Distribution of bitcoin wealth by owner

[rpietila]

TL;DR:  As a result of analyzing the "Mt.Gox leak", the number of bitcoin holders is likely 1.0 millions. Of these,
* the 400 bitcoin millionaires with at least BTC2,000 hold 40% of bitcoins.
* 100,000 owners with BTC10-BTC2,000 ($5,000-$1,000,000) hold 50% of the bitcoins.
* 900,000 owners have a holding of BTC0.002-BTC10, valued at $1-$5,000, and hold 10% of the bitcoins

This is NOT a largest addresses/wallets -list, we are talking about largest owners here. An owner can have many wallets, and a wallet can have many addresses.



22. Apr 2014

#People	#Bitcoins	#TotalBitcoins
70	BTC10k+	3.6M
930	BTC1k-10k	2.2M
13k	BTC100-1k	3.0M
85k	BTC10-100	2.3M
250k	BTC1-10	0.8M
340k	BTC0.1-1	0.1M
230k	BTC0.01-0.1	0.0M
90k	BTC0.002-0.01	0.0M

Total: 12.2M bitcoins (0.5M bitcoins assumed lost)

The changes from previous estimate:

- Total number of holders revised down from 2.0 million to 1.0 million. This did not change much in the distribution of coins. If new users are added, the large holders do sell according to an experimentally derived rate of 17% per doubling in price, but some newish holders also add to their positions. All-new entrants can come to any bracket, because no amount of coins is yet too expensive to buy. The perceived static totals of the analysis hide the fact that Bitcoin trade is quite brisk and the people who consist of a bracket do change all the time.

- Number of 10k+ holders recalculated because we now know better the average number of coins in each bracket (thanks to Mt.Gox data). So the large holders still have the same number of coins in total, but there appears to be more of the holders.

- Same for 1k+ and 100+. More people but approx the same number of total coins.

- 10+ category turned out to be larger than previously estimated. The Mt.Gox data gave us the confidence to use a steeper j parameter, which means a more "equitable" distribution with more coins in the middle brackets.

- 1+ category remained intact, and the fractional categories were significantly sized down. The lower threshold of "owner" was also raised to BTC0.002 because of the decline in price.

- Number of Bitcoin millionaires at this price ($500) is about 400. This means that only 400 people worldwide can raise a $million by selling bitcoins, but about 30,000,000 people can invest a $million to buy bitcoins (without going into debt).

- The Bitcoin millionaires command about 4.9 million bitcoins, which is 40% of all bitcoins. The control of world's gold and fiat currency is more centralized with a smaller number of individuals controlling higher percentage.




Earlier estimate of 27. Jan 2014

#People	#Bitcoins	#TotalBitcoins
46	BTC10k+	3.6M
820	BTC1k-10k	2.4M
10k	BTC100-1k	2.8M
68k	BTC10-100	2.0M
250k	BTC1-10	0.8M
550k	BTC0.1-1	0.2M
690k	BTC0.01-0.1	0.0M
430k	BTC0.001-0.01	0.0M

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
47	BTC10k+	3.5M
880	BTC1k-10k	2.6M
10k	BTC100-1k	3.0M
63k	BTC10-100	1.8M
210k	BTC1-10	0.6M
350k	BTC0.1-1	0.1M
350k	BTC0.01-0.1	0.0M
210k	BTC0.001-0.01	0.0M

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 ) 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
50	BTC10k+	2.9M
1100	BTC1k-10k	3.1M
12k	BTC100-1k	3.3M
58k	BTC10-100	1.8M
110k	BTC1-10	0.4M
110k	BTC0.1-1	0.1M
57k	BTC0-0.1	0.0M

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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[rpietila]

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
100	BTC10k+	5.5M
900	BTC1k-10k	2.9M
5000	BTC100-1k	1.6M
31k	BTC10-100	1.0M
167k	BTC1-10	0.5M
1M	BTC0.1-1	0.3M
3M	BTC0-0.1	0.0M

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
50	BTC10k+	2.9M
1100	BTC1k-10k	3.1M
12k	BTC100-1k	3.3M
58k	BTC10-100	1.8M
110k	BTC1-10	0.4M
110k	BTC0.1-1	0.1M
57k	BTC0-0.1	0.0M

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.

[rpietila]

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! 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.

[BitChick]

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! 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.

[Rassah]

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

[rpietila]

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

I so feel you. I also sold BTC1,000 a month ago   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  

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.

[Adrian-x]

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
63	BTC10k+	3M
1000	BTC1k-10k	3M
10k	BTC100-1k	3M
100k	BTC10-100	3M
1M	BTC1-10	3M
10M	BTC0.1-1	3M
600M	BTC0-0.1	3M

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.

[molecular]

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.

[molecular]

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

http://en.wikipedia.org/wiki/Diffusion_of_innovations

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.

[molecular]

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)

[rpietila]

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

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.

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.

- 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?

- 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!

- 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!

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

[Adrian-x]

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.

[justusranvier]

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

[Mike Christ]

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

Because they will lie

[Adrian-x]

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)

[Adrian-x]

So many millionaire in Bitcoiners. What if they decided to dump all of them at this high price

The exchange rate would drop, and they wouldn't be $ millionaires anymore

[justusranvier]

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...

[Adrian-x]

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.

[600watt]

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  

edit: nice thread

[molecular]

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

[...]

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!

#People	#Bitcoins	poeple * avg
1	BTC1m-1.5m	1.25M
2	BTC500k-1m	1.5M
3	BTC250k-500k	1.125M
7	BTC150k-250k	1.4M
15	BTC50k-150k	1.5M
50	BTC10k-50k	1.5M
300	BTC2.1k-10k	1.85M
1000	BTC100-2.1k	1.1M
5000	BTC10-100	275k
10000	BTC1-10	55k
50000	BTC0.1-1	27.5k
150000	BTC0.00000001-0.1	7.5k

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.