Are there statistics on how Bitcoin holdings are spread among addresses?

Question

I'm aware an address can belong to multiple people, and one person can have multiple addresses. Still, I'd like to assume the number of accounts per person is O(1) on average.

Are there statistics on how much the bitcoin holdings are spread between different addresses - in other words, on whether a few addresses hold a large portion of the bitcoins, or rather is it spreading out slowly?

Ideally I'd like to see a graph of this "measure of spread" over time.

Related Questions

Is it possible to estimate the Gini coefficient for Bitcoins and if the trend is increasing or decreasing?

Answer 1

I don't know if any of this data is of any use or significance, but...

I calculated the Gini coefficient at the end of each month of Bitcoin's history. I did it in two different ways:

• The vast majority of Bitcoin addresses that have ever been used are now empty. They don't represent the "have nots", they're just addresses that have been used and discarded, and so shouldn't be included in the calculation. Similarly there will be lots of addresses which are holding change from transactions. I arbitrarily decided to throw away all addresses with a balance of less than 1 BTC for this first calculation.
• Then I calculated the Gini coefficient for just the 100 richest accounts at the end of each month.

The results are shown below, with the columns in order:

• the date. "Jan 09" means "the end of Jan 09"
• the total number of addresses in existence at that date, including empty ones
• the number of addresses with 1 BTC or more in them
• the amount in the richest account
• the amount in the 100th richest account (notice how this stayed at 50.00 for over a year)
• the Gini coefficient of the >= 1BTC addresses
• the Gini coefficient of the top 100 addresses

 

-date-   addresses    >1 BTC   1st - 100th richest   Gini >1   Gini100
Jan 09       2,569     2,439     2775.00 -   50.00   0.04571   0.50862
Feb 09       5,975     5,642     9075.00 -   50.00   0.05064   0.71354
Mar 09       9,444     8,864    16675.33 -   50.00   0.05794   0.82048
Apr 09      12,893    12,120    21175.33 -   50.00   0.05715   0.85527
May 09      16,288    15,380    26675.33 -   50.00   0.05306   0.87075
Jun 09      18,528    17,534    30675.33 -   50.00   0.05118   0.87980
Jul 09      20,456    19,338    36675.33 -   50.00   0.05248   0.89165
Aug 09      22,021    20,741    44473.86 -   50.00   0.05617   0.90351
Sep 09      24,180    22,639    53974.86 -   50.00   0.06188   0.91664
Oct 09      26,311    24,366    61424.62 -   50.00   0.07208   0.92725
Nov 09      28,533    26,403    61424.62 -   50.00   0.07279   0.93164
Dec 09      32,611    29,818    61424.62 -   50.00   0.08352   0.92241

-date-   addresses    >1 BTC   1st - 100th richest   Gini >1   Gini100
Jan 10      37,647    34,333    72374.36 -   50.00   0.08571   0.92339
Feb 10      43,329    37,262    72374.36 -   50.00   0.13683   0.88570
Mar 10      48,615    40,316    72374.36 -   50.10   0.16674   0.82492
Apr 10      57,806    42,661    72374.36 -  500.00   0.21059   0.71037
May 10      63,368    44,583    72374.36 -  630.00   0.24448   0.65747
Jun 10      69,540    46,963    72374.36 -  750.00   0.26638   0.62843
Jul 10      94,992    51,628    72374.36 - 1757.14   0.32583   0.56689
Aug 10     107,172    53,578    72374.36 - 2100.02   0.35365   0.52483
Sep 10     120,562    53,492    72374.36 - 3000.00   0.39915   0.46956
Oct 10     135,952    54,637    85000.00 - 3333.33   0.42841   0.46050
Nov 10     155,639    55,756    90000.00 - 4150.00   0.45464   0.43790
Dec 10     176,326    57,247    90000.00 - 5000.00   0.47592   0.38625

-date-   addresses    >1 BTC   1st - 100th richest   Gini >1   Gini100
Jan 11     210,243    58,073   250000.00 - 5350.00   0.49987   0.47440
Feb 11     267,542    59,699   250000.00 - 5650.51   0.52439   0.47584
Mar 11     353,093    61,984   250000.01 - 5613.86   0.54646   0.45504
Apr 11     443,112    64,254   200000.00 - 6002.81   0.57161   0.46808
May 11     631,480    70,883   297000.00 - 6309.40   0.62830   0.49247
Jun 11   1,061,590    90,159   424242.42 - 6308.24   0.70803   0.52602
Jul 11   1,548,806   101,895   384587.42 - 6450.00   0.73473   0.50905
Aug 11   1,930,979   105,572   104895.01 - 7495.92   0.74448   0.41533
Sep 11   2,205,926   106,973   105000.00 - 6926.85   0.74847   0.45014
Oct 11   2,411,298   110,463   105000.00 - 7345.73   0.75422   0.44981
Nov 11   2,601,999   111,386   455501.30 - 6926.85   0.76065   0.51328
Dec 11   2,768,500   118,263   105555.00 - 6705.00   0.76137   0.41685

-date-   addresses    >1 BTC   1st - 100th richest   Gini >1   Gini100
Jan 12   2,956,869   123,003   105555.00 - 7000.00   0.76883   0.42408

Answer 2

There is TOP 100 rich list, but you have to take it with a grain of salt because:

• many holders have their money spread over multiple addresses
• I believe many of TOP 100 belong to MtGox account holders

If you want extended list, you could probably contact the author of that list or ask a programmer to build it. Should't be too hard to do.

Answer 3

There is no such concept as an "account" or "wallet" in the Bitcoin network. The Bitcoin network only records addresses. Some clients organize one or more addresses into an account and one or more accounts into a wallet however this structure is "client side" and the network/protocol is unaware of it. Not all clients use this type of organization.

If you are talking about addresses. Sure you can see which addresses have the most value and how many addresses exist with some value but that isn't easily correlated to a specific entity. As an example, my wallet currently has >200 unspent outputs in >100 addresses. There are also about 400 used addresses which contain no unspent outputs (0 value). An individual's coins are unlikely to be all stored in a single address even if they are stored in a single wallet unless they make a conscious decision to do so (i.e. offline paper wallet).