8Mon·

$BTC (-0.52%)
Power Law: Can a mathematical model predict the future price? 📈🔮


Today we're talking about the so-called Bitcoin Power Lawor in German, the power law of Bitcoin. This model attempts to explain the long-term price development of Bitcoin using mathematical principles.


But is it even possible to predict something that is based on the supply and demand of people - like the price of a good?


What is the Bitcoin Power Law model?

The Bitcoin Power Law is a mathematical model that describes how the price of Bitcoin grows over time. It is based on the power law, a concept that is used in many areas of nature and science. Simply put, it shows how one quantity (e.g. the price) grows as a power of another quantity (e.g. time).


Power laws occur primarily in nature, such as in the growth of organisms, and in networks.


Giovanni Santostasi and the Bitcoin Power Law

The astrophysicist Giovanni Santostasi was instrumental in developing and popularizing this model. He (and other physicists) have established that Bitcoin has approximately followed such a power law over the last 15 years - which is quite remarkable.


His scientific approach shifts the focus away from a financial instrument to a networkthat is similar to a living organism grows. This ties in directly with the idea of "Metcalfe's Law", which describes the value of a network in proportion to the number of participants squared. Bitcoin as a network therefore becomes exponentially more valuable with each new user - with decreasing growth.


But what exactly does this mean?

You can think of this model like a big ball of yarn. It all starts with the first user using Bitcoin and thereby giving it a certain value. The more users there are, the higher the value of Bitcoin rises. A higher price in turn attracts more miners, who invest more resources in mining. This increased activity leads to an increase in mining difficulty, which means that miners need more income per coin. At the same time, the growing hashrate (computing power of the network) increases the security of Bitcoin, which in turn attracts more users - and the cycle starts all over again.


Santostasi calls this feedback loop between price, miners and users the feedback logic. He describes it using a mathematical model based on exponential growth.


If you plot the Bitcoin chart not linearly as usual, but logarithmically (on the x & y axes), you can suddenly see that Bitcoin has been following a line with over- and under-performance so far.


-> This line (green) is the Bitcoin Power Law💪

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(Source: https://charts.bitbo.io/long-term-power-law/)


Does this now mean that we can predict the Bitcoin price for all time in the future?

I'm not entirely convinced yet, but at least there are already websites like https://bitcoinfairprice.com/where you can select any date in the past or future and then get the "fair value" of Bitcoin for that date based on the power law model😅


So when will we reach the $1 million mark according to this model?

The answer according to the power law is: 2033


For the next 10 years it would look like this:

2024: $68.434

2025: $99.794

2026: $142.232

2027: $198.653

2028: $272.486

2029: $367.749

2030: $489.108

2031: $641.941

2032: $832.407

2033: $1.067.513

2034: $1.355.187


Conclusion

The Bitcoin Power Law shows how Bitcoin grows exponentially through network effects and self-reinforcing processes. It is a useful tool to understand the long-term development of Bitcoin, but should definitely not be taken as absolute truth.

I always find it very difficult to make predictions for the future based on the past. After all, there are countless external factors, such as regulations, global crises and the like, which all have an influence on the price.


Nevertheless, it is interesting that this model can at least be applied to Bitcoin's recent past.


I deliberately wanted to keep this article a little shorter. If you want to find out more about the Bitcoin Power Law, I can recommend Giovanni Santostasi's blog page:

https://giovannisantostasi.medium.com/the-bitcoin-power-law-theory-962dfaf99ee9


What do you think, is there anything to the Bitcoin Power Law or is it only valid again anyway until the price does something completely different? :D


Have a nice afternoon/evening!


#bitcoin

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161 Comments

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In principle, the model fits so well in the past because it has of course been fitted in such a way that the deviations from the previous data are minimal. This allows you to "prove" any supposed correlations, especially if you allow for axis scaling.

However, it is true that, by nature, networks tend to satisfy exponential laws. Whether the price then also shows long-term exponential growth has nothing to do with this in the first instance.
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@RealMichaelScott I agree. However, the axis scaling is limited to the fact that both axes are displayed logarithmically. And in this respect, I find it interesting that the price more or less follows a linear line.
I agree that you can't predict the future based on this.
Especially since disruptive technologies usually follow an S-curve adaptation :)
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@stefan_21 I haven't looked in detail at exactly how the axes were scaled. If it is only the pure logarithmization, it is of course a stronger correlation than if the axes were scaled accordingly beforehand.
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@stefan_21 I have now looked again and the correlation of the Bitcoin price should be:

1.0117e-17*(days since genesis block)5.82

But that's exactly what I meant: the 1.0117e-17 and 5.82 are simply scaling factors on a logarithmic scale to get a particularly good fit. In this respect, it is as I wrote in the previous comment: a rather weak correlation if scaling factors are allowed.
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@RealMichaelScott Merci. Good point, I hadn't noticed that. Then there will certainly have been a bit of playing around to get that 5.82 factor.
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@stefan_21 Yes, certainly. The factor in front of it is also nothing more than an adjustment factor that fits the compression of the y-axis (i.e. Bitcoin price) in such a way that the deviation is minimal.

The website also claims that, in principle, a linear regression was carried out on a log-log basis.
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Instead of a ball of wool, you can also use a snowball. In other words, a snowball system that will eventually collapse if no new users are generated.
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@Beeftek Why should Bitcoin collapse if no new users are added?
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@stefan_21 because if you only buy tulip bulbs because you are speculating that it will be worth more soon, it will collapse. Or you speculate that Bitcoin is a hedge like gold, but I doubt that most people buy Bitcoin to achieve price stability.
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@Beeftek Okay, so what does Bitcoin have to do with it?
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@Beeftek People buy Bitcoin because of its properties. Please also read my article "BTC - The perfect store of value" :)
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@stefan_21 but most people don't buy Bitcoin to store it in order to protect themselves against inflation. But to become a millionaire quickly and achieve high returns, I think that's contradictory.
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@Beeftek The fast-ball system, the tulip crisis - the comparisons are no longer merely misleading, they have long since collapsed. Anyone who still believes that Bitcoin is just a passing phenomenon probably also thought in 1999 that the Internet would not catch on.
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@Beeftek The "get rich quick" train left the station a long time ago. To become a millionaire with an investment of just a few thousand euros, you need to bring a little more time with you.
This is more the case with all the crypto nonsense like memecoins.
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@stefan_21 I have a rather different impression, look at all the posts. Most of them are about getting rich quick with Bitcoin. Bullshit. Bitcoin is there to protect against inflation. That's why it's overvalued.
If most people realize that you can't make great returns with it, which is the point of Bitcoin, then what? Look at your contribution.
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@Beeftek But in essence, that's exactly what it is. Of course, there are plenty of people who think they can get rich quickly. But these are also the people who will sell at the next small setback.
I can only recommend that you take a neutral look at Bitcoin. There is more to it than you might initially think. After all, I was also a critic for years and argued in a similar way to you😂 I also always thought that it was a Ponzi scheme ist🤷‍♂️
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@stefan_21 Yes, but most people don't even know what Bitcoin is for. To hedge against inflation.

But inflation is not 10% per year or 50% per year.

Bitcoin (digital gold) will grow like gold. What is the return on gold? 0% after inflation.
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Finally a post that I could read in full WITHOUT scrolling down 3 times :D The price forecasts would be great
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In reality, such curve descriptions always have the problem that they only work within the set limits (with standard deviation). For fitted curves, this would be between the first and last value.

Of course, a regression curve like this is a more intelligent approach than guessing, but theoretically we could have an external influence at some point, as you say, which results in a tipping point and suddenly an exponential function with a*e^-(b*x) takes over.

A similar problem to trained neural networks, which only work well if the input is within the trained data sets.
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Thank you. Another interesting article. But as you say, I can't imagine that the price will be predictable in the future. Especially as the benchmark - i.e. Fiat - is also constantly fluctuating.
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@vise72 absolutely. I agree
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One could add to the feedback loop that the rising Bitcoin price also ensures that Bitcoin is increasingly in the news and elsewhere. When people talk about it more and it gets more attention, the price rises in turn
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@Stewie Absolutely, that's what I wrote in this post:
https://getqu.in/J56y9P/

I only described the feedback loop according to Giovanni in the Power Law article :)
There are several control loops that interlock perfectly
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And here we have the famous profit promise, which Stefan says doesn't exist. A million in 2033.

Extrapolated from past data. The way it's done. Stocks and such always do the same thing. Brrr
Deleted User
8Mon
Comment was deleted
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@Madhatter5566 Forecasts are not promises of profit... or is every stock analysis with expected returns a promise of profit? Are gold price forecasts a promise of profit?
@Seebi Yes, we only forecast millions. Yes yes.
@vise72 Stefan always says that Bitcoin doesn't have that.....
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@Madhatter5566 Did you not understand my message? I just said that forecasts are not promises of profit. Stefan isn't promising you a profit either. What's wrong with you?
@vise72 Then call it a promise of returns


My gosh you Ponzi users and your semantics.
Deleted User
8Mon
Comment was deleted
@Seebi Call it what you like. Ponzi schemes and their semantics.

It's not a pyramid, it's a pouring cone. I don't care.
Deleted User
8Mon
Comment was deleted
@Seebi How many coins should Satoshi have?

Like every other coin that comes onto the market every day, the old users benefit from the new users.
Until the intrinsic value is reached again and then the last one loses out.


I had a look:
According to estimates, Nakamoto owns between 750,000 and 1,100,000 Bitcoins in 2021.

How does that work despite the decentralized network? Roflmao
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It fuels it for sure
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Green number go up. Ape happy
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