Bitcoin Forum

An italian Bitcointalk forum member spent a whole month going over Bitcoin statistics and analyzing the blockchain and eventually came up (yesterday) with an equation for future Bitcoin price prediction. Italian Bitcointalk folks told him to publish all his studies on the international forum because it has 1000x more Bitcoin enthusiasts (BTC still not really famous in Italy) but the author answered that he's "too lazy  :D " and prefers to publish his studies in italian only.

The article is very long but contains a lot of interesting information (also graphs and numbers), maybe it will be valuable to translate all of it. But before doing so (or before somebody wants to do it), maybe it's better to see what math skilled BTC fans think about this (I'm just a fan...no math genius therefore not able to judge).

So first, the Formula he came up with:


Variables:

I = Total number of addresses
P = Price in US$
e = Euler's number (2.71828)

Have a look at the calculations he made at the end of the post. Maybe Google translator is also enough to give you an idea on how he came up with that equation.

Original forum thread (Italian): https://bitcointalk.org/index.php?topic=353156.0


[Italian Translation (http://translate.google.com/translate?hl=en&sl=it&tl=en&u=http%3A%2F%2Fixquick-proxy.com%2Fdo%2Fspg%2Fproxy%3Fep%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%26epile%3D4q6n41784q7n45794q7n41794q5638324q5335725n586o3q%26edata%3Dfc5a5c9a5d97a18f40c5a21299c725f1%26ek%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%26ekdata%3D994c7484e19747a35918a9bf2b6534e2) - Google Translator]

are the total number of addresses meant to be addresses with a balance, or just addresses (including empty addresses)

hi, I am the italian in subject:)

total addresses is non empty plus zero addresses (zero balance addresse are about 90% of total addresses).

Initially I think that the Active (not zero) addresses was the best, but
statistic analysis tell that the best fit is Total address (including zero)

This graph show how my equation (blue line) fit bitcoin price:

https://i.imgur.com/gptGZS0.png


here the translation of original thread:

http://translate.google.com/translate?hl=en&sl=it&tl=en&u=http%3A%2F%2Fixquick-proxy.com%2Fdo%2Fspg%2Fproxy%3Fep%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%26epile%3D4q6n41784q7n45794q7n41794q5638324q5335725n586o3q%26edata%3Dfc5a5c9a5d97a18f40c5a21299c725f1%26ek%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%26ekdata%3D994c7484e19747a35918a9bf2b6534e2

PS: sorry for bad english

I don't know Italian, but I do know maths, and a bit about fitting curves to data in particular. As far as I can see the author has simply assumed a power-law relationship between I(number of addresses) and P(price). In other words P=k*I^n, where k and n are constants to be found by data mining. He has done this in the standard way, by finding the best-fit line you get on a log-log plot. He gets n~=2.26 and k~=e^-26 (incidentally you may as well just give k as a very small number, there's no benefit in putting it in terms of e).

It's interesting but I don't know if it has much predictive power. But kudos for putting some maths into this stuff, we don't see enough of that in price speculation threads.

please take a look at process and assumption I used for the equation

here the google translator link of the thread:

http://translate.google.com/translate?hl=en&sl=it&tl=en&u=http%3A%2F%2Fixquick-proxy.com%2Fdo%2Fspg%2Fproxy%3Fep%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%26epile%3D4q6n41784q7n45794q7n41794q5638324q5335725n586o3q%26edata%3Dfc5a5c9a5d97a18f40c5a21299c725f1%26ek%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%26ekdata%3D994c7484e19747a35918a9bf2b6534e2

Update: added italian translation link at the end of the post.

Well it's interesting and surely I agree that I would expect the general price of BTC to go up...particularly because money is being printed at a fast rate and BTC is only coming out in limited quantity.  But it doesn't tell you too much, you just assume addresses will mean higher prices.

 The number of addresses is a reflection of the number of adopters, and probably can be used to predict the price statistically, but this could never be used as a true determinant because anyone can create new addresses.

this is true, but actually there are 24671534 addresses in the blockchain,
so the Law of large numbers is in action !

And remember that if someone create and address BUT dont use it, that adress don't appear in the blockchain !!!
The number of address in the blockchain give us a magnitude of total  bitcoin utilization !

sure this is true.  If your formula was ever incorporated into some real-world strategy, it could be very easily manipulated.

you should have kept it secret and used it as a hedge.  :)

but... "correlation does not imply causation."

very cool work though gbianchi.

 In real-world economics there is the Velocity of Money: http://www.investopedia.com/terms/v/velocity.asp

 which is somewhat related to what you're measuring.  The reason why you can't measure money velocity by measuring TX volume is that anyone can create TXs for free(perhaps not so true anymore).  Perhaps if you somehow included TX FEES, because this ensures that money is being transferred to a third party that cannot be pre-determined.

 The velocity of money certainly has real-world relationship to exchange rates and could be used as a more reliable determinant.

 ciao,

 -bm

At the end of my post, i wrote that I will do
some further investigation and explicate why the equation work...

but sintetically the total number of addresses

a)  depends on the number of users (as seen from the correlation with the number of active addresses)
b) and  also dependends on the velocity of circulation of bitcoin

I know, already wrote in the original post and here ;)

the next step of my work is to prove that number of addresses represent the aggregate value of
users and speed speed of circulation of bitcoins

you might be able to do some advanced operations with graph analysis.  I wrote a Bitcoin Block Chain graphDB importer:  https://github.com/BlueMeanie/bitcoingraphdb , it puts inputs and outputs on a graph so you can traverse them.

I had given thought to the problem once before- how do you measure velocity in the Bitcoin network?  you would need to know more information that just the basic block chain.

TX fees are perhaps somehow related to velocity because no one is going to make some kind of fake transaction to themselves with a TX fee.  So it's a more reliable measurement.

I too wrote a tool for analysing the blockchain... I product some tables and graph before derive my equation,
and I have really interesting result:

Fo example, Here we can see how the total address are moving in the time, divided in some category of capitalization:

the red line are the zero balance addresses... that are 90% of total addresses.
I think the zero balance addresess depends from bitcoin velocity of circulation !

Add you can seee that at end of 2011, the bitcoin world tend to stabilize, this is why I used
end of 2011 to 2013 data for derive my equation.

https://i.imgur.com/zfL37pa.png

some of the web wallets might for instance have incomplete, but statistically meaningful information that they MIGHT be able to use to predict the BTC price.

people always talk about all these security problems on here but no one ever seems to mention that the web wallets have massive database of Bitcoin address:IP mappings. Always seems more fun to discuss the security aspects of open source tools.

this was really part of why I invented confidence chains, the exchanges have really way too much power in this whole equation.

Ah yes. The comforting reminder that should there be a nuclear WWIII or some kind of near-extinction event, mankind will surely survive, as there will always be one guy sat with a graph, drawing a line through it.

interesting hypothesis.  I'd have to get back to you on that one. :)

Velocity of money has no direct relationship with money's value, because in equation MV=PQ, M means the money in circulation, not money in existence

For example, banks could put only 20% of the total money supply into circulation and put rest 80% in reserve, so that even velocity of money increased by 5 times, the price level still do not change

In bitcoin's case, since every one is their own bank, their saving/spending ratio will greatly affect the price level, even the money velocity stay the same. If everyone hold 90% of their coins, V must increase 10 times to keep the P constant, if V does not change, the P will drop 10 times, e.g. price per coin will rise 10 times. And that price appreciation will increase their saving/spending ratio

I derived my  equation from statistic analysis, now it need further investigation
for why it works (if it works for next year or so :) )

Your concept "propensity to save" is really interesting for my future work.

problem is that the total number of addresses can only go up, and btc price not -unfortunately.

not exactly: the addresses can stop growing at this speed ',
or in the worst case stop growing completely, then remain constant over time.

In this case surely there would be a negative fallout on prices.

The number of Bitcoin addresses is representative of the commerce and activity being done in the Bitcoin economy.
e.g.,
- Legitimate businesses like Bitpay
- grey market
- people sending and receiving Bitcoins to and fro from exchanges (internal trading in exchanges not included).

That is probably why it correlates in some form with the Bitcoin price.

It is a common place in network theory that the value of a network increases as the square of the number of nodes.  GB's model uses an exponent of 2.26.  The extra .26 would appear to be some confound which increases as sqrt(sqrt(n)).  Identifying that component might win you a  Nobel in economics, which you could then use to cudgel Paul Krugman into becoming an honest man.

A question for you, OP.

(By the way, don't take it personal, but I won't read through an auto-translated technical text, that's really not going to help me much.)

Since e is a constant, essentially your BTC price formula is an (exponential) function of the total number of BTC addresses. My question then is: how do you see it as significantly different form the countless attempts to model BTC price as an (exponential) function of time, the most well known one on this forum the linear regression of BTC price mapped to a log chart (recently rpietla made a big thread about this, IMO, rather uninformative method).

Looking at the graph in your Italian post (the blue line in the last graph, right?), it looks to me like your "formula" suffers from the same problem as the purely time dependent (linear regression) model: it gives a decent idea of the order of magnitude of BTC price at any time, but it is significantly off at times, and therefore more or less useless for trading -- more precisely: it is good to know that we can expect BTC price to be in the range of 1000 in mid 2014, but for example right now, your formula is "wrong", in an empirical sense, and it was even more off target a month ago.

As pointed out, there is likely also a correlation between amount of addresses and velocity. Or rather between the slope of amount of addresses and velocity.

More addresses being used and created indicates more different people use it (adoption) and that the same existing people use it more frequently (adoption + velocity).

The increase in velocity, however, would probably work against the increase in price caused by increased adoption.

It would be interesting to find a way to differentiate between these two powers affecting the price.