**The “Power Law” model is currently considered the hottest candidate for the final model to reflect the Bitcoin price. The power law is so universal that you can find it almost everywhere. Does this really apply to Bitcoin too? And what does it say about the future? Will we still get seven-figure Bitcoin prices in the 2030s?**

It would be nice if one could predict the future using mathematical models, such as those that predict the Bitcoin price.

The Bitcoin community is not short on such models, such as the rainbow or stock-to-flow model. What both models have in common, however, is that in principle they have already failed: the rainbow had to be adjusted so that it continued to reflect the price, while the stock-to-flow forecasts were in some cases so far away from the actual price that one could call it that a lot of elasticity has to interpret that not much statement is left.

The currently most popular model is the “Power Law”. It is based on general laws that go far beyond Bitcoin, but supposedly reflects the price of the cryptocurrency extremely accurately.

## Power laws, everywhere!

A power law is basically nothing more than a class of formulas that describe curves. For this it uses three sizes: a, x, b. The formulas that represent the curve “y” is a * x^{b}, where x is the variable value. One value – the position of the curve – changes with the power of the size x. How high this potency is is defined beforehand.

Power laws are often encountered in nature and society. This begins in geometry, when the area of a square plot of land increases with the second power of the side length (area = side length * side length), continues through physics, in which gravity decreases with the square of the distance, or energy according to the famous Einstein formula grows as the square of the mass (e = m*c²), reaches the population development of large cities, the growth of nails and horns, the connection between mass and metabolism in animals, the spread of viruses and much, much more. The power law is more or less everywhere, we grow, live and die with it.

Power laws “always occur when you describe an iterative process in which the output becomes the new input,” explains Giovanni Santostasi, actually an astrophysicist. The power law applies to any type of self-reinforcing system. One could list endless examples:

A city becomes more attractive the more people live in it? Power Law. YouTube shows a band the more often the more views it has? Power Law. Algae spread faster in a lake the more dominant the population is? A star grows the faster the greater its mass and thus its attraction? Psychosis causes relationships to break down, and loneliness causes psychosis? Power Law. Power Law. Power Law. The poor get poorer, the rich get richer, whoever has gets given, and so on and so forth.

Almost everything that happens can be described by a power law. Basically, the S2F and rainbow charts are also power law formulas, although these use logarithmic or exponential growth curves in which the power itself changes as time progresses.

## Bitcoins Feedback-Logik

The trick now is to find the right formula to apply the power law to Bitcoin. To this end, Santostasi has developed a model that “explains all important onchain parameters and describes the growth of Bitcoin adoption in a scientifically coherent and falsifiable way.”

You can imagine the model as a big ball of yarn that starts with the first user using Bitcoin, thereby giving it value. The value increases the more users there are; the higher price ensures that more resources are invested in mining, which increases the difficulty, which is why miners need higher income per coin; the higher the hashrate, the higher the security, which in turn attracts new users and so on.

Santostasi therefore assumes a feedback logic between price, miner and user, which reinforce or inhibit each other. He gives the growth of users the power of three in order to form a kind of general formula for adoption:

Addresses=t^{3}

Price=Addresses^{2}=(t^{3})^{2}=t^{6}

Hash-Rate=Price^{2}=(t^{6})^{2}=t^{12}

On this basis, Santostasi and others developed a system of curves that gives a main line that follows the formula

P = $38,788 * (B/15)^{5.41}

According to her, the Bitcoin price grows by a factor of 5.41 depending on the block time. This formula has proven to be extremely accurate over the past 13 years.

## The “fair price” of Bitcoin

On the website bitcoinfairprice, Santostasi presents the price according to his power law. The “fair price” is therefore $62,835, which means that Bitcoin is currently slightly overvalued.

However, since Bitcoin does not grow constantly – not even in a logarithmic perspective – but through bubbles and valleys, sometimes too much, sometimes too little, the model only works on average. “Bubbles,” explains Santostani, “are not part of the theory, at least not yet. They can be understood as temporary disturbances of the power law. When the bubbles contract, the price always falls back to the general trend.”

Nevertheless, he and others have supplemented the average – fair – powers with maximum and minimum powers to define lower and upper limits. You can find them on the Bitbo chart page. The upper limit is, in trading language, the “resistance” – the resistance beyond which the price does not go – and the lower limit is the “support” – the support or floor through which the price does not fall.

Depending on how you read it, the Power Law falls into the same trap as any other model: it can’t work if you take it too literally, but the more you loosen the scope of interpretation, the less meaning you’ll be left with. Currently the range is from $27,000 to almost $300,000, according to Bitbo’s chart, with an ideal value currently around $70,000. So we’re pretty much there, but we could also be somewhere else entirely.

But of course the most interesting thing is looking into the future. What does the Power Law predict for future Bitcoin prices?

## A (pleasant) look into the future

Let’s take some future points in time:

- Am
*21. September*The minimum is 32,000 dollars, the maximum is almost 350,000 and the “fair” price is around 90,000. - Am
*March 13, 2025*i.e. in almost a year, the lower limit is only 38,000, but the maximum is already more than 400,000, and the “fair price” is almost 110,000 dollars. - If we then look ahead another year,
*March 24, 2026*we already have a floor of almost $55,000, a maximum of almost $550,000, and a middle of a strong $150,000. - And if we then take a leap into the future, let’s say into the
*March 2028*the rate is already between 100,000 and 950,000 while we are already*End of 2033*arrive at a fair price of around 1.3 million dollars, and*Early 2040*almost five million dollars…

— so if the dollar is still worth something during this time, and if the Power Law remains in effect until then, we probably don’t have to worry much about our pension. However, it is more likely that the power law in Bitcoin is also stranded by the old rule that nothing grows forever. No fingernails, no cities, no algae populations, not even stars, and certainly not the price of Bitcoin.

There is much to suggest that power law growth is often just the start of an “S-curve”. This is not a mathematical formula, but a concept of innovation management that shows how new technologies, after a phase of initial strong, exponential growth – which here means both further development and spread – transition into a phase of slow, linear growth that slowly fades away. if there are no further breakthroughs.

## When the S-curve hits

“S-curves are typical for the spread of many technologies, such as televisions, refrigerators, cars, cell phones and so on,” explains Santostasi, “but Bitcoin does not follow an S-curve that starts exponentially, but rather a power law with a factor of 3. Many Phenomena that spread according to an S-curve (such as a virus) follow the power law if they have a mechanism of containment.”

In exponential growth, the power is the variable, which is why it initially grows slower but then grows much more aggressively than power law growth, where the power is fixed.

With Bitcoin, Santostasi continues, both the adjustment of the difficulty and the risk that accompanies every investment act as inhibiting mechanisms that delay the transition from the steep to the flat curve. But it will still be unavoidable.

When exactly is, of course, an open question. A Bitcoiner who has studied the Power Law speculates that the usual S-curve cycles last 30-50 years. Even if that is far too optimistic, Bitcoin could still have a few years left to continue on the power law path.

Source: https://bitcoinblog.de/2024/03/18/das-power-law-des-bitcoin-kurses-das-perfekte-modell-um-den-kurs-vorauszusagen/