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Author Topic: Distribution of bitcoin wealth by owner  (Read 45429 times)
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rpietila
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October 22, 2013, 06:30:06 PM
#1


TL;DR:  The number of bitcoin holders has just surpassed 2 million mark! The growth is happening in the holdings of 70 bitcoins or less, especially in micro-holdings of 1 bitcoin or less.

The intent of this thread is to find out and update the statistic on how bitcoins as investment/holdings are distributed according to the size of actual holding (note that this differs from the largest addresses -list).

The intent is not to try to identify individual holders or the size of their holdings.

Methodology and discussion of 27 Jan results.


27. Jan 2014

#People#Bitcoins#TotalBitcoins
46BTC10k+3.6M
820BTC1k-10k2.4M
10kBTC100-1k2.8M
68kBTC10-1002.0M
250kBTC1-100.8M
550kBTC0.1-10.2M
690kBTC0.01-0.10.0M
430kBTC0.001-0.010.0M

Total: 11.8M bitcoins (0.5M bitcoins assumed lost)

There is less holders than before in the category of BTC70+. The number of holdings smaller than this increased.

The number of bitcoin millionaires, previously estimated 930, decreased to 790 (-15%). Their combined wealth is 5.9M bitcoins, which is 50% of all bitcoins.




Earlier estimate of 3. Dec 2013

#People#Bitcoins#TotalBitcoins
47BTC10k+3.5M
880BTC1k-10k2.6M
10kBTC100-1k3.0M
63kBTC10-1001.8M
210kBTC1-100.6M
350kBTC0.1-10.1M
350kBTC0.01-0.10.0M
210kBTC0.001-0.010.0M

Total: 11.6M bitcoins (0.5M bitcoins assumed lost)

1,200,000 people own bitcoins that are valued at more than $1 (BTC0.001 or more)
280,000 people own bitcoins that are valued at more than $1,000 (BTC1 or more), up from 120,000 last month
930 people own bitcoin that are valued at more than $1 million (BTC1,000 or more)
1 person owns bitcoins that are valued at more than $1 billion (Satoshi, estimated to be BTC980,000)

Changes from previous month:
- Bitcoin total number adjusted to account for increase in money supply
- Thoroughly re-engineered the number of bitcoin users from original data of the userbases of several services + blockchain usage. This shows that the last month estimate was probably too small, and perhaps 50% of the growth in number of users can be attributed to correction of a previous underestimate.
- Corrected the highest bracket a little bit (BTC0.6M Smiley ) upwards because it was over-corrected downwards last time. Number of holders in this category went down a little but we have better estimate of the holdings. As this is a base case model, we do not assume large, completely anonymous entities without at least circumstantial evidence of their holdings.
- Number of people in each bracket behaves according to binomial distribution as found in another data with the parameters: total=1.2 million users, highest bracket=fixed, #of_coins=fixed.

As a result:
- Bracket 1,000-10,000 saw the greatest loss -20%, bracket 100-1,000 lost 10%. Sub-BTC10 holdings gained a lot.


Earlier estimate of 26. Oct 2013

#People#Bitcoins#TotalBitcoins
50BTC10k+2.9M
1100BTC1k-10k3.1M
12kBTC100-1k3.3M
58kBTC10-1001.8M
110kBTC1-100.4M
110kBTC0.1-10.1M
57kBTC0-0.10.0M

Total: 11.5M bitcoins, 350k owners
120,000 people own bitcoins that are valued at more than $1,000 (BTC5 or more).

Changes from previous estimate:
- Bitcoin total number adjusted to 11.5M to account for lost coins
- Significantly reduced the number of bitcoin users to account for the assumption that few people would play with stashes that are <$10 in value, and other evidence pointing to a lower number
- Significantly reduced the number of bitcoins owned by the highest bracket due to the lack of evidence that there are many large holders. As this is a base case model, nefarious premine schemes are not assumed without proof. Sorry for falling into that initially.
- Number of people in each bracket behaves according to binomial distribution as found in another data.


Thread is self-moderated to retain readability; user content will be amalgamated to the table and possibly deleted. If this happens, don't take it personally.

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If you donít believe me or donít get it, I donít have time to try to convince you, sorry. -Satoshi
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October 22, 2013, 06:51:14 PM
#2

What we need to make this analysis more accurate, is to gain answers to the following:

- Does Satoshi have access to the "backbone miner" keys or are they lost?
- What is the likely stash DPR controls
- How many individuals have BTC100,000+ holdings in addition to the previous
- How many bitcoin investors there are in total.

The gaps are rather easy to fill with the law of large numbers, and probability distribution. Of course we need to reach consensus which one to use!



Edit. Original estimate archived (moved from OP):

22. Oct 2013:

#People#Bitcoins#TotalBitcoins
100BTC10k+5.5M
900BTC1k-10k2.9M
5000BTC100-1k1.6M
31kBTC10-1001.0M
167kBTC1-100.5M
1MBTC0.1-10.3M
3MBTC0-0.10.0M

Total: 11.8M bitcoins, 4.2M owners
80,000 people own bitcoins that are valued at more than $1,000 (BTC5 or more).



ADD2: First consensus estimate:

26. Oct 2013

#People#Bitcoins#TotalBitcoins
50BTC10k+2.9M
1100BTC1k-10k3.1M
12kBTC100-1k3.3M
58kBTC10-1001.8M
110kBTC1-100.4M
110kBTC0.1-10.1M
57kBTC0-0.10.0M


Total: 11.5M bitcoins, 350k owners
120,000 people own bitcoins that are valued at more than $1,000 (BTC5 or more).

Changes from previous estimate:
- Bitcoin total number adjusted to 11.5M to account for lost coins
- Significantly reduced the number of bitcoin users to account for the assumption that few people would play with stashes that are <$10 in value, and other evidence pointing to a lower number
- Significantly reduced the number of bitcoins owned by the highest bracket due to the lack of evidence that there are many large holders. As this is a base case model, nefarious premine schemes are not assumed without proof. Sorry for falling into that initially.
- Number of people in each bracket behaves according to binomial distribution as found in another data.

President etc. of Silvervault, Hopea.fi, EIH among others.
If you donít believe me or donít get it, I donít have time to try to convince you, sorry. -Satoshi
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October 22, 2013, 07:00:41 PM
#3

So the numbers are speculated?  Any thoughts at all to why the brackets and distribution is in that range though?  I always imagined that there were far more holders in the 1000+ range than that.

"Far more" holders there cannot be. I know personally several people that have more than BTC1,000. The mean of their holdings is significantly higher than that. I don't know exact figures because everybody wants to retain privacy, but my estimate is BTC4,000. To reach a mean of BTC4,000, we might have for example 4 people, one owning BTC10k, and the rest BTC3k, BTC2k and BTC1k, respectively. The large holders raise the mean significantly.

To drive in the point, if all the bitcoins are divided equally to people who have BTC1,000, there would still be less than 12,000 such people, since there is less than 12 million bitcoins! Smiley But since many own much more, assuming mean of BTC4k, this actually leaves us with only 3,000 people!! I agree that it is shockingly few. And this assumes that nobody owns anything in between BTC0.00000001 and BTC1,000, which is clearly incorrect.

The values in the table are my current guesses and now it is up to the community to develop them.

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If you donít believe me or donít get it, I donít have time to try to convince you, sorry. -Satoshi
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October 22, 2013, 07:05:23 PM
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So the numbers are speculated?  Any thoughts at all to why the brackets and distribution is in that range though?  I always imagined that there were far more holders in the 1000+ range than that.

"Far more" holders there cannot be. I know personally several people that have more than BTC1,000. The mean of their holdings is significantly higher than that. I don't know exact figures because everybody wants to retain privacy, but my estimate is BTC4,000. To reach a mean of BTC4,000, we might have for example 4 people, one owning BTC10k, and the rest BTC3k, BTC2k and BTC1k, respectively. The large holders raise the mean significantly.

To drive in the point, if all the bitcoins are divided equally to people who have BTC1,000, there would still be less than 12,000 such people, since there is less than 12 million bitcoins! Smiley But since many own much more, assuming mean of BTC4k, this actually leaves us with only 3,000 people!! I agree that it is shockingly few. And this assumes that nobody owns anything in between BTC0.00000001 and BTC1,000, which is clearly incorrect.

The values in the table are my current guesses and now it is up to the community to develop them.

That makes sense.  I guess knowing the total number of bitcoins gives the parameters in which to get some numbers for sure. As the price rises it does become even more difficult for there to be large holders. 

Are most of the large holders, beside the Winklvii, early miners?  My husband thinks that many of them sold off their coin.  In that case the winners in this "game" if you want to call it that are those that buy the earliest and just hold the longest.

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October 22, 2013, 08:52:21 PM
#5

FYI, I sold a bit over BTC1,000, a lot of it as cash through localbitcoins.com, back when they were $22  Tongue

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October 22, 2013, 09:41:07 PM
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FYI, I sold a bit over BTC1,000, a lot of it as cash through localbitcoins.com, back when they were $22  Tongue

I so feel you. I also sold BTC1,000 a month ago  Cry Luckily I came to the party so late, I haven't had time to squander any large holdings as I never had any.

But although surprising, it seems that with our remaining stash of BTC1,000 we both fit into Bitcoin top-1000  Grin

I would like to have some information from the blockchain to sharpen the analysis.. How many of the 2009-6/2010 coins are still in original addresses? Some percentage of the ones not belonging to Satoshi are likely lost.

Is it realistic to assume 4 million people have fractional bitcoin holdings? Does anyone know such people or is Bitcoin still totally in the hands of very few? Do we only have the about 100,000 holders who hold minimum USD 1,000 worth? Worldwide?

This is in very early stage. The only way for bitcoin to accommodate 1 million people willing to invest $1,000, is for the pyramid to stay where it is, but Bitcoin's value goes up 10-fold and therefore the "owning bitcoins worth $1,000 cut-off" goes down one bracket. It has already done so many times in the past, to accommodate people like me.

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If you donít believe me or donít get it, I donít have time to try to convince you, sorry. -Satoshi
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October 23, 2013, 12:04:07 AM
#7

I thought I would add this ( missing bit) the distribution of large numbers is a nice key to understanding the target distribution.  

There are only so many bitcoins...

In 2010, you could effortlessly buy BTC10,000. But only 2100 people will be able to hold it.
In 2011-2012, you could buy BTC1,000. But only 21,000 people will be able to.
In 2013, most can buy BTC100. Still, that is only 210,000 people.

There are more than a million bitcoin users now, so obviously most hold less than BTC100.

Once the bitcoin userbase grows to one billion, only 21 million at most can hold even a single bitcoin. It does not take a scientist to see that BTC1 is very valuable, and a stash of BTC100 bought in 2013 is immensely valuable.

More statistics of bitcoin ownership. Warning: simple math and advanced logic.

Situation later:

#People#Bitcoins#TotalBitcoins
63BTC10k+3M
1000BTC1k-10k3M
10kBTC100-1k3M
100kBTC10-1003M
1MBTC1-103M
10MBTC0.1-13M
600MBTC0-0.13M

Total: 21M bitcoins, 611M owners


Of course the numbers in ownership brackets can be off by a factor of 2, but it is mathematically impossible for them to be off by a factor of 10! Therefore we conclude that by buying and holding BTC1, you are forever guaranteed to be among the top 1 million bitcoin owners, regardless of how cheap you managed to buy it, or how valuable it gets in the nearest years.

Iirc, it takes $10M+ to get to the top 1 million in dollar wealth, so we are talking about royal money.


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October 23, 2013, 06:32:06 AM
#8

rpietila, in general I think your table is roughly accurate. It matches quite well what I have in my head about the BTC holdings distribution. Thanks for sharing!

What we need to make this analysis more accurate, is to gain answers to the following:

- Does Satoshi have access to the "mystery miner" keys or are they lost?

we won't know until he moves these coins. Afaik they are still sitting there (~1 million coins unmoved, see my post linked below for more exact data). I suggest we simply assume he still has access to them.

We use different meaning of the term "mystery miner". Back in 2011 there was a miner popping up with lots of power for a short period of time, noone knew who he was. He mined for a while, then disappeared. He was named "the mystery miner", or short: MM). Back then his coins remained unmoved for months. Not sure they're still sitting there (see spike in the following graph and click graph for more info)


(click for larger version and background info)

I also did some analysis on 2009 coins back in 2011: https://bitcointalk.org/index.php?topic=37333.msg458441#msg458441

That whole thread contains relevant info to this discussion here, so the inclined might want to read a bit from it.


- What is the likely stash DPR controls

my guess is 100-200kBTC

- How many individuals have BTC100,000+ holdings in addition to the previous

This is hard to guess. I would guess: Satoshi (1 million), 2-3 friends of Satoshi (2.5 * 500k), about 3-4 early GPU miners (3.5 * 250k), about 5-10 dudes like DPR (7.5 * 150k). Sum: 4.25 million BTC.

- How many bitcoin investors there are in total.

This is very hard to guess. We can put an upper bound using the blockchain (number of addresses ever used) assuming they hold their keys privately. In early 2012 this was about 500k Addresses. Anyone have newer data? We can probably divide this by at least 10 due to people using multiple addresses (I'm pretty sure I used 200 addresses myself already).

The gaps are rather easy to fill with the law of large numbers, and probability distribution. Of course we need to reach consensus which one to use!

I agree. But first I'd like to try to collect more data and do more guessing / estimating. I will likely reactivate my bitcoin-abe database so I can pull some figures (like above-references 2009 coin age (maybe also 2010) and number of distinct addresses used). This might happen this weekend.

I have loads of ideas how to pull different kinds of relevant data from the blockchain... but these analyses are not simple to conduct.

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October 23, 2013, 06:44:34 AM
#9

just found an interesting link referenced from the thread I linke from above:


Diffusion of Innovations is a theory that seeks to explain how, why, and at what rate new ideas and technology spread through cultures.

I don't know if it applies to bitcoin holdings distribution.

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October 23, 2013, 06:52:56 AM
#10

I don't know why a tab in my browser is open with this link: http://bitslog.wordpress.com/2013/09/03/new-mystery-about-satoshi/

was it linked from here?

Highly interesting stuff about early mining (maybe signatures)

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October 23, 2013, 02:56:47 PM
#11

rpietila, in general I think your table is roughly accurate. It matches quite well what I have in my head about the BTC holdings distribution. Thanks for sharing!

Perhaps you send your proposal as a table for all to see Smiley

What we need to make this analysis more accurate, is to gain answers to the following:

- Does Satoshi have access to the "mystery miner" keys or are they lost?
we won't know until he moves these coins. Afaik they are still sitting there (~1 million coins unmoved, see my post linked below for more exact data). I suggest we simply assume he still has access to them.

In Finnish forums it is vehemently opposed that Satoshi even has mined the coins. I can't see why and by what grounds it should be opposed... I think Sergio's analysis is very clear in this matter, even measuring in 0.1% accuracy that Satoshi has 980k coins.

Quote
We use different meaning of the term "mystery miner". Back in 2011 there was a miner popping up with lots of power for a short period of time, noone knew who he was. He mined for a while, then disappeared. He was named "the mystery miner", or short: MM). Back then his coins remained unmoved for months. Not sure they're still sitting there (see spike in the following graph and click graph for more info)

Corrected my usage.

Quote
- What is the likely stash DPR controls

my guess is 100-200kBTC

DPR is not known to have spent much money. I think it cannot be assumed that 400-500k has just been lost in the span of only 2 years.

This assumes that the figure FBI published (600k total revenue to the site during its existence) is correct. But I thought they extracted it from SR own database. In my understanding these are commissions against which there are essentially no costs.

Until there is some evidence to the contrary, I would be inclined to use 500k as DPR figure. Very eager to hear thoughts?

Quote
- How many individuals have BTC100,000+ holdings in addition to the previous

This is hard to guess. I would guess: Satoshi (1 million), 2-3 friends of Satoshi (2.5 * 500k), about 3-4 early GPU miners (3.5 * 250k), about 5-10 dudes like DPR (7.5 * 150k). Sum: 4.25 million BTC.

If your estimate is correct, the bitcoin holding is even more top-heavy than in my calculation. Since you will have to add 100 holders in between 10-100k (100*30k) = 3.0 million to the equation.

Therefore all smaller holders would have <5 million, combined. Show me the results as a table! Smiley

Quote
- How many bitcoin investors there are in total.

This is very hard to guess. We can put an upper bound using the blockchain (number of addresses ever used) assuming they hold their keys privately. In early 2012 this was about 500k Addresses. Anyone have newer data? We can probably divide this by at least 10 due to people using multiple addresses (I'm pretty sure I used 200 addresses myself already).

Does anyone have the table for all addresses that have a balance, grouped similarly as here? It might give quite good clues: if we take a sample of people holding different amounts of bitcoins, and then they post their data on how it resides in different addresses, we can estimate the "conversion function" on how to convert the distribution table of addresses to the distribution table of holders!

Quote
I have loads of ideas how to pull different kinds of relevant data from the blockchain... but these analyses are not simple to conduct.

This is the place to post them Smiley



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If you donít believe me or donít get it, I donít have time to try to convince you, sorry. -Satoshi
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October 23, 2013, 04:02:51 PM
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I don't know if it applies to bitcoin holdings distribution.

Diffusion of Innovations, sure it applies to distribution of holdings, for Bitcoin to be effective it need to be distributed optimaly among the users, rpietila's final distribution estimate may be wrong but it's close.

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October 23, 2013, 05:36:39 PM
#13

Why not create a poll here asking readers which of the brackets they fall into?

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October 23, 2013, 05:42:34 PM
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Why not create a poll here asking readers which of the brackets they fall into?

Because they will lie Tongue

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October 23, 2013, 05:42:46 PM
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Why not create a poll here asking readers which of the brackets they fall into?

like I want to give that info away, (in addition poll participants are small samples)

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October 23, 2013, 05:45:05 PM
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So many millionaire in Bitcoiners. What if they decided to dump all of them at this high price Smiley
The exchange rate would drop, and they wouldn't be $ millionaires anymore

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October 23, 2013, 05:46:40 PM
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Personally, I'd vote in a poll where I specified the logarithmic range of my holdings long before I'd consider giving out the exact value, like some other threads ask for...

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October 23, 2013, 05:59:14 PM
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Personally, I'd vote in a poll where I specified the logarithmic range of my holdings long before I'd consider giving out the exact value, like some other threads ask for...

There is a lot of merit in how the question is asked, and what the goal is for gathering the info.
I had in mind something akin to polls of the past.

I tried to get a glimpse into this pattern in this pole (also molecular Simon Sinek has a great TED talk link in the pole about Law of Diffusion of Innovations.)

We are still in the innovators stage, although the law of large numbers will spared out over a similar bell cure, it is hard to see the mechanism by which it will happen.

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October 23, 2013, 06:07:14 PM
#19

who has majored in statistics and can help us with this analysis ? there must be ways to squeeze out more info about this out of the public data.

those figures may be of some value for bitcoin companies. besides that it is really interesting to see where one stands.

maybe satoshi wakes up one morning with the brilliant idea not to sell his stash for dollars but rather giving it away for free to people in need mediocre early adopters  Cool

edit: nice thread

join the international "when-bitcoin-reaches-1000-dollar" party !

https://bitcointalk.org/index.php?topic=285771.0
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October 23, 2013, 06:32:08 PM
#20

rpietila, in general I think your table is roughly accurate. It matches quite well what I have in my head about the BTC holdings distribution. Thanks for sharing!

Perhaps you send your proposal as a table for all to see Smiley

[...]

If your estimate is correct, the bitcoin holding is even more top-heavy than in my calculation. Since you will have to add 100 holders in between 10-100k (100*30k) = 3.0 million to the equation.

Therefore all smaller holders would have <5 million, combined. Show me the results as a table! Smiley

#People#Bitcoinspoeple * avg
1BTC1m-1.5m1.25M
2BTC500k-1m1.5M
3BTC250k-500k1.125M
7BTC150k-250k1.4M
15BTC50k-150k1.5M
50BTC10k-50k1.5M
300BTC2.1k-10k1.85M
1000BTC100-2.1k1.1M
5000BTC10-100275k
10000BTC1-1055k
50000BTC0.1-127.5k
150000BTC0.00000001-0.17.5k

total sum of last column: 11,555,000 BTC

into the last column I put the avg("from", "to") * "# of people" . In below chart this avg was used for the blue bars.



pulled out of my ass and yes: it's extremely top heavy compared to rpietilas distribution.

It's interesting that the groups down to and including the "100-2.1k" group all sum up to pretty much the same amount. (I didn't manipulate this, it was a surprise to me). Maybe I'm underestimating the number of people in the lower groups ("0.00000001-0.1" through "10-100")? There's probably more that 10,000 people with holding of 1 to 10 BTC, no? I'm really not sure.

I somehow hope I'm completely wrong with this guesswork of mine.

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