Stephen Reed's Million Dollar Logistic Model

[marcus_of_augustus]

Agreed that the Log(Log) graph fits recent data better, however there is no principle behind the equation as there is with a logistic model of population growth with resource constraints.  The Log(Log) model suggests that prices during 2014 will reach 100000 USD by summer 2014. To me, this is not a plausible growth rate for bitcoin prices.

I believe that 2012 simply under performed and that 2013 over performed with regard to the log trend line.

justusranvier brought up a great point in that USD purchasing power has been following an exponential decay model.  Doesn't that suggest the growth should be super exponential, at least for some phase?

https://bitcointalk.org/index.php?topic=178336.msg4210004#msg4210004

Right, but the dollar decay has traditionally had a much slower time constant than bitcoin adoption ... although it could be that the two wont always be unrelated. At some point, if there is a widespread loss of confidence, and a rush out of the dollar into bitcoin (the bitexit holy grail) then the two will become very much related functions in a hyper-inflation $, hyper-monetisation BTC event. A super-exponential decay of dollar purchasing power pumping up a super-exponential rise in btc/usd price.

[1714926755]

1714926755

[1714926755]

1714926755

[rpietila]

A simple metric would be to divide the bitcoin market cap by the number of users. Anybody care to estimate the monthly number of users some time back? (I have a thread estimating the ongoing development)

[SlipperySlope]

A simple metric would be to divide the bitcoin market cap by the number of users. Anybody care to estimate the monthly number of users some time back? (I have a thread estimating the ongoing development)

Good idea!

I can get monthly download statistics for the bitcoin software from the SourceForge code repository, and derive a cumulative total by date of the number of bitcoin wallets that indicate a relative number of users. The statistics available from blockchain.info regarding number of online wallets starts only in 2012.

The data series for total bitcoins in circulation is available from blockchain.info. Give me a little time and I will produce a graph of the suggested metric.

[kdrop22]

A simple metric would be to divide the bitcoin market cap by the number of users. Anybody care to estimate the monthly number of users some time back? (I have a thread estimating the ongoing development)

Good idea!

I can get monthly download statistics for the bitcoin software from the SourceForge code repository, and derive a cumulative total by date of the number of bitcoin wallets that indicate a relative number of users. The statistics available from blockchain.info regarding number of online wallets starts only in 2012.

The data series for total bitcoins in circulation is available from blockchain.info. Give me a little time and I will produce a graph of the suggested metric.

Thanks, that seems like a good idea.

[bitrider]

A simple metric would be to divide the bitcoin market cap by the number of users. Anybody care to estimate the monthly number of users some time back? (I have a thread estimating the ongoing development)

While I think that is useful metric, and I would like to see it tracked, it seems to ignore the fact that from this point forward much larger "users" are going to be in the game. Including the funds, and institutional players not to mention the already rich who will all have a much great impact/user effect than we have mostly seen to this point.

Missing something?

[loopgate88]

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. 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.

This goes back to Ray Kurzweil's persistent emphasis on the exponential nature of our singular time. You, Sir, are dead on. Thank you for the excellent work.

[BitDreams]

Would the number of developers be of interest as well?

http://nl.reddit.com/r/Bitcoin/comments/1u0qej/bitcoin_big_hit_with_developers_growing_4x_as/cedfyek

Since 11/1/13, there have been:
602 Bitcoin
187 Dropbox
100 Paypal
74 Uber
48 FourSquare
Github repos created.

Edit: found the chart where I'd first learned of this... http://blog.bitcoinpulse.com/bitcoin-big-hit-with-developers-predicting-the-future-with-github/

[marcus_of_augustus]

I have a few more back-of-envelope figures that might be relevant for the "1 million" or other saturation level choice ...

Gross World Product http://en.wikipedia.org/wiki/Gross_world_product

... approx. GWP= 85 x10^12 [us$]  ..... (trillion, round figure, PPP basis.)

Typical money velocity for widely held/used money http://en.wikipedia.org/wiki/Velocity_of_money

... approx. V= 4.1

Money stock circulating, M = 18 x10^6 [xbt] ... (assume some irretrievably lost and circa 2025 stock mined)

Bitcoin price, B [us$]

Governing equation;

GWP = B.M.V

B = GWP/(M.V)

=> Upper bound case where bitcoin denominates ALL global transactions

B = 1.152 x10^6 [us$]

=> 10% GWP denominated in [xbt]

B = 115.2 x10^3 [us$]

=> 1% GWP denominated in [xbt]

B = 11,520 [us$]


(NB: this is based purely on white trade and discounts black/grey market monetary demand, including transfers that circumvent capital controls, private transfers, off-balance sheet, etc monetary TX and storage demands.)

[kdrop22]

Thanks for the analysis. While the Global GDP is 87 Trillion. Online Sales is just 1 Trillion.

[marcus_of_augustus]

Thanks for the analysis. While the Global GDP is 87 Trillion. Online Sales is just 1 Trillion.

Ok, Bitcoin probably wont have significant uptake for on-line sales for some time, imho.

It can however compete immediately and directly with any electronic transfers of value information (SWIFT, FEDWIRE, etc) today, particularly across borders where capital controls and other political censorship or other interference in payment systems is taking place. Care to put a number on that for me? Thnx.

[Dragonkiller]

Thanks for the analysis. While the Global GDP is 87 Trillion. Online Sales is just 1 Trillion.

Ok, Bitcoin probably wont have significant uptake for on-line sales for some time, imho.

It can however compete immediately and directly with any electronic transfers of value information (SWIFT, FEDWIRE, etc) today, particularly across borders where capital controls and other political censorship or other interference in payment systems is taking place. Care to put a number on that for me? Thnx.

I spent some time recently reading up on how SWIFT actually works, it's a very dated system. From what I've learnt I think bitcoin would be the perfect replacement, and I think it's one of the areas it has the highest chance of success in.

My understanding of SWIFT is it's basically a secure message between banks, however the actual money needs to move too, this is not a problem if the transfer is between two large banks. However smaller banks need an intermediary bank (which takes their own set of fees). Basically both the bank sending the money and the bank receiving the money need to have accounts at an intermediary bank which settles the transfer.

SWIFT transfer around $6 trillion per day.

[SlipperySlope]

Relative Growth of Bitcoin Market Capitalization vs Cumulative Wallets

A simple metric would be to divide the bitcoin market cap by the number of users. Anybody care to estimate the monthly number of users some time back? (I have a thread estimating the ongoing development)

Below is the relative growth of Bitcoin market capitalization vs wallet growth. The shared data spreadsheet and chart are here.



The data suggests that over time, users are more willing to bid up the price of bitcoin. Its not simply the addition of more users that causes bitcoin's price to grow. I suppose that this is because as Bitcoin matures, the perceived risks recede and network effects drive value up for each wallet user.

From the spreadsheet the requested metric is . . .

Code:

Date      Market Cap per Wallet
1-Sep-2010	9.199265512
1-Oct-2010	8.31156594
1-Nov-2010	24.44845805
1-Dec-2010	21.72825755
1-Jan-2011	27.20551529
1-Feb-2011	61.77197397
1-Mar-2011	50.69862048
1-Apr-2011	34.78586103
1-May-2011	80.51902012
1-Jun-2011	94.24233851
1-Jul-2011	147.7402516
1-Aug-2011	108.7838713
1-Sep-2011	65.33783406
1-Oct-2011	39.88800029
1-Nov-2011	24.71858162
1-Dec-2011	22.83534428
1-Jan-2012	36.87445205
1-Feb-2012	39.22018699
1-Mar-2012	33.80519442
1-Apr-2012	32.65323934
1-May-2012	32.32932281
1-Jun-2012	33.52715043
1-Jul-2012	41.78422829
1-Aug-2012	58.15863505
1-Sep-2012	62.12124562
1-Oct-2012	72.73124219
1-Nov-2012	64.10586921
1-Dec-2012	70.06403119
1-Jan-2013	71.18179877
1-Feb-2013	105.0337642
1-Mar-2013	147.2198882
1-Apr-2013	349.4214284
1-May-2013	425.7523625
1-Jun-2013	394.1813518
1-Jul-2013	282.1449121
1-Aug-2013	308.5201805
1-Sep-2013	412.1366222
1-Oct-2013	389.1771141
1-Nov-2013	511.4515785
1-Dec-2013	2420.932006
1-Jan-2014	1631.277105

[kdrop22]

Thanks Slippery.

[BitDreams]

Re: "users are more willing to bid up the price of bitcoin" -- I'm in this camp. I started buying Feb in 2013 if I recall with my most recent purchase in December. I'm pretty sure that any coins I purchase this year will be used to replenish what I spend.

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

[rpietila]

Relative Growth of Bitcoin Market Capitalization vs Cumulative Wallets

A simple metric would be to divide the bitcoin market cap by the number of users. Anybody care to estimate the monthly number of users some time back? (I have a thread estimating the ongoing development)

Below is the relative growth of Bitcoin market capitalization vs wallet growth. The shared data spreadsheet and chart are here.



The data suggests that over time, users are more willing to bid up the price of bitcoin. Its not simply the addition of more users that causes bitcoin's price to grow. I suppose that this is because as Bitcoin matures, the perceived risks recede and network effects drive value up for each wallet user.

From the spreadsheet the requested metric is . . .

Code:

Date      Market Cap per Wallet
1-Sep-2010	9.199265512
1-Oct-2010	8.31156594
1-Nov-2010	24.44845805
1-Dec-2010	21.72825755
1-Jan-2011	27.20551529
1-Feb-2011	61.77197397
1-Mar-2011	50.69862048
1-Apr-2011	34.78586103
1-May-2011	80.51902012
1-Jun-2011	94.24233851
1-Jul-2011	147.7402516
1-Aug-2011	108.7838713
1-Sep-2011	65.33783406
1-Oct-2011	39.88800029
1-Nov-2011	24.71858162
1-Dec-2011	22.83534428
1-Jan-2012	36.87445205
1-Feb-2012	39.22018699
1-Mar-2012	33.80519442
1-Apr-2012	32.65323934
1-May-2012	32.32932281
1-Jun-2012	33.52715043
1-Jul-2012	41.78422829
1-Aug-2012	58.15863505
1-Sep-2012	62.12124562
1-Oct-2012	72.73124219
1-Nov-2012	64.10586921
1-Dec-2012	70.06403119
1-Jan-2013	71.18179877
1-Feb-2013	105.0337642
1-Mar-2013	147.2198882
1-Apr-2013	349.4214284
1-May-2013	425.7523625
1-Jun-2013	394.1813518
1-Jul-2013	282.1449121
1-Aug-2013	308.5201805
1-Sep-2013	412.1366222
1-Oct-2013	389.1771141
1-Nov-2013	511.4515785
1-Dec-2013	2420.932006
1-Jan-2014	1631.277105

This is just wow. I would never have thought that bitcoin could have had so many users already in 2011. Even now I distrust the numbers because there has to be a lot of double-counting, but... that $100 would have been crossed only in 2013!!

The person who helped me into bitcoin told that it's very simple - the system will always be worth about $1,000 per user. At the time the market cap was about $500k, so that implied 500 active users, we thought. According to this data it would have been more like 10,000!

Now this raises again the doubts, whether there will be a gigantic asset bubble in bitcoin in the near future. (I almost thought that we could avoid it based on the fact that bitcoin is so much more valuable than anybody can think, and thus cannot become overvalued  ). 

If I use all the data since the beginning, there seemed to be 1.73x faster growth in market cap compared to the # of wallets. If the data before 6/2011 is left out, this is increased to 2.68x.

With the 1.73x growth factor, assuming that both trends stay the same, the projections are as follows:

12/2014 bitcoin price 3k, users 35M, per user 1.2k
12/2015 bitcoin price 32k, users 145M, per user 3.2k
12/2016 bitcoin price 344k, users 596M, per user 9.3k.

Looks interesting.

[wobber]

What software have you used to graph this?

[SlipperySlope]

What software have you used to graph this?

Google Drive is a cloud based facility for shared documents. I used their spreadsheet function - familiar charting operations and very easy to share via a URL. The one drawback for my purposes is that Google charts do not directly support log axis scaling, so I must compute log 10 values for charting.

https://docs.google.com/spreadsheets/d/1VoVBIO0WDMRnB_GzjykZ5iAR4Bd7ODyPaPTDGh3LeMo

[SlipperySlope]

Bitcoin Merchant Adoption - Influence Diagram

Here is a diagram of the situation resulting from more merchant adoption of Bitcoin, that I drew. Each of the situations could be measured, i.e. observed. The directed arrows indicate a postulated causal relationship in a Bayesian inference model.



The diagram is shared here.

[mestar]

Ah, the cool $1 million per Bitcoin in 2018.  Let's see what this means. 

If miners decide to sell all their mined Bitcoins, (or 50%), this is how much daily fresh money is needed on the exchanges for the price to be stable:

2014-2016 :   $3.6 billion ($1.8 billion if 50% sold)
2017-2020:   $1.8 billion ($0.9 billion)
2021-2024:   $0.9 billion ($.45 billion)
etc.

So, if Bitcoin is $1 million in 2018, good luck in finding that daily one billion dollars. (0.3$ trillion in a year). Dr. Evil would be proud.

[BitchicksHusband]

Ah, the cool $1 million per Bitcoin in 2018.  Let's see what this means.  

If miners decide to sell all their mined Bitcoins, (or 50%), this is how much daily fresh money is needed on the exchanges for the price to be stable:

2014-2016 :   $3.6 billion ($1.8 billion if 50% sold)
2017-2020:   $1.8 billion ($0.9 billion)
2021-2024:   $0.9 billion ($.45 billion)
etc.

So, if Bitcoin is $1 million in 2018, good luck in finding that daily one billion dollars. (0.3$ trillion in a year). Dr. Evil would be proud.

You do realize that this situation would be full adoption, meaning that there will be 1 billion users and every store would take bitcoin, right?

OMG, everybody has to come up with $1 for bitcoin every day on average.