TL;DR
The Bitcoin Power Law model isn’t new but has gained renewed attention in recent months. It has been holding up well and is easy to use. Contrary to common log-linear plots, the Bitcoin Power Law utilizes logarithmic scales on both the x-axis and y-axis. This way of plotting strips away day-to-day volatility and reveals an interesting relation between price increase and time increase.
It’s remarkable that BTC seems to obey a direct relationship between the variables price and time – but only after you strip away the noise of the day-to-day volatility. And that’s what the power law corridor model does: it uses logarithmic scales to plot the price and the time.
Number of days go up -> Price go up. But what’s the relation exactly? Before we dive in, let’s first look at some more well-known competitor models.
Competitors
There are two main competitors to the Power Law Model: The Stock-to-flow Model and Rainbow Chart.
Stock-to-flow Model
The stock-to-flow model was all the rage in the previous bull market. Created in 2019 by pseudonymous Dutch financial analyst PlanB, it seemed to have predicted the Bitcoin price reasonably well. When the bear market unfolded in earnest, the model didn’t look so good anymore: price has been deviating a lot from the projected price. This is not to say it isn’t directionally right or couldn’t be redeemed.
The stock-to-flow model posits that the price of Bitcoin is directly influenced by its scarcity, which is defined by the stock-to-flow ratio. The stock-to-flow model implicitly assumes that demand for Bitcoin will remain consistent. It does not account for fluctuations in demand due to for example regulatory changes or shifts in investor sentiment. It also doesn’t take into account that the supply shock that is each halving will become less and less important in both absolute and relative terms.
Also, the model is set up in such a way that it almost HAS to break at some point. Or is it even remotely likely that BTC will reach a price of 250 billion dollars in 2045?
Rainbow Chart
The Rainbow Chart is a logarithmic regression model. Log-Linear Regression. In this case, the y-axis (BTC price) is log-transformed. This means that each step up means a 10x in price. This compresses the y-axis, which is crucial in the case of BTC. You could not plot its spectacular growth on a linear scale and still accurately read the price points across all time.
The rainbow chart uses multiple colored bands to represent different price levels of Bitcoin over time. Each color band typically corresponds to a sentiment or market behavior, ranging from Red (“Maximum Bubble Territory”) to Dark Blue (“Basically a Fire Sale”).
The idea is that Bitcoin’s price tends to return to the regression line over time, so prices significantly above or below the line are seen as unsustainable in the long term.
The Power Law Model for Bitcoin
Ok, so let’s jump into the model under discussion, originally proposed in this Reddit post by Giovanni Santostasi (on X). he and a co-author updated the model in 2024.
We all know that Bitcoin’s price increase is not linear. Just to illustrate this: it took the Orange Coin roughly a year, in 2011, to move from 1 dollar to 5 dollars. Extrapolating this trend of 4 dollars per year linearly would bring us at a current price of…
Erik started as a freelance writer around the time Satoshi was brewing on the whitepaper.
As a crypto investor, he is class of 2020. More of a holder than a trader, but never shy to experiment with new protocols.
