Saylor's Bitcoin24 Scenarios
vs. Power Law Model
Figure 1. Three Saylor Bitcoin24 scenarios (Bear, Base, Bull) plotted forward in time and my extrapolation of those into the past, shown as dashed lines on this log10 price - linear time chart. None of the back extrapolations is a good fit of the early past data, whereas the Power Law in solid green fits the data with R^2 of 0.95. In the early days the three scenarios differ by up to a factor of 800.
On August 30, Michael Saylor and his team put up a set of scenarios for future Bitcoin prices that he named “Bitcoin24”.
There are three: Bear, Base and Bull. I also have 3 concerns about these, and this is why I call them scenarios, rather than models:
They are arbitrary and empirical with no fundamental justification discussed
The dynamic range of the three cases in the 2045 time frame is very high at 15:1
They require 4 parameters each, so there is a totality of 12 parameters across the three cases, each requires a starting growth rate, an annual decrement in growth rate, and a minimum growth rate. For the fourth parameter of each they require a starting price (fair value).
The chart above shows the log10 of Bitcoin’s price expectation for each of the 3 scenarios as dashed lines from 2025 to 2045. It was not quite clear what starting price they use for the beginning of 2025, I have adopted $100,000 but everything would scale with a different choice for starting price in January 2025.
Saylor’s base case starts with a 50% growth rate and stair-steps down to an asymptotic rate of 20% per annum. For the bear case it is 25%, decreasing to a minimum of 18%, and for the bull case it is 75% decrease down to an asymptote of 25% minimum.
In any case their ending prices are $3.2 million, $8 million and $49 million for the three cases.
Also shown is the price history of Bitcoin from 2011 to 2025, during which time it grew by a factor a million. And we show a power law fit with an index of 5.7 (price goes as age of Bitcoin to the 5.7 power) as the solid green curve.
Finally, I have back extrapolated the three Saylor scenarios by assuming the same yearly change going backward in time as the decrement for that case going forward. So for example, the base case that starts at 50% for 2025 and decreases to 47.5% in 2026 would have had at 52.5% rate in 2024 under the same rules. The three dashed lines from 2011 to 2025 reflect those extrapolations.
What we see is that none of the Saylor scenarios fit the historical price history. The first rule of model building is consistency with the existing data and they offer no explanation for how their model reflects the 15 years of data already acquired for Bitcoin.
In contrast, the Power Law requires only 2 parameters, not 4. These are a power law index and a constant multiplicative scale factor (which can also be expressed as the trend price at any chosen reference time).
The Power Law works for Bitcoin vs. gold as well as Bitcoin vs. the dollar and it works in both Gregorian calendar time and in Block calendar time (block years of 52,500 blocks).
It looks like this on a log-log plot: it appears as a straight line. This chart uses the log of Bitcoin’s age in block years. The one sigma standard deviation corresponds to 2/3 of the data within a dynamic range of a multiplicative factor of 4 for linear price.
We prefer a power law because of Occam’s razor, with just 2 parameters it is more parsimonious, offers a simpler explanation and is more easily falsified.
It also has a fundamental underpinning in Moore’s law of networks. The value of those goes as the square of the number of nodes, and since Bitcoin’s user community has grown at close to the 3rd power of time, one would expect price to rise close to the 6th power of time.
“Why use an ugly stairstep function when you can have a simple two-parameter smooth, continuous, differentiable function?” - @moneyordebt
“The truth always turns out to be simpler than you thought” - Richard Feynman