Topic: Stephen Reed's Million Dollar Logistic Model - page 19. (Read 123190 times)

I find Metcalfe's Law a convincing fit to the data. Peter_R can best defend it.

Thanks for steering me to Kelly. I found the original paper easiest to understand as I know a little about information theory, and the examples given were clear.


Mostly, I assume what you characterized as asymmetric information flow. You said it better than I.

As i've mentioned in the other forum, the above graph is extremely misleading.

For example, look at the mountain in 2011.  Does anyone honestly believe that this was people "adopting" bitcoin as a currency?  Absolutely not, it was 99.9% speculative trading.  The values on that graph cannot be used to predict anything in terms of adoption, because both the price and the number of transactions are swamped by speculation.

I don't think Metcalfe's law applies to speculation.  Or at least, speculative trading adds value at a much lower rate than trading for goods and services.  Speculators only trade with one other network participant:  the exchange.  Real users trade with whoever is selling something they want.

Don't get me wrong, there may actually be a nice correlation to the number of real transactions with the real (non-speculative) value of bitcoin.  But in order to get those numbers you need to know who's trading bitcoin for goods and services, and be able to factor out the speculative part of the price.  The former might be possible, but the latter probably is not.

Chiefly those employed by the excellent site: bitcoin pulse.

We are far from 50% adoption. In a couple more years I expect the economic Ivory Tower to be shaken to its very foundations, and for others to follow, and greatly improve upon, the ideas that have been surfacing here.

Metcalfe's Law and Complete Triumph of Bitcoin Indicate $100 per Satoshi in 2022.


Here is the outstanding chart provided by Peter R that best illustrates the application of Metcalfe's Law to bitcoin prices . . .



And here are relevant daily transaction quantities as reported by coinometrics.com . . .



Peter_R's formula for transactions is V = $1.50 * Tx² , where V is the bitcoin market cap.
Using today's quantity of transactions: V = $1.5 * 58244² = $5,088,545,304 as compared to the actual market cap $6,117,800,905 reported by bitcoin charts. Note that the figure I used for quantity of transactions varies by time of day and day of week, but 58K is a fair approximation.

Here is the weird part, and by weird, I mean the cognitive difficulty of believing the future math given a simple assumption. The assumption is that Bitcoin completely replaces the current financial transactions performed by credit cards and consumer international payments. The arguments in favor of this assumption are that bitcoin is more efficient, is faster to settle, is not subject to fraud, has no danger of identity theft, and that bitcoin technology cannot be adopted by the incumbents without cannibalizing their legacy business model.

Here then is the math. I figure a total of 356,034,000 daily transactions for the incumbents today. Suppose that bitcoin transactions merely replace the incumbents, and ignore the additional quantity of possible bitcoin transactions, e.g. micropayments and other bot-to-bot low-fee payment activity permitted by programmable money,  

Plugging the incumbent transaction quantity into Peter_R's Metcalfe Law model, V = $1.5 * 356,034,000² = $190,140,313,734,000,000. Although the total number of mined bitcoins is currently 12,679,275, assume 19 million bitcoins at the time when bitcoin transactions replace the incumbents.

Accordingly, the price of a single bitcoin as predicted by Peter_R's Metcalfe Law model is $10,007,384,933, which equals $100 per Satoshi, supposing that Bitcoin transactions replace the incumbents.

My logistic adoption model can predict the soonest when that price value can be reached, using the 10x average annual growth expected before the halfway point of adoption. By the logistic adoption model we reach $100K in 2016. To reach a value six orders of magnitude greater would require six more years beyond 2016, namely 2022.

A consequence of this projection is that because the quantity of bitcoin transactions merely increases by 3.2x annually on average, In the year 2020, the Bitcoin Economy would be only one-tenth of so of the size of the incumbents yet would be very, very valuable, priced by Peter_R's model at $1 per Satoshi.

I ask you, how could such a price per bitcoin be justified? What properties of the Bitcoin Economy and human nature would permit such a possible world to exist?

The best idea I have come up with, is that Bitcoin is very precious and holders will be loathe to spend it. The idiom is that everyone has their price. Given the projections of the models, I conclude that for bitcoin that price will be very high. Capital flows to its wisest custodian. It may be then that as the years pass, bitcoin will increasingly be held by those who will not sell, or if they do then it is only the smallest portion of their holdings.

It is helpful to consider the value of the incumbent daily transactions. Again Coinmetrics.com has the data . . .



The sum of the incumbent dollar volume is $37,526,000,000. Given the replacement assumption, what fraction of the projected bitcoin market capitalization is used for daily transactions? I divide  $37,526,000,000 by $190,140,313,734,000,000 which yields 0.0000001973595145.

The Metcalfe Law model, and the assumption of complete replacement of the incumbents, indicates that only the tiniest fraction of bitcoin will transact - less than one coin in a million will suffice.

I'm following your logistic model. Thanks for this thread. Even Bitcoin can't reach 1 million dollar, it will be huge when all world's adoption complete. As rpietila says it may be 300.000$, but it will definitely raise for the next years.

Hey Slippery, could you expand on this point?  What is the "weird argument" you could make, just out of curiosity.  And what measures do you plan on using to find the halfway point?

I wanted to say a few words on those.


I think this is a useful assumption in a conversation setting. But it is not true. Gold and silver can still be transacted with, and they hold their value. Although silver lost 75% of its value relative to gold in the last 150 years, gold is still keeping its purchasing power and, relative to dollar, has gone up more than 30x in 50 years.

If Bitcoin fails, the most probable failure modes I would say, are the ones where it falls far short of its potential of $10M (fixed money supply) or $1M (augmented supply) per coin. Anything below $100k would be considered a failure, and I cannot say, which order of magnitude is more probable than the other ($100k, $10k, $1k, $100, $10?). Definitely there is also the possibility for going to zero, but most of that possibility comes from black swan events, not as a result of normal market moves. Markets like diversity.

Notably Kelly formula gives you wrong results if you flat-out assume that the outcome is binary. Because then you could only invest P(I win) amount, regardless of the winning odds.


Here I would like to hear, what are the actual traits you refer to!


This is the novel thing, whose understanding makes some wealthy and others bite their nails. It is so simple, so easy to understand (took several years for me to understand though but at least I am trying to make it easier for the others), yet so paradigm-shifting.


There are several interconnections that form the purchasing power, and therefore everybody cannot be arbitrarily rich. There would be less people to serve others for example, and the lack of service indicates misery, not wealth. I would say the hard limit of the market cap of Bitcoin is the total market cap of world stocks, bonds, (similar instruments), bank accounts and gold combined. OR about 100% of the market value of all the land, infrastructure, real estate and other physical things. My off-the hat analysis shows that both of these figures are about 200-300 trillion USD. Maximum per bitcoin would be $10 million.

It can be less, if the supply of bitcoins would be softened by the use of real bills, for instance. Or if there are other cryptos that eat a share of the pie (highly unlikely - they may be transactional, but for the storing of wealth, the current situation shows that BTC is the only one).


I would not be too worried of that. If it looks like sustained self-feeding exponential growth, we want to participate nevertheless, because the odds are so great!  

The Assumptions of the Logistic Model

The sound math of the logistic model rests on a foundation of assumptions the validity of which we can only guess at.

Here are the notable assumptions of the model to ponder . . .

• Whether Bitcoin succeeds or fails is a binary decision. It either completely takes over the existing fiat system and therefore becomes extremely valuable, or it utterly fails to do so and its value becomes zero. This opinion is widely held and makes sense - winner takes all, so to speak.
• The behavior of those who learned about Bitcoin already and adopted it, indicates the likely behavior of those who have not yet learned about Bitcoin and may adopt it. Works so far.
• Despite the presence of serial price bubbles, the average price trend can be modeled as a logistic adoption of technology. Never been tried before. Academic financial literature makes no connection between technology adoption and a price series.
• The maximum price at full adoption is one million USD. This is the weakest assumption of the model. We could possibly be past the halfway point of adoption now - but I think that is unlikely. Indeed, I can make a weird argument based on the quantity of transactions and Metcalfe's Law that the maximum price could be way, way higher - which the average price of bitcoin would reach by continuing to increase 10x per year until say 2020 should that be the halfway point of adoption. Very hard to believe but the math says so.
• The logistic model has two other parameters that I fit by hand to make the average trend line fit the price series. This is a weak assumption because there is no math to support it. It very well could be the case that the data series is not long enough to see the true trend. Had I constructed this model in 2011 that is the mistake that I would have made. Only time will tell - perhaps another year to gain more confidence in the hand-fit model parameters.

Thank you for this chart!

I believe that Peter R today pointed out the value of contributing to the community.

Thanks for adding the Log10 Differences From the Logistic Model Trendline Slipperyslope.
You and a few others are really adding some value to this forum!

This whole thread and this graph in particular are inspired by our Finnish Friend.

This is a graph of what Risto (rpietila) has been saying all along.

Log10 Differences From the Logistic Model Trendline

I added a column to the calculations sheet of the Bitcoin Logistic Model. This column subtracts the Log10 model price from the Log10 actual price. By using Log10, the result allows comparison of the relative price deviation from the trend regardless of the time frame. Buy, sell and hold technical indicators could be extracted from the data for the April 2013 and November 2013 bubbles that would be very useful assuming that the next bitcoin price bubble is similar in shape to the previous two. For example, suppose a value of +0.3 indicates an opportunity to sell near the bubble high, -0.3 indicates an opportunity to sell near the bubble low, and other values indicate hold.

Buy October 26, 2012 at $10
Sell April 5, 2013 at $140
Buy October 3, 2013 at $110
Sell November 22, 2013 at $743
Buy April 1, 2014 at $478

This thread should be a sticky and a must-read for noobs and perma-bears.

Physical stores enjoy the same cost savings that online stores gain via bitcoin. However, online stores must overcome privacy and identity theft issues that customers are more likely to associate with them. Consequently, as trust in the bitcoin payment method attaches itself to online stores, then indeed a barrier to online sales growth diminishes.

I believe global GDP growth will accelerate as bitcoin adoption removes the immense friction caused by the current financial infrastructure and reallocates the 10% of the developed nations' workforce who maintain that legacy.

Now I'm wondering how much bitcoin can grow online sales, increasing Global GDP along with it.