Giovanni Santostasi - The Bitcoin Power Law Theory

[franky1]

The Bitcoin Power Law is a model by Giovanni Santostasi that aims to show the price of Bitcoin over time based on its historical growth pattern. The core of the Bitcoin Power Law is expressed algebraically as:

Estimated Price = A * (days from GB)^n

Where:
"GB" stands for the Genesis Block of Bitcoin, mined on January 3, 2009
"A" is a constant (10^-16.493)
"n" is 5.68

A very interesting tweet by Giovanni about one question I already had in my mind: How stable is the relationship he found? How the parameters changed during the lifetime of bitcoin?

Here you have the answer:



You can appreciate how stable the relationship is thought the years.

1st quote: "A" is a constant (10^-16.493) "n" is 5.68
2nd quote: "A" is a constant (10^-17.624) "n" is 5.912

doesnt seem constant to me.. so not a power number

[fillippone]

An interesting debate is the one comparing power laws, that exhibit an infinite growth potential, with S curve, or logistic, models, where there is a set cap on the price.
Here on the forum we have some proponent of these kind of models:

A logistic model of Bitcoin's price

Giovanni made his thoughts clear on the matter:

[MainIbem]

An interesting debate is the one comparing power laws, that exhibit an infinite growth potential, with S curve, or logistic, models, where there is a set cap on the price.
Here on the forum we have some proponent of these kind of models:

A logistic model of Bitcoin's price

Giovanni made his thoughts clear on the matter:

I love this Giovanni's approach concerning Bitcoin it's highly educative and interesting, one thing about this forum is that the more you engage in it daily, you'll get new knowledge, ideas and logic behind satoshi's creation (Bitcoin) many people are yet to be informed about this and are only informed about the basics which is buying and holding for long-term but I believe in having a deep knowledge concerning certain things and Bitcoin is definitely one of them, it's turned out to be on of the best investment option, therefore broadening one's knowledge about it is very important and threads like these would ensure that, something worth knowing is worth it and shying away from it is never a good approach. We've seen Bitcoin's potential and the evidence is there, with how well it's improved therefore learning the theory behind that is worth it, thanks to men like Giovannig for breaking down the logic models of Bitcoin.

[nondormomai]

That is the best thread i ever seen on this topic, thank you guys.

I just have come through the Santostasi theory.
For me, it is not very convincing.

I have the impression that the model explains the behavior as long as reality matches the prediction.

Take the case of the power law applied to the city.
According to a power law, Can a city infinitely grow?
I don't think so.

[Orluemma]

Adding to what’s been said here, I think the core of Giovanni’s Power Law Theory is less about trying to predict exact prices and more about understanding Bitcoin’s deep structural behavior over time and the consistency of that behavior in mathematical terms. It’s refreshing because instead of chasing short-term market noise or narratives, it takes a step back and asks: What if Bitcoin behaves like a natural law?

Now, sure, some folks (like franky1) rightly point out that adjusting parameters across cycles weakens the “law” status. That’s a fair critique if your model needs constant tweaking, is it really a law or just a fancy fit? But I’d argue that what Giovanni is offering isn’t about perfection; it’s about probabilistic guidance. That’s still valuable, especially in a space where chaos and speculation are the norms.

Also, what struck me was the analogy to living systems cities, mountains, even organisms. That’s powerful. It reframes Bitcoin not just as digital gold or a financial tool, but as something with its own internal logic, a kind of economic biology driven by scarcity, time, and energy.

Where this theory shines is in its philosophical implications:

Bitcoin isn’t just “money” it’s a self-governing system of economic order.

Halving doesn’t break it it amplifies the law of conservation.

Scarcity isn’t a constraint it’s the source of its value continuity.

That said, we should be cautious about hero-worshipping any one model. Giovanni’s work is exciting, but science thrives on falsifiability. If it’s a real theory, it should hold up under scrutiny, over time, and without needing to fudge the inputs every few years.

Maybe the real takeaway isn’t that he’s predicted the future but that he’s pointing us toward a different way of thinking about Bitcoin: not just in charts and cycles, but in laws and lifecycles.

[fillippone]

Take the case of the power law applied to the city.
According to a power law, Can a city infinitely grow?
I don't think so.

No, the power law doesn't tell you a city can infinitely grow.
Also, Giovanni says he wouldn't take his own model valid after a couple of orders of magnitude growth.

The model says that the growth of animals, cities, and other living creatures observed so far, follows such a scheme.
Of course, if we don't see animals that are 10x bigger than the blue whale, probably other factors impact the growth of such an animal. Of cours,e the model is not complete.

[Call_Me_Guru]

Giovanni Santostasi's power law is a near-perfect view, for me. This power law predicted what we see in Bitcoin today, where it will get to a stage that the returns start diminishing, that is the true reflection of it if we look towards that angle as it matures. Bitcoin tendency to give return at $100k, is not the Bitcoin tendency to give return $30K. The return will greatly decrease as prices increases. For example, at $500k, it will take Bitcoin at $1m to deliver the double of the investment. But at lower price, multiples of that can be made easily. This is a true reflection of the future reality and this formula speaks best of the future obvious.

Price=A×Time^B

A and B are constants. A= Scaling factor and B= Exponent (growth).

Thank you fillippone for sharing this rarely looked into but useful article.

Take the case of the power law applied to the city.
According to a power law, Can a city infinitely grow?
I don't think so.

The model says that the growth of animals, cities, and other living creatures observed so far, follows such a scheme.
Of course, if we don't see animals that are 10x bigger than the blue whale, probably other factors impact the growth of such an animal. Of cours,e the model is not complete.

The animals, cities and other living creature's growth suggested are not to compare but to acknowledge the developmental stages. In babies, the growth is rapid, which continues through to some adult stages where the growth start slowing down until full maturity. Cities too, the infrastructural development and new building are rapid at a point, but it gets to a point where they start diminishing for most places have been developed and procurement of land and properties will be expensive by then.

[fillippone]

New update from Giovanni on the status of Bitcoin power law:



Seems compelling about the resilience of the 40% support.

[fillippone]

I am signalling here a beautiful calculator made by Hostfat, using the Power law as a pricing engine.

Bitcoin Power Law Based Loan Simulator




I privately made a Google version of this tool, but it's so much more convenient, and really makes you appreciate the effect of power laws in the long run.

[fillippone]

Reupping this thread, so we can appreciate how the power law model is behaving in these turbulent times:



Model is holding quite well, and the local low at 60,000 was very close to the lower bound of the model, sitting at 53K.
Yes, we can go further down from here, but the risk assessment points to an asymmetry at these levels.

[Ambatman]

Model is holding quite well, and the local low at 60,000 was very close to the lower bound of the model, sitting at 53K.
Yes, we can go further down from here, but the risk assessment points to an asymmetry at these levels.

Unlike the Stock flow model which haven't been keeping up for some years now
I think it was affected by adoption of ETFs and other options that may allow rehypothecation
But the power law has stayed true since its not tied to supply shock.

It's bottom is quite similar to SMA 200 on how it's around $58K and still rising
Like that of the power law
Bottom and top are growing slowly and organic
Though like every body it explains the past but doesn't really guarantee the future
But so far Bitcoin price has been doing well with time.

[fillippone]

It's bottom is quite similar to SMA 200 on how it's around $58K and still rising
Like that of the power law
Bottom and top are growing slowly and organic
Though like every body it explains the past but doesn't really guarantee the future
But so far Bitcoin price has been doing well with time.

It's nice to see how the lower bound acted as a nice support when everybody was crying in panic.
The model survived its first major crash. Now it has to be tested on the upside!

[As-Soon-As]

Sharing this chart showing the inflation-adjusted market capitalization of gold and silver since 1900, with Bitcoin added in 2010. The bubbles show the 5-year price inflation rate (CPI) and the shading show the 5-year monetary inflation rate (M2). Gold is at $35 trillion, and silver and Bitcoin are at $1.8 trillion (using some creative assumptions on my part to determine the “above ground” supply of silver).

It’s amazing to me that it took Bitcoin 18 years to reach a market cap of $1.8 trillion it took silver five millennia.  Apples to oranges of course, but still.



Source Link: https://x.com/i/status/2019838720782852545

Although the above post is not relevant here, I brought it here because I want to show this community how quickly Bitcoin has been able to reach advanced levels. Gold, silver have been influencing people for a long time, but Bitcoin has been able to reach the highest level in just a few days and in the future, Bitcoin will show the highest performance of all time. Here is the proof that Bitcoin is the best.