How to Replace the Bitcoin “Floor” with Probability

SevenSteps to an Age-adjusted Percentile level

Two-sided residuals with reciprocal decay

Bitcoin investors often ask whether price has hit the “floor”. There is no floor. A better question is: What percentile of Bitcoin’s historical age-adjusted valuation distribution does today’s price occupy? This article shows how to calculate that percentile in seven simple steps. The power law ingredients have been prepared for you in advance and we share those.

For this article we use a two-sided residual model with reciprocal decay to estimate the expected magnitude of positive and negative deviations from Bitcoin’s long-term power-law trend. These estimates are then converted into local volatility and age-adjusted Z-scores, allowing every point in Bitcoin’s history to be expressed as a comparable percentile.

But you say, why not just look up recent one-year volatility and take it from there? It’s probably fine in many instances, but an age-adjusted residual method takes into account the full Bitcoin history and long-term scaling. It evolves the volatility value smoothly as Bitcoin matures and allows deviations from different eras to be compared on the same statistical scale.

Quantile regression is one valid method of looking at percentile levels; the reciprocal of Bitcoin age residual method used here is a different approach, and the table below outlines the differences between the two approaches.

Table 1. Quantile regression and the reciprocal residual method address different questions. Quantile regression estimates a historical percentile curve directly and makes few assumptions about the residual distribution. The reciprocal residual method instead models how the typical magnitude of deviations from the power-law trend changes as Bitcoin matures. This allows every observation to be expressed as an age-adjusted (normalized) Z-score and corresponding Gaussian-equivalent percentile, making deviations observed early in Bitcoin’s history directly comparable with those observed today.

In a previous article, Bitcoin’s Two Leashes, I showed that the residuals on either side of the power law trend can be reasonably modeled by two log-normal distributions, at least for purposes of ordering and normalized Z-scores. The residuals overall skew positive and are narrower than normal (possess negative kurtosis). However dual log-normals, one for each side of the power law trend, provide a reasonable approximation, allowing us to remove most of the age dependence of the volatility, and estimate percentage levels.

Bitcoin’s Two Leashes

Figure 1. Bitcoin price (gray) plotted against age on logarithmic axes together with the long-term power-law trend (black) and the empirical conditional mean positive (orange) and negative (green) residuals. The power-law trend is given by log P= -1.928 + 5.690 log {Age}, while the mean positive and negative residuals are modeled as reciprocal functions of Bitcoin age: E [r | r>0] = 2.63 / (Age +2.5) or, E [r | r<0]= -3.44 / (Age +8.78). These curves are not statistical bounds or support and resistance levels. Rather, they represent the average magnitude of positive and negative deviations from the power-law trend, conditioned on the residual being positive or negative. The contraction of both curves with age illustrates Bitcoin’s long-term contraction in the typical magnitude of residuals around the power-law attractor.

Figure 2. Log price residual history after removing the fitted power law. The amplitude of the residuals has contracted substantially as Bitcoin has matured, falling by 60% over this history. The orange and green dashed curves are the best fit reciprocal declines for the positive and negative residuals, respectively. As calibration, a 0.5 (0.2) plus or minus residual represents a factor of 3.16 x (1.58 x) up or down in linrst price relative to the power law trend.

7 Steps to a Percentile

We now have the background and ingredients for a 7-step procedure to calculate a Z-score for a given day and price level.

Step 1

Calculate Bitcoin age and log age. Example: If today is July 3, 2026, Bitcoin is 17.5 years old.

Log age = log10 (17.5) = 1.243. All logs are log10 herein.

Step 2

Calculate the power-law price.

log P_{PL} = -1.928 + 5.690*log (Age) = -1.928 + 5.69*1.243 = 5.145.

Price = 10^5.145 = $139,637, on power law trend at age 17.5.

Step 3

Calculate the residual for the price level. Example $58K; log P = log10(58000) = 4.763

r = log P - log P_{PL}= 4.763 - 5.145 = -0.382

Step 4

Determine which reciprocal equation to use.

If residual > 0 use:

E(r|r>0) = 2.63 / (Age+2.5)

otherwise, as in our present case:

E(r|r<0) = -3.44 / (Age+8.78) = 3.44/(17.5+8.78) = 0.131

Step 5

Convert the conditional mean residual to an equivalent σ (sigma). Assuming the positive and negative residuals are approximately half-normal, the standard deviation σ is estimated from the mean by multiplying by a factor equal to the square root of π/2 = 1.253. Thus the resulting

σ = 0.131*1.253 = 0.164 .

Step 6

Calculate:

Z = r / σ = -0.382 / 0.164= -2.329

Step 7

Convert Z to a percentile. One can use a table (or ask AI), it turns out for Z = -2.33 we are at the 1% percentile exactly. A Z-score vs. percentile level table is below.

In other words, at $58,000 and if one is at the beginning of July 2026, only about 1% of the history has been as deeply below the power-law trend, after accounting for Bitcoin’s age to normalize Z-values.

Bitcoin is at the 1st percentile of its age-adjusted residual distribution. That is a much more informative statement than saying Bitcoin has “broken the floor.” There is no single floor; there is a probability distribution.

Summary

A power law is the center of an age-dependent probability distribution. The seven-step procedure above converts any Bitcoin price into an age-adjusted Z-score and Gaussian-equivalent percentile, making valuations directly comparable across Bitcoin’s entire history.

Z-score Percentile Levels

Z-score: Normal Equivalent Percentile

+3.0 99.87%

+2.5 99.38%

+2.0 97.72%

+1.5 93.32%

+1.0 84.13%

+0.5. 69.15%

0.0. 50.00%

-0.5. 30.85%

-1.0 15.87%

-1.5 6.68%

-2.0 2.28%

-2.5. 0.62%

-3.0. 0.13%

Disclaimer: This article is for educational and informational purposes only and should not be construed as investment, financial, legal, or tax advice. The methodology described is a statistical framework for interpreting Bitcoin’s historical deviations from a long-term power-law trend and does not predict future prices or guarantee investment outcomes.

About the Author: Stephen Perrenod is Associate Director of the Scientific Bitcoin Institute (SBI), a not-for-profit organization dedicated to research and education on Bitcoin, economics, and complex systems. The views expressed here are his own.