Criticism of the Bitcoin Power Law: The Model's Weaknesses

What is the most important criticism of the bitcoin Power Law? It is a curve fitted to 16 years of price history, not a law of nature. Its high goodness of fit overstates how much it knows, small assumptions shift the forecast a lot, and since January 2026 the price has been below the trend. It remains useful as a corridor, not as a price target.

Why you should know the weaknesses

On bitcoin-powerlaw.com you meet the Power Law everywhere: in the zones, in the floor, in the calculators. If you build your plan on it, you need to know where it can be wrong. Otherwise you will rely on a number at the wrong moment.

This article collects the serious criticism of the bitcoin Power Law, not the polemics. For each point you will find what the data say and what it means for you. All figures are based on daily closing prices from Jul 18, 2010 to Nov 12, 2026.

Criticism of the bitcoin Power Law at a glance

1. A curve is not a cause

The Power Law says: bitcoin's price grows with a fixed power of the time since the genesis block. That is an observation. The formula gives no reason why time should drive the price.

Giovanni Santostasi, who made the model well known, explains it with the growth of the network: more users, quadratically more value. But this explanation came after the curve already fitted. It doesn't predict whether the number of users will keep growing like that.

What holds up: a lot. If no one buys any more, no formula helps. On top of that, bitcoin survived, and only for that reason is there a curve that can be fitted. No one asks about a Power Law for failed coins.

2. The R² overstates the certainty

Over all days since 2010, the formula explains 96.1% of the variation in log prices. That sounds like an almost perfect model. But statisticians have warned for decades: two quantities that both grow steadily almost always fit well together. Even an ordinary exponential curve reaches an R² of 0.86 on the same data.

What's more, the days are not independent. If bitcoin is far below the trend today, it will be almost exactly as far tomorrow (correlation 0.998). The real information lies mainly in the cycles, and there have been five of them.

What holds up: justified. The R² shows that the curve traces history well, not how surely it knows the future.

3. Small assumptions, big differences

The formula counts the days from January 3, 2009. That is plausible, but it is a choice: bitcoin was only traded from July 2010. Shifting the starting point by just half a year changes the exponent clearly. The same happens if you only look at the more recent years.

This is how the Power Law line, i.e. the value of the formula, for January 1, 2035 changes if you do the same calculation with other assumptions:

Euros at the ECB reference rate of Nov 12, 2026 (€1 = $1.1081). Every row fits the past well, yet the values for 2035 are almost a factor of 3 apart. The researchers Carlos Baquero and Raquel Menezes came to the same conclusion in 2026: the exponent is weakly determined.

Floor and trend hang on this line. The floor is at 0.42 × line. Our trend is the line itself until January 2022 and since then the middle between the floor and the top band on the log chart: on Jan 1, 2035 that is $688’000 (€620’000), 0.51 times the line. This middle is our own step; it isn't in the published formula. It has no fitted number of its own, but it rests on the top band, which only five cycle highs determine, and on the choice of halfway: 40% or 60% of the way from the floor to the top band fit the prices almost as well. Today's trend of around $109’000 would thus lie somewhere between $99’000 and $120’000, and the one for Jan 1, 2035 between around $0.66 and $0.71 million.

What holds up: justified. For you this means: the further a target lies in the future, the less you should rely on it. The values for 2030, 2035 and 2040 with this uncertainty are shown in the bitcoin forecast based on the Power Law.

4. The price has been below the trend since January 2026

On Jan 28, 2026, bitcoin closed above the trend for the last time. Since then it has been below for 288 days, on Nov 12, 2026 at $71’461 (€64’490, CHF 59’537), 0.66 times. In the four years up to today, the price was on average 8% below the trend.

The criticism targets the Power Law line, which is the trend on other Power Law sites: it is said to be too steep. The price has been below it since Oct 28, 2025, at 0.45 times on Nov 12, 2026. In the four years up to today it closed above it on only 22% of days and was on average 28% below it. Even the high of October 2025 only reached 1.1 times the line. An own regression with the data up to today does in fact lie around 9% below the formula. Up to the end of 2025 it still confirmed the formula to within about 1%.

This criticism hits home, and our trend takes it on board: since January 2022 it is not the line, but the middle between the floor and the top band, and gets closer to the floor every year. On Nov 12, 2026 it is at $108’723, 0.68 times the line ($159’661).

But long phases below the trend are nothing new: on 53% of all days since 2010, bitcoin closed below it. From January 2015 to May 2017 it was below the trend for 873 days in a row, from June 2022 to February 2024 for 616 days. The current phase is shorter than both. Both followed a cycle high, as described by the four-year cycle.

What holds up: justified as regards the line: as the middle of the prices it was too high, which is why our trend lies lower. It is open whether the floor also rises too steeply, because it keeps the slope of the line. The weak prices of 2026 are the critics' strongest current argument for this. It will be decided in the next two years (see below).

5. The floor doesn't always hold

The floor is at 42 % of the Power Law line. It is called "floor", but it is not a lower bound: on 218 of 5’962 days bitcoin closed below it, that is 3.7%. In August 2015 it fell as low as 0.37 times the line, on Jun 30, 2026 to 0.41 times.

Anyone who treats the floor as safe ground and buys on credit can be forced to sell on exactly those days. How deep bitcoin has fallen so far and how long it lasted is shown in the article The Power Law floor.

What holds up: justified, but rare. Plan so that a price 10 to 15% below the floor doesn't force you to sell.

6. The lines are adjusted after the fact

A frequent accusation: if the model doesn't fit, it gets rebuilt. That is partly true, of us too. In November 2026 we recalculated the trend and top band. Until then, the trend was the line itself. Because the price was mostly below it for four years, it is now the line only until January 2022 and since then the middle between the floor and the top band. The top band is a curve through the cycle highs, measured against the floor. It rests on only five highs, and every new high shifts it and the trend with it.

The zones are also fitted to the same history they assess. That every day in the accumulation zone was followed by a higher price a year later is measured in hindsight. More about the zones and what came after is in The bitcoin valuation zones.

The floor, on the other hand, is fixed: 0.42 × 10^−16.493 × days^5.688, the same numbers as on other Power Law sites. We don't adjust it to the market. Our trend doesn't match these sites: there it is the line, so $159’661 on Nov 12, 2026; with us it is $108’723.

What holds up: partly. The fairer check is tests with data a model didn't know when it was fitted. There, the simple Power Law came out ahead of five alternatives for one to four years ahead. Our trend passes this check so far: with the top band fitted only to the highs known at cut-off dates from 2014 to 2024, it was on average closer to the prices of the four years afterwards than the line. But the evidence that the middle of the prices has left the line comes from the last cycle alone. All the tests are in our research paper on the Power Law.

7. It can't go on like this forever

The trend grows more slowly every year, but it always grows. Extrapolated to all bitcoin, it gives a market value that at some point exceeds everything:

The entire world economy produced goods and services worth around $110 trillion in 2024 (IMF). In 2047, bitcoin on the trend would be above that. Even if the world economy grows by 5% every year, bitcoin overtakes it in 2062. By then at the latest, growth has to slow more than the formula says.

What holds up: justified, but distant. Every Power Law breaks at some point. For a plan up to 2035 that is not yet an argument; for one up to 2060 it is.

What speaks for the Power Law

The criticism shows the limits. But it doesn't mean the model is useless.

• It predicted better than the alternatives. In tests from 2014 on, the simple Power Law was closer to later prices one to four years ahead than curves that bend or flatten. Baquero and Menezes found the same for 12 to 24 months.
• The lows haven't changed. Every bear market ended between 0.41 and 0.56 times the line, including that of 2026.
• The floor formula is fixed. A given day's floor never changes after the fact. That lets the model be measured against reality.
• It can be refuted. That sets it apart from most price targets.

The test that can refute the Power Law

The floor rises every day. In Dec 2028 it reaches the previous all-time high of October 2025, $124’673 (€112’510, CHF 103’870). If bitcoin hasn't closed above that by then, it is below the floor, and the Power Law in this form no longer describes it.

So the verdict doesn't depend on opinions. The test is a good two years away. You can see the state every day on the Power Law page, all formulas and data in the methodology.

Worked example: planning with a model that can be wrong

On the floor you need about a fifth more bitcoin than on the trend. Anyone who only calculates with the trend is planning with a price that bitcoin was below on 53% of all days. And even the floor assumes that the model holds until 2035.

How widely possible paths spread when you factor in past fluctuations is shown by the Monte Carlo calculator:

How to use a model with weaknesses

1. Plan with the floor, not the trend. If your goal only works out on the trend, it is calculated too tightly. You set your own goal in My Goal.
2. Use the zone as a yardstick, not a signal. It shows whether the price is high or low measured against history, not what happens tomorrow.
3. No loans against the floor. 3.7% of all days were below it. A loan that is called there turns a model error into a real loss.
4. Write down when you would stop trusting the model. The floor test in Dec 2028 is such a point. Decide beforehand what you will do then.