Bitcoin Bubble? Not this time. A qualitative analysis of Bitcoin’s price cycle and unusual economy of scale

Edit: If you find my claims speculative and full of muck, here is the math, and a google drive to some plots the source code in mathematica.  

This isn’t a bubble

Bitcoin is experiencing some rapid growth at the moment that is once again turning heads in the media.  Everyone wants to know when to sell their Bitcoin just before the bubble pops – that is clear.  While the exact timing of the bubble pop is difficult to predict, it is easy to use some key metrics to show that what we are experiencing now is in fact long overdue growth as the past months represented the fallout of the last bubble.

Don’t get me wrong.  There will be another Bitcoin bubble someday. And likely another after that.  It is the natural cycle that bitcoin lives on, which is illuminated plainly by taking the logarithm of the price history.

The Bitcoin Price-Epochs 

You can detect Bitcoin bubbles by realizing a few facts:

1) on average, Bitcoin price increases about 1000% / yr

2) short term deviations from this behavior represent recessions and bubbles

3) Bitcoin’s natural mode (for the moment, because it is young and had not reached equilibrium with other currencies) is to exhibit incredibly fast growth – it’s worth repeating: Bitcoin has gained a staggering 1000% year average growth since its inception.  That rate of increase is so massive, that a recession superimposed over it has the appearance of price stability or even small, slow growth.



Shown above is the entire price history of Bitcoin.  There was a “little” $11 bubble followed by a BIG bubble in April…and now we’re gearing up for an even BIGGER BUBBLE! Right?

Wrong.  Here’s the log plot, which effectively filters out  Bitcoins automatic repeated doubling every few months.


This is a very illuminating chart.  It really makes me happy as a clam, because almost everything about it falls in line with the basic tenets linear impulse response. Bitcoin is quite well behaved in fact.  Notice:

• The truly daunting growth rate of bitcoin is to attain about 10 times its price the previous year (I know, I’ve mentioned this now three times.  I just can’t get over it).

• The bubble in 2011 was actually a much greater deviation from this standard behavior than the bubble in April 2013.  This is entirely expected.  Mark my words – the next bubble will appear quite large on the linear axis, but indeed be smaller than the last in the log linear sense

• Because the 2011 Bitcoin Bubble was so much bigger than the one in April 2013, the associated recession was quite long.  The recession following the 2013 bubble was shorter because it was a smaller bubble.

• The recession periods are in proportion to the size of the bubble.  This is to be anticipated, as just about anything in the universe has a response proportionate in amplitude to that of the impulse which disturbed it.

• The price today is actually the natural expected log linear price – Bitcoin has stayed true to this line since it began.  It cannot rise in this manner forever, but there is no reason to think Bitcoin has left its rapid growth state yet – the currency is still brand new and relatively few people in the world have interacted with it.  The upside will continue until of course it cannot sustain log linear growth.  But it is, to put it lightly, kind for Bitcoin investors that the day has not yet come.

Economy of Scale

Bitcoin will probably continue to follow this pattern for quite some time because of the extremely low friction within the Bitcoin system.  The principle is known as economy of scale.  The simple fact is, there is very little stopping Bitcoin from growing.  Unlike a company, which feels considerable growing pains as its stock price shoots up, and eventually levels off when growth is impossible due to diminishing returns, Bitcoin doesn’t experience any backlash for attracting more users, more excitement, more of everything.  Bitcoin doesn’t feel growing pains. Nothing works like that – not usually anyway, which is why Bitcoin has fooled the silver haired finance veterans, who, despite their vast experience in markets, have gone their entire lives never having met a beast that has nothing to stop it from gaining velocity.

Conclusion:  Bitcoin has a truly unique economy of scale, limited only by the flow of information and technology around the world, and the robustness of the Bitcoin protocol itself.

If I lost you on the last part, watch this TED talk by a particularly captivating scientist who researches economies of scale in both biological and economic systems:

“Geoffrey West: The surprising math of cities and corporations.”

You will be reminded of the Bitcoin price when he characterizes the economies of scale in organisms and likens this to the development and life cycle of an entire city – its people, its culture, its structural map, and its entire social being.

It is not very difficult to swallow, for me, that this really is the way the Bitcoin economy works.  A city is nothing if not a set of connections – the social and economic influences, and the relationships between people in close proximity.  In 2013, where “close proximity” has been redefined to mean “within arms reach of a keyboard” it is no wonder we see the topological structures inherent in the growth of economic centers emerging in the cloud.

You’ll also (hopefully) be entertained by his breakdown of economies of scale, and almost certainly will be enlightened.

Thesis: hold your coins, and watch the log plot.


BTC: 17NA1jYg5u6ejboArdM7HW4MwSa6cWfnEd


XPM: AejVQ34ntJAwUhebe7GMtC8aQ2oPg4bHDf

PPC: PQzT1tFMB5ECbQPhp41R5cTc7jpbgGUDfb

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Posted in Bitcoin, Stuff
12 comments on “Bitcoin Bubble? Not this time. A qualitative analysis of Bitcoin’s price cycle and unusual economy of scale
  1. Altoidnerd says:

    Here is an image of the logs of the sequence of the top 118 minable cryptocurrencies market capitalizations from

    Raw data here :

    Gathering tx per day data now, little more difficult.

  2. At a glace my first thought and/or intuition is: The total number of businesses accepting bitcoin; or perhaps something akin to the ratio BTC market cap:Value of all currencies (or net value of all “stores of value” etc)?

    Re-reading your reply I see that you proffered ‘User base’, so I think our intuitions are close.

    And I also missed that last line the on the first read “transactions per day” is another suitable indicator.

  3. Altoidnerd says:

    >> Do you think the Bitcoin Market Cap growth is sub-linear or super-linear, and why?

    I’d have to think about the question itself for a moment.

    At 7:05 in the video, we see sub linear logplot of metabolic rates of various creatures.

    For cities, we saw super-linear salaries as a function of city population. Yet once again, the plots represented data point from distinct cities.

    It is the sublinearity of a plot for many animals that determines the time evolution of the growth of a particular animal.

    It seems we should like to construct such a plot for bitcoin to answer the question since it is the slope of these plots which determines whether the measured quantity is sub linear or super linear. What would such a plot be? It would have to be the market cap of various cryptocurrencies.

    In November when I wrote this, I would not have thought it possible to create such a plot, but today it perhaps is. will produce market caps. What is left is to define the variable against which to compare the log of the market caps. User base?

    One can take the log of the market cap (I in fact just made such a plot) but it is not sufficient to have as the horizontal axis simply the rank of the market cap. We need a metric to rank the “weight” of each coin – playing an analogous role to body mass and population in animals and cities.

    I do not know how to obtain that data at the moment, but I will think about it. Transactions per day is one idea.

  4. Awesome article and Ted Talk. My question is this: Do you think the Bitcoin Market Cap growth is sub-linear or super-linear, and why? Also, how much upside in the price of Bitcoin do you think is left? If the market cap growth of Bitcoin is sub-linear, shouldn’t we see a gradual stabilization on price in the near future? Even if bitcoin goes to “only” 5-10K USD per coin, thats nothing compared to its growth so far (ie only 10-20x more than current (Feb 2014) prices, in comparison to the 100X gains it made in 2013). To me, this suggest a sub-linear growth in the market cap – which plays a huge role in determining price IMHO.

    In the Ted video, ~16:30, West extrapolates his Walmart data, and, using his conclusion that companies have sub-linear growth, predicts the future sales of Wal-mart quite nicely. Is it possible to do something similar with the Bitcoin Market Cap, assuming you know if its growth is sub/super linear.

    Cool blog and many thanks – Andrew

  5. […] a log plot and fitted to two parameters, as I have done before, just to demonstrate that since bitcoin grows in powers of 10, (seemingly large) contemporary fluctuations may look alarming. This rests on the observation I and […]

  6. Altoidnerd says:

    Darn. Using an iWalledGarden5

  7. The following Android widget allows you to follow the chart of bitcoins, using the log scale …

  8. Altoidnerd says:

    +1 this. Bitcoin’s value as an intellectual pursuit alone will forever be self evident. This is candy for researchers from all fields and of all levels of skill.

  9. […] like it did back then – the price surging to amazing highs and fluctuating wildly. I’ve seen reports, however, that try to explain that this is just normal growth, and that Bitcoin will settle around […]

  10. Very interesting analyse, thanks for the insights.

    You’re right about the finance guru’s who don’t seem to understand what is happening with Bitcoin. It’s not their fault, the fact is, simply put, Bitcoin is a much more complex thing than we’ve ever seen before in the field of technology and economy.

    There are a lot of traders and economists who try to speculate about Bitcoin, and most of these articles always contain a flaw in understanding some basic technical principle of bitcoin. On the other hand, most the techies do not understand what bitcoin really means in term of macro economies. I am part of the second group and I must admit that before bitcoin I had never thaught I would be interested by finance and economy as much as it is right now.

    What is even more fascinating is that many years from now we will be able to study and learn so much more about the relation between technology/society and economy just by looking at the blockchain / price graphs and the technologies that will emerge from bitcoin.

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