A logistic model of bitcoin adoption by speculators predicts that exponential growth will eventually end.

Here is the widely used general model . , ,



In this multi-year thread I will update and monitor a particular model that assumes a million dollar maximum bitcoin price. I chose a high price because plausible arguments can be made that bitcoin will eventually replace fiat currency worldwide.

I use the MtGox price series through 2011 and Bitstamp prices thereafter as the input data. The logistic trendline passes through the earliest recorded bitcoin price, and is subsequently hand-fit to the remainder of the price series in November, 2013.

I simply guessed at the maximum bitcoin price. Periodic review will determine when the rapid exponential growth of bitcoin stops. Note that this model ignores the fact that when bitcoin is fully adopted by the underlying economy, it will continue to grow in price at least in proportion to economic growth.

The below chart is plotted with a log price axis . . .



Here is the same logistic model using a linear price axis . . .



Log10 delta from the trend . . .



The entire spreadsheet of data and analysis is published here and is updated daily.


Whatever price one selects for the maximum, the slope of the exponential portion of the log-S-Curve is the same - as I discovered when I performed sensitivity analysis on the model. Accordingly, the rate of growth that we have so far witnessed will continue at the same breathtaking acceleration until it inevitably begins to rapidly taper off.

Your modeler - Stephen Reed



I dedicate this thread to long term bitcoin holders, and to the author of this classic forum post from June 2011, at a time when bitcoin was priced at $13 - having risen 260x from $0.05 only a year before. ...

I am pretty confident we are the new wealthy elite, gentlemen


Here are the thread music video themes . . .

Zhou Tonged - Holding (Billy Joel - The Longest Time)
"The sky's the limit, and I'm in it to win it".

Laura Saggers - 10,000 Bitcoins
"Its having someone to share the dream, I'm so glad you share yours with me"

Here is the thread destination image . . .

To The Moon !!!

Stephen Reed's Relevant posts . . .

• The Logistic S-Curve
• A logistic graph of European smartphone adoption, as an analogy for bitcoin adoption
• Some Plausible Estimates of Maximum Bitcoin Value
• Bitcoin price doubles about three times a year on average, and will keep going up at this rate until the final growth slowdown
• The Million Dollar Bitcoin S-Curve
• What events in 2014 can propel bitcoin higher?
• Relative Growth of Bitcoin Market Capitalization vs Cumulative Wallets
• Bitcoin Merchant Adoption - Influence Diagram
• Bitcoin mining and electricity consumption at $1 million per bitcoin
• The Joy of Mining
• The Logistic Model is now revised to use mainly Bitstamp prices
• March 2014 Logistic Model Status
• Metcalfe's Law Explains 10x Price Growth Vs. 3.2x Transaction Quantity Growth
• Summer 2014 Bitcoin Bubble - First Projection
• Log10 Differences From the Logistic Model Trendline
• The assumptions of the Logistic Model
• Metcalfe's Law and Complete Triumph of Bitcoin Indicate $100 per Satoshi in 2022.
• The Bitcoin Network Will Probably Be Compelled To Abandon Electricity-Consuming Proof-Of-Work in 2018
• May 5, 2014 Update
• Summer 2014 Bitcoin Bubble - moral_agent's BubbleWatch from reddit

Notable conversations started by others . . .

• super exponential and other alternative models
• amount of daily fresh money required for million dollar bitcoin
• parametric price model
• amount of daily fresh money required for million dollar bitcoin
• Coinbase 80% buy-and-holders an indicator of Bitcoin's store of value?
• applicability of technical analysis
• March 25, 2014 - are we near a bottom?
• banks and bitcoin

Memorable quotes by others . . .

The Logistic S-Curve



The logistic function F(x) = 1 / (1 + e^-x) was developed to model the growth of a population that multiplies until constrained by exhausted resources. It has the property of exponential growth to the midpoint, followed by exponentially slowing growth.

In my application of the model, the population consists of all speculators who will ever buy bitcoins. That population grows as bitcoin knowledge spreads to new speculators, and that population is eventually limited by the finite number of available speculators. The price series of bitcoin is subject to bubbles and crashes that are ignored by the model, rather the model addresses the price trend.

The S Curve is plotted on my chart using a logarithmic price axis, and thus does not directly resemble the Sigmoid graph above.
  

so the end of 2014 looks to be around $6k and end of 2015 looks to be about $100k. Not a bad little chart. Im guessing 2014 will be higher than the chart has it, and 2015 will be a little lower

The rate of increase is about 10x annually. My model assumes that about 10x more speculators are buying bitcoin each year. In three years that is about 1000x more speculators buying bitcoin than now.  Perhaps in three years we will see participation by large companies, commercial banks, or central banks as speculators.

I urge you to invest whatever more you think is prudent NOW.

There is a plausible case to be made for bitcoin maxing out above $1M. A thousand fold increase from here is possible, but according to logistic models, next year the remaining increase will be only one hundred fold, .. and so forth.

Furthermore, my own research on bitcoin holdings over time, suggests that when holders realize 100-1000x return on their mining/investment, they cash out.

Interestingly, the technology of smartphone apps enables a much faster adoption than that of the hardware smartphone.

An well funded app, launching on iOS and Android, can swiftly be adopted, e.g. Google Maps - months to full adoption, not 10 years, which is relevant provided point-of-sale devices are upgraded.

Excellent point.   I stand corrected, software can move much faster.   POS updates (at scale) can be remarkably slow though so perhaps a counter balance is there.

Not included are all the efficiencies Bitcoin will introduce into the economy if it goes mainstream. A fully internationalized, frictionless division of labor will be an incredible boon to the economy. And there's so much more. I think a price target of $100 million, conservatively, is more realistic.

If Bitcoin goes big, it pretty much has to go whole hog. We are witnessing nothing less than a global transition from physical goods and trust-based money to an unimpeachable universal asset ledger. Anything else will look archaic by comparison, and the value added to the economy in the next 10 years will blow even these first 20 years of the modern Internet out of the water.

If bitcoin went to $100 million, according to the logistic model fitted to that maximum price, that would add only about two more years of exponential growth beyond the $1 million point - to 2018-2019.

What is the $100.000,- target based on? Wishfull thinking? Very well possible that 10k is the limit right?