Distribution of bitcoin wealth by owner

[molecular]

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

The ones in the high brackets will lie and the ones in the low brackets aren't here.

[dserrano5]

Does anyone have the table for all addresses that have a balance, grouped similarly as here?

Someone posted in august a list of all addresses with balance. I saved a copy and can easily aggregate the balances in log buckets. Would that be ok for your purposes considering that it's 2.5 months old?

[rpietila]

Does anyone have the table for all addresses that have a balance, grouped similarly as here?

Someone posted in august a list of all addresses with balance. I saved a copy and can easily aggregate the balances in log buckets. Would that be ok for your purposes considering that it's 2.5 months old?

I think it works just fine. Thanks a lot!

[dserrano5]

I think it works just fine. Thanks a lot!

Code:

      1 >=100000 BTC
     96 10000-99999.99 BTC
   1420 1000-9999.99 BTC
   9896 100-999.99 BTC
  80257 10-99.99 BTC
 121541 1-9.99 BTC
 147693 0.1-0.99 BTC
1477264 <0.1 BTC

Edit: one has to consider that the 10-99.99 BTC is somewhat inflated due to the sheer amount of addresses with 50 BTC coming from 4 years of mining rewards.

[Rassah]

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

Our remaining stash? How do you come to conclusion that I have a BTC1,000 stash?

[Rassah]

Does anyone have the table for all addresses that have a balance, grouped similarly as here?

Someone posted in august a list of all addresses with balance. I saved a copy and can easily aggregate the balances in log buckets. Would that be ok for your purposes considering that it's 2.5 months old?

This may be somewhat useless for this, as active wealthy bitcoin holders split up their holdings into lots of smaller parts, so as not to reveal their learge wealth moving around whenever they want to buy something.

[dserrano5]

This may be somewhat useless for this, as active wealthy bitcoin holders split up their holdings into lots of smaller parts, so as not to reveal their learge wealth moving around whenever they want to buy something.

Yeah but I assume OP understands the difference between people and addresses. This is another reason I asked before cooking the data.

[rpietila]

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

I will soon update, this is just the theory part to my reply

Your guesswork does not obey the mathematical distribution models that I firmly believe it should obey. This flaw is apparently because you did not use equilength (in log scale) brackets.

The distribution of bitcoins should, in my understanding, conform to one of these distributions, where X=log(number of bitcoins) and Y=(number of owners of the given number of bitcoins).

Now, if we calculate the integral over a bracket (which is one unit-length of the X-axis), we find the total number of bitcoins held by people in that bracket.

From the mathematical, probabilistic nature of the distributions, follows that the total bitcoins owned by people in different brackets cannot behave arbitrarily. Ie. the parameters are:
-how many bitcoins do the top owner(s) have
-how many owners are there in total
-one or two parameters to define the shape of the curve.

This can easily be checked by arranging the data to log-equilength brackets and demanding that the number of bitcoins owned by people in the bracket is either continuously higher than in previous bracket, or lower. At most the 1st derivative should have 1 root and behave nicely.

[rpietila]

I think it works just fine. Thanks a lot!

Code:

      1 >=100000 BTC
     96 10000-99999.99 BTC
   1420 1000-9999.99 BTC
   9896 100-999.99 BTC
  80257 10-99.99 BTC
 121541 1-9.99 BTC
 147693 0.1-0.99 BTC
1477264 <0.1 BTC

Edit: one has to consider that the 10-99.99 BTC is somewhat inflated due to the sheer amount of addresses with 50 BTC coming from 4 years of mining rewards.

Thanks, very good! Might it be possible to have the sums also, so that:
#bracket, #totalBtcInBracket

This would verify my above thesis about the "well-behavior" constraint for the distribution, and also be useful for calculating the average holding inside a given bracket. These all matters are interrelated.

Unless it is difficult, you could leave out unspent 50 BTC:s from this one.

[rpietila]

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

Our remaining stash? How do you come to conclusion that I have a BTC1,000 stash?

The logic is as follows:

Evidence

1. Your forum account is created in June-2011.

2. You have been forum active ever since and are Director in bitcoin-something.

3. You told you sold more than BTC1000 at $22 (Feb. 8, 2013)

Deduction


1. It is very rare to have a Jun-2011 account. This points to a person who has (with good probability) been able to mine/buy large amounts with
small cash outlay. (Hardly anyone creates an account without having the coins already.)

2. Being able to sell a significant amount at $22 points to me a long-term holding:

i) A believer who had bought recently would not have sold but bought more after being proven right. But you have been in all along.

ii) A newcomer who does not believe, would have likely sold more than a part after a quick double. Probably all of it. The newcomer would not be here today with thousands of messages though. And would probably not have had BTC1,000 in the first place.

iii) For a person with a good stash, who is in it for the long term, it makes perfect sense to sell a part after a quick double, after waiting for so long. Selling a part means selling at most half, which leaves at least half remaining. (The proceeds are enough to live from that day even until this day so no need to sell more.)

3. It is a lower bound that you would have BTC1,000 today. If you play wisely, you only sell a little at a time, and can earn BTC every year, so that your current holdings should be at least BTC3,000. The upper bound is that you resort to borderline lying, where you downplay the amount sold, and forget to tell that you bought back, and sold after very tight analysis only 10% of your holdings, then you might have BTC10,000 or more. I assume that anyone whose forum account is from 2011 or earlier, has BTC1,000-BTC10,000 unless proven otherwise.

4. Yes I know that bitcoin is not life and life can go wrong and you lose most of your bitcoins to bad bets as you don't realize how precious they are. But even in this case, considering your position, I think here we have a 4-figure Countess.

[dserrano5]

Thanks, very good! Might it be possible to have the sums also, so that:
#bracket, #totalBtcInBracket

Code:

Bracket        Outputs       BTC/bracket          Total BTC 
>=100000             1   111111.12658933    111111.12658933
10000-99999.99      96  2235807.30026651   2346918.42685584
1000-9999.99      1420  3149284.08119431   5496202.50805015
100-999.99        9896  2489353.90452616   7985556.41257631
10-99.99         80257  3128061.68383352  11113618.09640983
1-9.99          121541   346214.05777858  11459832.15418841
0.1-0.99        147693    56458.49332222  11516290.64751063
<0.1           1477264     7906.10863763  11524196.75614826

Unless it is difficult, you could leave out unspent 50 BTC:s from this one.

D'oh I forgot. So above listing include all 50 BTC outputs, the following one doesn't :

Code:

Bracket        Outputs       BTC/bracket          Total BTC 
>=100000             1   111111.12658933    111111.12658933
10000-99999.99      96  2235807.30026651   2346918.42685584
1000-9999.99      1420  3149284.08119431   5496202.50805015
100-999.99        9896  2489353.90452616   7985556.41257631
10-99.99         41634  1196911.68383354   9182468.09640985
1-9.99          121541   346214.05777858   9528682.15418843
0.1-0.99        147693    56458.49332222   9585140.64751065
<0.1           1477264     7906.10863763   9593046.75614828

[rpietila]

#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

I have converted your table to the "standard format"

Bracket	#TotalBitcoins	log(total)	1 derivative	2 der.
10k+	BTC8.28M	6.92
1k-10k	BTC2.40M	6.38	0.54
100-1k	BTC0.55M	5.74	0.64	0.10
10-100	BTC0.28M	5.44	0.30	-0.34
1-10	BTC0.06M	4.74	0.70	0.40
0.1-1	BTC0.03M	4.44	0.30	-0.40
-0.1	BTC0.00M	3.88	0.56	0.26

My hypothesis is that a valid data should not have erratic behavior in second derivative. (This uncovers the place where you pulled the numbers from..) I will run the same check to the actual data regarding bitcoin address balances that dserrano5 just posted. That should behave nicely, since the data is generated by a statistical, probabilistic manner.

[rpietila]

Code:

Bracket        Outputs       BTC/bracket          Total BTC 
>=100000             1   111111.12658933    111111.12658933
10000-99999.99      96  2235807.30026651   2346918.42685584
1000-9999.99      1420  3149284.08119431   5496202.50805015
100-999.99        9896  2489353.90452616   7985556.41257631
10-99.99         41634  1196911.68383354   9182468.09640985
1-9.99          121541   346214.05777858   9528682.15418843
0.1-0.99        147693    56458.49332222   9585140.64751065
<0.1           1477264     7906.10863763   9593046.75614828

Now we are using this data.

I have converted your table to the "standard format" to put it in the same kind of "validity test" as Molecular's data:

Bracket	#TotalBitcoins	log(total)	1 derivative	2 der.
10k+	BTC2.35M	6.37
1k-10k	BTC3.15M	6.50	-0.13
100-1k	BTC2.49M	6.40	0.10	0.23
10-100	BTC1.20M	6.08	0.32	0.22
1-10	BTC0.35M	5.54	0.54	0.22
0.1-1	BTC0.05M	4.75	0.79	0.25
-0.1	BTC0.01M	3.90	0.85	0.07

Have a look at the 2nd derivative! This is the kind of behavior that is expected from a probabilistic process. I can conclude that Molecular's data is wrong, and your data is valid.

Now, the original question remains: how to parse a table of the bitcoin holdership, as opposed to address balance distribution.

In my opinion, this one gives us a great deal of hint of the parameters of the distribution though. Eg. the averages per bracket is good to know:

24k, 2.2k, 251, 29, 2.85, 0.38 - there is a certain logic in these also.

[imrer]

Very interesting. Do you think all of these guys are still somewhere around? Will they ever sell it?

[rpietila]

The same analysis applied to my original proposal yields the following results:

Bracket	#TotalBitcoins	log(total)	1 derivative	2 der.
10k+	BTC5.50M	6.74
1k-10k	BTC2.88M	6.46	0.28
100-1k	BTC1.60M	6.20	0.26	-0.03
10-100	BTC1.00M	6.00	0.20	-0.05
1-10	BTC0.50M	5.70	0.30	0.10
0.1-1	BTC0.30M	5.48	0.22	-0.08
-0.1	BTC0.03M	4.48	1.00	0.78

Now, this is my guess, and it is now verified to behave quite well (smooth 2nd derivative) according to what we would expect from a statistical distribution (I will iron out the kinks hopefully today to have a revised model, but that will not alter much - the parameters are more significant now and there is much to be done).

[rpietila]

Here is a list of bitcoin-related activity. I would like to have better estimates available also, so please refer them here. Anyway, according to this one, bitcoin is overwhelmingly a first world thing (second world is now part of first FYI), and due to its highly technological nature, it is likely to appeal to the rich in medium and low-income countries.

A corollary would be that people who have bought bitcoins are wealthy, and therefore it is reasonable to conclude that they buy with rather large sums. My guesstimate of a typical first buy would be $100-$10000 with rather few buying either less or more. I run a precious metals shop, and also an automated silver depository. I have access to the statistical distribution of our customers' holdings, which has inspired this analysis.

Before this year, $100 would have fetched you an average of BTC10, and $10,000 would translate to BTC1,000. In 2013, $100 is about BTC1 and $10,000 would net you BTC100.

The important thing is that only a minority of people who have invested into bitcoins have less than BTC1. To fall into that category, one would have to be both poor and extremely conservative (yet willing to invest the time to learn..) and have bought in March or later, this year. All other scenarios lead to higher balance.

The history of mining can be divided into two periods: mining with existing equipment and mining with specialized equipment. When existing equipment was used, mining generated essentially free coins, and lots of them. Therefore all such miners have large balance (if any - we will later analyse the sold out phenomenon). After mining became an industry with investment calculations and GPU/FPGA/ASIC farms, the investments have generally been on par with the expected number of bitcoins generated. This kind of activity also produces rather large holders.

I have no knowledge if the bitcoin faucets and similar things have ever produced new bitcoin users/holders. I don't know what has generated the 1.5 million dust addresses (please help me!), but I doubt that it corresponds to many actual users.

On the other hand, services such as Easywallet or Instawallet (defunct) can host many users and mask their activity from the blockchain. Also exchanges can obscure the relationship between their cold wallets and the customers' balances that are stored there.

After delving into this matter in the last 1-2 days, I am tempted to drastically reduce the total number of bitcoin users, because I haven't found the mechanism that actually would have produced millions of sub-BTC1 holders so far. The number of investors will likely stay quite much the same after the update.

[rpietila]

I checked the Silvervault numbers a bit more carefully and found out that the median holding is roughly $1000. Translated to Bitcoinworld, we would have equal number of people involved in Bitcoin, with a holding above BTC5 than we have below BTC5. If this is true, the whole bitcointhing would rest on very few shoulders.

What could cause it to be untrue?
- Faucets, donations, etc. combined with difficulty to sell (can these people be counted users? If you evangelized your friends by giving them a bitcoin in 2011, it is easily forgotten and lost) In Silvervault people can easily sell if they want out so this explains a small number of small holdings.
- ...

I also arranged the Silvervault data in log-scale brackets (I used 1-2, 2-4, 4-8, ... (AGD) for granularity) and found out that the greatest density of people is in the bracket with holding value of $3,000. If we apply this, the largest number of bitcoin holders would be in BTC10-BTC100 category, followed closely by BTC1-BTC10.

Silver is currently lagging behind. Bitcoin otoh is in its ATH. After a steep runup we do well to take into account that the bitcoin holders paid a lot less for their coins than what their price now is. It might lead to a top-heavy situation with inordinate number of excessive positions. Right now I see no special need for this, since most of the bitcoin holders by number have started in 2013, and the price has been roughly stable this year at $100 as well as 2012 investors can be approximated to have bought at $10.

[jl2012]

18,741.71395637XBT are verifiably lost ( https://docs.google.com/a/ij.hk/spreadsheet/ccc?key=0Ahdy3Je_nYdOdFVocm4yTzhZOW1waWd6SFJIVHUwYUE&usp=drive_web#gid=0 ). You should deduct it

It's pretty sure that Satoshi owns/owned 1M  ( http://bitslog.wordpress.com/2013/04/17/the-well-deserved-fortune-of-satoshi-nakamoto/ ). Whether he has lost the private keys or not is irrelevant. You should deduct this amount.

The twins said they own 1% (http://www.businessinsider.com/the-winklevoss-twins-bitcoins-2013-4). Whether it means 108k or or 210k is a bit vague.

Loaded ( https://bitcointalk.org/index.php?action=profile;u=73652 ) of this forum owns 40k. Recently he had moved his coins to a new address but I guess he is still exclusively holding it.

Any other known big holders?

TL;DR:  At present only 80,000 people in the world (1 in every 20,000 people with the capability to do so) have a bitcoin holding valued at least $1,000.

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.

Assumptions and conventions:
- Bitcoins are overwhelmingly controlled by individuals (ie. no significant corporate/public sector holdings exist); if bitcoins are held by an institution, they are credited to the beneficial owner(s)
- The brackets are logarithmic; the highest bracket is BTC10,000+, second highest is 1,000-10,000, etc.  

The consensus is as follows:

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).

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.

[TheKoziTwo]

Any other known big holders?

knightmb once admitted to owning 371,000 BTC.

https://bitcointalk.org/index.php?topic=564.0

However later he made up a long story about how people asked for money and that he ended up giving away everything and donating the rest to wikileaks.

[jl2012]

Any other known big holders?

knightmb once admitted to owning 371,000 BTC.

https://bitcointalk.org/index.php?topic=564.0

However later he made up a long story about how people asked for money and that he ended up giving away everything and donating the rest to wikileaks.

Can't count it as he might have really sold or spent most of it