter and energy.

“This is a magic trick, and [Santostasi] is performing a sleight of hand. That’s all there is to it,” said Morris.

“He’s putting a statistics bunny into the hat, and then he’s pulling a physics bunny back out of it.”

Santostasi, however, rejects this argument, saying that while humans are clearly involved in the maintenance and growth of Bitcoin — both the network and its market value — it can still be viewed as a physical system, albeit with human involvement. 

“It’s still a physical system because there are fundamentally physical constraints, like the number of interactions that we as humans can have and the amount of information we transmit,” said Santostasi.

Additionally, Santostasi noted that many of Bitcoin’s key data points — including its difficulty adjustment algorithm, various machine-based feedback loops and the energy demands of miners — can all be considered as belonging to the realm of physics.

Santostasi pointed to the work of British physicist Geoffrey West, who wrote the book Scale as essential reading for anyone who remains unconvinced by the existence of power laws in human systems.

Doubling down on this assertion, Santostasi added that the study of Bitcoin’s data falls firmly into disciplines known as “social physics” or “econophysics,” which use mathematical tools to study social networks and their effects.

As a result, Santostasi said Bitcoin’s price action since its inception perfectly maps to a power law and can, therefore, be used as a powerful tool for modeling its growth into the future. 

The power law is more like a “horoscope,” says Morris

Morris’ next major criticism of the power law is that it weaponizes “hindsight bias” and encapsulates such a wide range of data that it cannot be relied upon to make useful predictions about the future.

Morris concluded that the power law is more like a “horoscope” and less of a predictive model.

“Under the power law, the price of Bitcoin in 2045 might be $200,000. It could also be $10 million. That’s not very, very predictive,” he said.

“It’s disingenuous to say that price could fall within six standard deviations and that means it has a high level of predictability,” Morris added.

“The power law is just looking back in time with a hindsight bias and using mathematics to confirm that bias. This is literally just confirmation bias being modeled out in graphical terms.”

Bitcoin advocate and network economist Timothy Peterson shared a similar criticism of the power law in a May 23 post to X, saying that the power law and the Never Look Back (NLB) metric cannot be considered “models” that could be used to make predictions. 

“They are based on time which is not an independent variable. They are historical relationships, but not models,” he said.

How could the Bitcoin power law be invalidated? 

Santostasi conceded that the Bitcoin power law — like all power laws — is not a completely perfect predictive tool and could be disproven by any outsized and sustained shift that causes its price to fall below — or spike above — the current trend line in any drastic way. 

He noted that as of today, Bitcoin’s price would need to fall to as low as $30,000 for an extended period for the power law to be disproved.

“People will see with their own eyes if this doesn’t work anymore,” Santostasi said, noting that any major deviation from the trend would be empirical proof of an invalidation.

Equally, he said the advent of “hyperbitcoinization,” which could look like the United States embracing Bitcoin as its currency and sending the price to over $250,000 in a matter of weeks, would also invalidate the model.