Pricin' Modellin' & Predictin' ₿
Building on the Power Law, the Quantile Model extends analysis into prediction
In a previous article I described the statistical phenomenon that the price of Bitcoin follows a so-called Power Law, a law of nature. As this Power Law model gained traction, a few data analysis experts started to think about how to enhance its predictive and price-analytical capabilities. This culminated in the Bitcoin Quantile Model, authored by PlanC and Sina. In this article I will try and explain this new model, using as little statistics jargon as possible.
PlanC and Sina, the builders of the Bitcoin Quantile Model, as introduced by their X-profiles.
Start At The Beginning - What Is A Quantile?
The word “quantile” comes from the word quantity. A quantile is basically a dataset which is divided into more or less equal-sized groups. A quantile therefore can represent a range or a band in which price-points have been plotted over time. Each band contains a certain percentage of the data.
The Bitcoin Quantile Model uses 8 of these bands, quantiles or percentiles as they are sometimes called, namely 0.1%, 10%, 25%, 50%, 75%, 90%, 99%, and 99.9%. For example, the third quantile (aka the 25 percentile) contains 25% or less of all the available pricing data. We’ll get back to that.
Quantiles or percentiles or bands describe all the same thing and I use these words interchangeably throughout this article.
What Does The Bitcoin Quantile Model Do?
The Bitcoin Quantile Model has several key characteristics that make it a powerful tool for analyzing & predicting Bitcoin's price behavior.
Price Analysis
The model segments Bitcoin's historical price data into quantiles, allowing for a probabilistic assessment of where Bitcoin's price might fall within a given range and approximately for how long it will stay (or oscillate) there.
Probabilities of Future Price
By focusing on the distribution of Bitcoin's price over time, the model provides insights into potential (probable) future price movements. This also provides insights into support or resistance zones.
Market Sentiment Levels
The model shows critical price levels based on the entire price history of Bitcoin since inception. These levels act as benchmarks for assessing market sentiment and potential turning points in Bitcoin's price trajectory.
Risk Management
The model helps investors assess risk by highlighting the amount of time Bitcoin's price stays at certain thresholds. This can inform decision-making around entry and exit points, as well as risk management strategies.
Show It To Me In A Graph
Using the total amount of available historical price data for Bitcoin, the model plots out these price points and discovers various bands where price points logically group together. Based on that it calculates a few trend lines.
The bottoms and tops of these price point form a price channel. The price will fluctuate within such a channel. Using statistical analysis on the data the model can also quantify the probability of each price occurring at certain points in and around the bands. Below is what that looks like in somewhat raw form - all the dots are price points, grouped together and having their own place in the upper, middle or lower points in the price bands and plotted over time.
These bands are not derived from technical analysis or hand-drawn; they are statistically generated. As data gets refreshed or added the model adjusts in order to stay current.
What Does The Quantile Model Look like?
Below you see the finished Quantile Model in one chart. There is a lot going on here so let’s take a look.
First, in big letters, it shows the Bitcoin price on 28 January 2025 at 102,265 USD which corresponds to somewhere between the 50 and 75 Quantile on the chart (in fact, 67.6 to be precise).
In that sloping curve with the Bitcoin priceline you can see 4 colored bands. These correspond to the table which splits the four bands into further quantiles. For example the 1st quantile (green) contains the 0.1 and 10 percentiles, the second (blue) 25 and 50, the median band (yellow) has only one quantile (75) and the upper (red) band contains three (90, 99 and 99.9). These number indicate what percentage of the data is contained in these bands.
Looking at price points - take the 2026 Jan 28 column for example - and one can see that the price band is made up of a $55K bottom and a top of $346K. The median price is around the 157K level.
A separate table (at the right, middle, of the chart) has the price plotted between 2030 and 2040 - the chart give you three bands for this time frame, low, median and high. For example, it’s likely that at some time in 2034 the price will reach $1M as a median prediction. Depending on market sentiment it can also go higher of course and reach the upper band where it could touch $2M.
Even though the model has timelines it cannot tell you when exactly we get to a certain price level. The market will do what the market does and this is just a model, but it gives you some direction at least. The more important information is that it tells you approximately how much time is spent at a certain price point.
If you follow the red band at the top - representing the top 5% of the data - it tells you that when price gets there, it’s probably fairly short lived, ie we will only spend 5% of the time in that upper quantile. That means weeks, not months. You can also see that the blue band is where Bitcoin spends most of its time because it’s the widest.
Another detail of note is that the bottom two bands do not narrow, but the top red band does. This is because the Quantile Model captures the reduction in volatility over time for the more euphoric peaks when positive market sentiment is at its highest.
The bottom 33% of the distribution represents the stable growth phase and long-term trend of Bitcoin. The top 33% of the distribution corresponds to the parabolic euphoric or mania phase. This typically is where FOMO kicks in. The middle 33% of the distribution is the transition phase between stability and mania.
From a risk management perspective or trading perspective, this model can therefore tell you that once price gets into the red zone, a) it won’t stay there for long, and b) it may make sense to take some money off the table because the B-price is at a somewhat overheated area. You can see that clearly in the graph below.
Predictive Power Of The Bitcoin Quantile Model
We can test the accuracy of this model by looking back in history. If you ran this model at the end of 2018 (Bitcoin price was at $3700), it would very closely predict the top and bottom of the last cycle. These results are rather remarkable.
On April 2021 the Actual Price of Bitcoin was $64K
The 99th (top) Quantile Prediction was $84K. This is within $20K of the actual price. Not bad.
On November 2022 the Actual Price of Bitcoin was $16K
The 1st (bottom) Quantile Prediction was $19K, ie within only $3K of the actual price !
Bitcoin Quantile Model vs Power Law Model
Like in any profession experts tend to disagree :-) and different people might have different opinion here, but Sina and PlanC opine that the Quantile model optimizes around finding the best-fitting lines for each portion of the price distribution data.
Quantile 1 and Quantile 99 lines fit the top & bottom 1% of the data - this is an automated calculation which creates a narrow and pretty accurate top and bottom channel.
The Power Law model gives an average and when adding the standard deviation bands (2 Standard Deviations up & down), you can see that it starts to deviates from the price.
Comparing the Quantile Model above with the Power Law model below and note that there is more space between the Bitcoin price line and the upper and lower bands. The Quantile Model provides a tighter fit than the Power Law model.
In summary that means that the Quantile Model has two advantages:
It more accurately captures the tops because it takes into account diminishing volatility.
It more accurately captures the bottoms because it takes into account the asymmetric nature of bitcoin (i.e. most of the data points are concentrated at the lower range).
And it does all these with a unified model, using all the price data at once, without the need for the analyst to manually intervene by chopping up the dataset. Any type of manual intervention creates a risk of bias as at some point the creator of the model has to make a choice on how the data is organized.
Below are the two models put in once chart. You can see they are directionally similar, but different in slope and fit.
What Is Bitcoin's Price in 2030?
Let’s give the Bitcoin Quantile Model a try and answer that question.
The thesis is that Bitcoin could reach a high of $1M by the end of 2030.
To get to this number, focus only on two quantiles: 1st and 99th. The 99th quantile line means that 99% of data points fall below it. Similarly, the 1st quantile finds the line where 1% of data falls below it.
Looking at these lines, you can see a Bitcoin channel whose upper bound touches $1M ($947K) at the end of 2031 and the beginning of 2032. The absolute bottom of the channel is at +/-$250K by the same dates.
Below you will see the same result but in a slightly different chart, using the familiar slope. Note that the upper bound touches $1M ($947K) at the end of 2030/beginning of 2031.
Lastly, another way of looking at ₿ price points. The price histogram below models the full distribution of possible Bitcoin prices and gives it a probability rating (Y-axis on the left).
So, there you have it. The Bitcoin Quantile Model is a very important tool for anyone invested or just interested in Bitcoin. The model provides the most complete and detailed predictive analysis of B Price x time we have today. 🎩 to Sina and PlanC.