Bitcoin’s Logarithmic Growth Rates, Facebook’s S-curve, and Future Projections

Awe & Wonder
Oct 19, 2018 · 4 min read

By: Awe & Wonder

Disclaimer: Not financial advice. Past performance is not indicative of future results.

Let's dive right in. BTC’s long-term trend is growing at a statistically significant rate of 5.04% per month and projected to hit $50,000 by the end of 2022. The 50% confidence interval, in this case, is a range between $28,000 and $85,000 at that point in time. This method worked well in the past but obviously, anything can happen.

Bitcoin’s logarithmic regression - mapping out Bitcoin’s powerful price and time dynamics

In a way, this model is accounting for actual user growth rates through price. A good example of this is the growth rate of Facebook’s S-curve (log scale). Notice how the user growth rates are increasing at a decreasing rate. This same type of logarithmic growth can be witnessed in the cryptocurrency market. One can speculate that the surge of growth in users seen between 2007–2008 is yet to happen in the cryptocurrency space. According to Willy Woo, the space is currently somewhere in the early adopters phase.

Facebook’s S-curve (log scale)

The red log curve was fitted and extrapolated using data pre September 2008 at approximately 100M users after the early majority growth spike. Overall this projection served well to project the user adoption curve ten years out. Although admittedly, it undershot real adoption in the middle.

All models are wrong, but some are useful — George Box.

BTC is increasing in price at a decreasing rate

Unlike linear regression, logarithmic (non-linear) regression tracks growth proportionally through time. For every proportional change in x, there is a proportional change in y.

Currently, for every 1% increase in time there is a corresponding 5.87% increase in price.

Again, similar to Facebook’s adoption S-curve, BTC is increasing in price at a decreasing rate.

Bull runs historically start when rolling returns flip positive

Digging in deeper, when price oscillates around the log trend line its rate of growth changes accordingly. If the rolling average rate of returns underperform the log trend’s rate of growth its reasonable to expect downward/sideways price action. If the rolling average returns are at par with the log trend’s growth one can expect a lower volatility environment where the new trend is trying to establish some sort of base before yielding a breakout. Once enough momentum builds, the trend is primed for exponential growth and begins to outperform the log trend’s growth significantly. Eventually, this growth rate becomes unsustainable and a new cycle repeats.

A closer look displays the same concept. Each cycle’s weekly growth rate is less than the previous one. This makes perfect sense, as continuous and constant exponential growth is unsustainable.

The B/B Ratios above represent the the proportionality between the bear and bull cycles in log units. In other words, it’s the portion of the bull run that was erased by the bear cycle . In order to have logarithmically proportionate bear and bull cycles across the board, price should to drop to about 4800. This adds further confidence to the 4400–5000 area described in my previous work. However, this is pure coincidental phenomena. Plus, current price action looks a bit strange. Almost as if there is an unnatural floor in price. There may be a large algo-based market participant swinging large volume that may have other things in mind.

With that said, lets look at other B/B ratios. The height of the green bull cycles are logarithmically proportional. The volatility to the upside is decreasing by a ratio of .72 log units each cycle. Same concept applies to the drawdown that followed (.31). Volatility to the downside is also decreasing proportionally. The width of the bear market (.28) is increasing proportionally due to the width increase in bull cycles. Considering that price is increasing at a decreasing rate, it’s reasonable that a lower rate of growth takes more time to cover the same “ground.” Applying this concept to the current bear market, an identically proportional fractal suggests that the highest odds for the next bull cycle is around mid-2019. — Updated 10/23/18. Thanks to Marc De Mesel for his observations that led to this update.

In conclusion, logarithmic regression has proven itself to be the best forecasting tool for BTC. Exponential regression overshoots actual growth rates over long time horizons, and logistic analysis requires very strong assumptions regarding the inflection point and estimated max price. Again, any type of analysis should not be used in isolation. Rather, it should only serve as a fraction of evidence to come to a sound conclusion.

Thanks for reading. Please follow me on twitter and share this article to show your support.

Welcome to a place where words matter. On Medium, smart voices and original ideas take center stage - with no ads in sight. Watch
Follow all the topics you care about, and we’ll deliver the best stories for you to your homepage and inbox. Explore
Get unlimited access to the best stories on Medium — and support writers while you’re at it. Just $5/month. Upgrade