A BITCOIN PRICE THEORYThis short work is an attempt to find a law of bitcoin price . It is a work in progress ,
there may be errors even coarse that you reported to me , so critical and / or additions .
After about a month of work , I edit this first post to summarize the results obtained.
terminology
Zero address : A Bitcoin address tha was used, then it appears in blockchain ,
but currently has a zero balance.
Active address : A Bitcoin address tha was used, then it appears in blockchain ,
and currently has a NON zero balance .
Total addresses : Zero + active addresses.
Active user : Any user who has one or more active addresses .
working steps :
1 ) Obtain the tables with data from the blockchain (number of addresses for range of balance,)
number of bitcoins for range of balances, Total addresses, etc. .. )
2 ) Obtain the tables on prices.
3 ) Obtain the regressions of 2) and look for the data that best correlate with 1 )
4) derive a (possible) pricing formula
at the end, I added some faq and a
PRICE THEORY PROPOSAL
STEP 1: BLOCKCHAIN ANALYSIS For the determination of an equation of bitcoin price, I started from the idea of
analyze the data contained in blockchain .So , I started to write a program
that parses the blockchain to extract the data in a structured way .
With continued work, more and more I realized that the blockchain
is a source of valuable information , since it allows to evaluate even the smallest
details of the evolution in the bitcoin universe.
From discussions with users of the forum ( thank you in particular ercolinux ,
giubi66 , ovijunno for interesting suggestions) I have improved the methods of
data extraction.
In particular , I created the reference range of balances in BTC ,
and of these I extracted data on a daily basis.
In summary, to avoid publishing dozens of graphics and / or tables
with tedious data, I have found that the "total number of addresses"
has two interesting properties ' :
1) from October 2011 are growing on a regularexponential basis.
2) apparently are not affected by changes in prices and the news good or bad
(either in April 2013 or the recent peak in November !!!!)
( The line at top of chart is the total number of addresses present in blockchain )
From this chart we can see that at the beginning of 2011 had not yet been well-established
the ranges of capital and the speed ' of growth, while from mid-2011 onwards are consolidated
certain proportions that remain fundamentally unchanged until today.
The same conclusion, that towards the end of 2011 the world is bitcoin "stabilizes"
is obtained by looking at the chart for the total value of BTC in every range of balance:
The universe bitcoin enters 2012 with the social classes of the rich and the poor already
well-defined and basically unchanged ratios since now !
Here is a graphical representation of the distribution of bitcoin addresses for range of balance:
As we see more than 90% of the addresses are empty. I think the total number of addresses
(consisting largely of empty address as is easily seen here) and that I use in my formula,
accurately measures the use of the bitcoin network , and the number of transactions.
So it could lead to a "network value" as given by the famous Metcalfe's Law
If the exponent that I have found to be 2.26 instead was more close to 2, maybe I could say
have discovered something really important !
interesting comparison between the graph of the total number of addresses ( without the addresses to balance 0)
and the graph of the total capital in BTC :
Please note that in the two charts the order of the data is inverted for clarity:
the left chart and the first data is small capitalization in right chart first data is hight capitalization.
0.05% of addresses ( those with balance > 1000 ) that are a slice of the graph to the left absolutely invisible ,
has more 'than 42 % of the capital, the largest slice in the right chart !
STEP 2: PRICES ANALISYS The price analysis was definitely more simple: I wrote a simple program
that takes prices from blochckain.info .
The interesting consideration is that the prices ( although in a more irregular way)
are growing exponentially, and so I created the regressions
on a logarithmic scale in order to have the indicators less " nervous " of proce speed growth .
Here is the result :
As you can see I have 3 calculated regression lines : since the beginning of 2011 , by the beginning of 2012 and beginning of 2013.
STEP 3: COMPARISON OF BLOCKCHAIN DATA / PRICE The comparison between the two "worlds" , the seemingly chaotic and irregular prices, and the
completely "calculable" of blockchain , led me to some interesting results .
the growth curve of the totla addresses , has a nearly perfect correlation ( by end of 2011)
with the regression line price !
STEP 4: THE PRICE EQUATION with a little elementary math, was easy to derive from this series of observations
an "Hypothetical" (but very effective ) price equation :
definitions:
I = total number of addresses (From blockchain)
P = price in dollars (The result)
m = coefficient angular straight line ( constant to be determined)
P = ordinate at the origin (constant to be determined)
^ = Exponentiation
We derive the equation of the price from the period of strong correlation identified
from previous studies of price in dollars and the total number of addresses .
since the linear correlation on logarithmic axes, we can assume:
m * log (I) + p = log ( P)
for the values of I p , we use addresses and prices
the extremes of the strong correlation :
I1 = number addresses to 01/01/2012 = 2773046
P1 = price at 01/01/2012 = $ 5.2
I2 = number addresses to 24/01/2013 = 24,296,059
P2 = price = $ 698.43 01/24/2013
can easily be obtained
m = (log (P2 ) -log ( P1 ) ) / (log (I2 ) -log (I1 ) ) = 2.25776380522923
p = log ( P1) - log (I1) * m = - 31.8462990266051
then the final equation will be :
2.25776380522923 * log (I) - 31.8462990266051 = log ( P)
e ^ ( ( 2.25776380522923 * log (I) - 31.8462990266051 ) ) = P
( I ^ 2.25776380522923 ) / ( e ^ 31.8462990266051 ) = P
Reduce the decimal places, that does not change the substance but make equation
easy to remember and even more elegant:
P = ( I ^ 2.26) / (e ^ 32 ) 
FAQ1 ) So how much is the bitcoin tomorrow ?
Of course, as is easily seen from the graph, the function give a trend of prices ( llittle overestimated
than the average ) , this means that we do not give the exact price tomorrow or in a week , but rather
an indication of what can be a consistent price .
2 ) Does it work?
would have more or less worked for two years from early 2012 to now (though often overestimate )
but the trend was clearly indicated right . For the future, we will check together, if it continues to be valid
or not.
3 ) why it work?
This is a typical case in which we get a hypothetical "reads" from a statistical analysis. Now it is right to ask
'why it should work. I did have some idea , namely that in the end the total number of addresses is
a great aggragato of important factors in determining the price, in particular:
a) definitely depends on the number of users ( as seen from the correlation with the number of active addresses )
b ) and definitely ' also dependent on the speed' of movement, ie the number of remains , operations and overall
new addresses that are handled in the course of operations.
c) the square (plus .26) give me to think at something like Metcalfe's law ....
But I intend to deepen the investigation on this topic .
4) Please fit us a function for the price dependent on time P(t) = function (time-offset) Thanks.
here the function you request:
P = e^(((days from 01/01/2012) * 0.0067) + 1.641))
example: price at 31/12/2014 =
days from 01/01/2012 to 31/12/2014 = 366 + 365 + 365 = 1096
P = e^((1096*0.0067) + 1.641) = 7976.06132258175
5) the total number of addresses as a function of time ?
here the answer:
Addresses = 2764582*e^((days from 01/01/2012)*0.00297)
that extimate for the end of 2014 about 71.000.000 of total addresses (active + zero)
PRICE THEORY PROPOSALAfter several trial and error, I found a function that has a good correlation with the trend of the price,
and has the great advantage of having a quadratic relationship with the performance of the addresses :
P = (IZ ^ 2 ) / ( e ^ 27.5 )
Where IZ is the number of zero addresses.
This complies with the law of metcalfe:
http://en.wikipedia.org/wiki/Metcalfe%27s_lawI also think that zero addresses match better with the law of metcalfe for these properties:
1) each zero balance address has at least one entry operation, in fact, appears in blockchain.
2) Each zero balance address has at least one operation in output that perfectly compensates the previous.
3) The addresses at a zero balance are more than 90% of the total addresses , so perfectly represent the trend
the whole network.
zero addresses have interacted in some way between them, creating network effect,
while many addresses with a positive balance may not have interact with anyone
(many addresses are used for storage who have never output operations).
I propose the following theory :
Bitcoin is a network and its value depends on the square of the addresses in zero balance,
that represent the nodes that interact, in accordance with the Metcalfe law:
P = (IZ ^ 2 ) / ( e ^ 27.5 )
Here the plot of the original function (the one with addresses in total)
and the new ( function address zero)
If you find this work useful and / or interesting and ' welcome a donation to support the project: 1LJuCmvbzk7Xph1LQRsSzjYYQVu81N53GN
