Stephen Reed's Million Dollar Logistic Model

[SlipperySlope]

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

http://astrohacker.com/ahc/bitcoin-is-the-economic-singularity/

After reading this, the scale of black market and digital economies and the effect Bitcoin will have on them I am pretty certain we are going to be very wealthy men -- even with a sum as small as 10 Bitcoins. It's just so hard to believe. We are only in the beginning storms with these significant rallies from 10 to 20 dollars. I will not be surprised to see prices from hundreds to thousands in the coming months.

The world just isn't going to be the same and we have been blessed as the pioneers.

What are you going to do with your Bitcoin wealth once your coins hit upwards of $10,000 a pop?

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 . . .

No financial planner would have my goals.  If they did, they would be institutionalized.  Also, I can't afford to hire anyone smarter than me, and I won't hire anyone dumber than me.  

(editor: Hal Finney's prescient reply to Satoshi Nakamoto's announcement back in 2009 - the very beginning . . .)
http://www.mail-archive.com/cryptography@metzdowd.com/msg10152.html

As an amusing thought experiment, imagine that Bitcoin is successful and
becomes the dominant payment system in use throughout the world.  Then the
total value of the currency should be equal to the total value of all
the wealth in the world. Current estimates of total worldwide household
wealth that I have found range from $100 trillion to $300 trillion. With
20 million coins, that gives each coin a value of about $10 million.

So the possibility of generating coins today with a few cents of compute
time may be quite a good bet, with a payoff of something like 100 million
to 1! Even if the odds of Bitcoin succeeding to this degree are slim,
are they really 100 million to one against? Something to think about...

If the projection is correct my miniature Bitcoin holding will no longer be so miniature. LOL.

I assure you, nothing resists corruption.

There is already ample evidence of corruption in Bitcoin, both in the early days and now.

(editor: SWIFT is the 2000+ employee firm managing existing bank transfers in 212 countries)

Re: 'SWIFT' -- could adopt Bitcoin and campaign with 'All the money in the world handled by all the nodes in the world'.

In 1982 there were only 12 billionaires.   In 2000 there were about 300.   And now 1,500.   So in 2025 maybe 10,000+ billionaires.  

Leadership from Bitcoin, innovation from the Altcoins. I wonder what consolidation among coins will look like? I hope enthusiasts discover methods of gracefully merging those deserving more than abandonment. Nothing sadder than pulling up a QT wallet and finding no peers.

I still think you're kinda nuts, but it's fun to keep dreaming with you during this fun ride, up, down, up, down...

You can manipulate charts/lines almost anyway you want to make a point.  I'm not saying you specifically are doing this, but you are certainly "reaching" a bit.

TA practitioners and sages eventually all suffer from Apophenia. They can't even help themselves at some point, they will chart a cockroach running up a wall to  look for patterns.

Technical analysis is always trumped by fundamentals over the long run.

Start with an anti-fragile base and build on top of it. Just like Microsoft has chosen to stop supporting WindowsXP on April 8th, Bitcoin developers can dump the old code and build from the ground up with the goal of lasting more than 27 years.

Bitcoin works at the core so enforcers can concentrate on the edges.

I believe the more the law understands bitcoin the more they will work to support it. Bitcoin benefits everyone but the sharks.

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[I_bitcoin]

May be interesting to compare to smartphone adoption s-curve and the total population.   Slope is likely to be similar from a technology adoption perspective.   If you assume all fiat replaced then not sure 1M is enough.   

[SlipperySlope]

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.
  

[SlipperySlope]

A logistic graph of European smartphone adoption, as an analogy for bitcoin adoption

May be interesting to compare to smartphone adoption s-curve and the total population.   Slope is likely to be similar from a technology adoption perspective.   If you assume all fiat replaced then not sure 1M is enough.  

When I began fitting a logistic model to bitcoin prices, I understood that adoption by speculators can occur much faster, i.e. steeper slope, than is the case for adoption of bitcoin as replacement of, and enhancement of, currency for transactions.

[Philj]

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

[bitrider]

Great work, Slippery! Very clean. Thanks for staying on this.

[SlipperySlope]

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.

[BitchicksHusband]

A logistic graph of European smartphone adoption, as an analogy for bitcoin adoption

May be interesting to compare to smartphone adoption s-curve and the total population.   Slope is likely to be similar from a technology adoption perspective.   If you assume all fiat replaced then not sure 1M is enough.  

When I began fitting a logistic model to bitcoin prices, I understood that adoption by speculators can occur much faster, i.e. steeper slope, than is the case for adoption of bitcoin as replacement of, and enhancement of, currency for transactions.

I had a Palm Phone in 2001. 

Wish I had Bitcoins in 2009...

[SlipperySlope]

Wish I had Bitcoins in 2009...

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.

[I_bitcoin]

I think we are closer to the stage of Winmo.     Lots of fragmented approaches etc...    Either innovators or early adopters is my guess.   Agree that "speculators" are pretty heavily engaged already.   I wonder how many of them there are?

For adopting the technology the mobile phone chart seems to indicate 10 years or so till we get to laggard adopters and the curve begins to settle.   We have a long way to go!

[SlipperySlope]

I think we are closer to the stage of Winmo.     Lots of fragmented approaches etc...    Either innovators or early adopters is my guess.   Agree that "speculators" are pretty heavily engaged already.   I wonder how many of them there are?

For adopting the technology the mobile phone chart seems to indicate 10 years or so till we get to laggard adopters and the curve begins to settle.   We have a long way to go!

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.

[BitDreams]

Thanks for the chart and link.

[I_bitcoin]

I think we are closer to the stage of Winmo.     Lots of fragmented approaches etc...    Either innovators or early adopters is my guess.   Agree that "speculators" are pretty heavily engaged already.   I wonder how many of them there are?

For adopting the technology the mobile phone chart seems to indicate 10 years or so till we get to laggard adopters and the curve begins to settle.   We have a long way to go!

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.

[2017orso]

Brilliant work yet again.

Just reserving my spot on the first page of this inevitably historic thread.

[Zangelbert Bingledack]

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.

[Siegfried]

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.

100 million dollars per bitcoin is ridiculous, in my opinion. Given that there are 10,000 people with over 100 bitcoins, there would be 10,000 people worth over 10 billion dollars. Today, there are only 1,500 people in the world worth one billion dollars or more.

[SlipperySlope]

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.

[AnonyMint]

May be interesting to compare to smartphone adoption s-curve and the total population.   Slope is likely to be similar from a technology adoption perspective.   If you assume all fiat replaced then not sure 1M is enough.  

In my application of the model, the population consists of all speculators who will ever buy bitcoins.

Problem is that speculators sell, and adopters of washing machines didn't (c.f. the linked chart of technology adoptions over the past 100 years).

Wrong model.

[Lewis2]

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

[SlipperySlope]

Some Plausible Estimates of Maximum Bitcoin Value

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

Indeed wishful thinking, but also an acceptance of the most plausible estimates, such as those of Rick Falkvinge circa. 2011, when bitcoin transaction volume was one tenth of today's. . . .

     Bitcoins Four Drivers: Part One - Unlawful Trade - estimates $60 Billion of bitcoin capitalization

     Bitcoins Four Drivers: Part Two - International Trade - estimates another $600 Billion of bitcoin capitalization assuming 10% market penetration

     Bitcoins Four Drivers: Part Three - Merchant Trade - estimates another $600 Billion of bitcoin capitalization assuming 10% market penetration

     Bitcoins Four Drivers: Part Four - Investment - estimates another $600 Billion of bitcoin capitalization assuming 0.1% market penetration

     An estimated total $2 Trillion market capitalization, implies $95 thousand valuation per bitcoin.

Falkvinge shows how bitcoin is superior with regard to current financial practice in four realms, and estimates bitcoin valuation at a 10% penetration rate. He sidesteps the role of bitcoin as a deflating store of value.

I also accept another widely held point of view that bitcoin will either fall to a relatively very low value, or totally disrupt the current financial infrastructure. Thus I extend the probability distribution of maximum bitcoin price to well over one million, covering cases where bitcoin achieves 80 - 100% market penetration.