With Monero, the blockchain provides no help in determining balances. So the distribution of holdings must be constructed purely theoretically. What we use in the analysis of this post is just the following information:
- Number of XMR (about 2.2 million when this was done);
- Assumption that the distribution follows power law for the highest 3% of the holders (it does if we are talking about general wealth) - the power law distribution has the property that the owners of 100-200 coins collectively own the same number of coins as the ones owning 200-400 coins etc. But their number is 2x higher (because the other group was 2x richer), and the density is 4x more (because not only there was 2x the number of people, but also the bracket is in absolute terms only half the size);
- Below that, the distribution forms a nice bulge centered around the median holding and drops quickly towards insignificant holdings;
I have calculated 2 possibilities that give the result for both 5,200 and 13,200 holders. The results are presented in logarithmic brackets that are 0.333 log10 units wide (unlike my usual precision of 1 log unit, this gives 3 times more information). The exact form of the very top (holdings of the top-5 or so holders) affects the distribution somewhat, but with XMR it cannot be deduced either directly or statistically. I have assumed that the Case A scenario has a large outlier but Case B does not have it.
Case A - 5,200 holders:
Code:
min max avg #ppl tot.xmr
17 280 000 1 280 000
16 100 000 - 215 443 142 600 1 171 034
15 46 416 - 100 000 66 189 3 171 034
14 21 544 - 46 416 30 722 6 171 034
13 10 000 - 21 544 14 260 12 171 034
12 4 642 - 10 000 6 619 26 171 034
11 2 154 - 4 642 3 072 56 171 034
10 1 000 - 2 154 1 426 120 171 034
9 464 - 1 000 662 300 198 468
8 215 - 464 307 750 230 301
7 100 - 215 143 1 349 192 413
6 46 - 100 66 1 349 89 310
5 22 - 46 31 750 23 030
4 10 - 22 14 300 4 276
3 5 - 10 7 120 794
2 2 - 5 3 36 111
1 1 - 2 1 11 15
17 280 000 1 280 000
16 100 000 - 215 443 142 600 1 171 034
15 46 416 - 100 000 66 189 3 171 034
14 21 544 - 46 416 30 722 6 171 034
13 10 000 - 21 544 14 260 12 171 034
12 4 642 - 10 000 6 619 26 171 034
11 2 154 - 4 642 3 072 56 171 034
10 1 000 - 2 154 1 426 120 171 034
9 464 - 1 000 662 300 198 468
8 215 - 464 307 750 230 301
7 100 - 215 143 1 349 192 413
6 46 - 100 66 1 349 89 310
5 22 - 46 31 750 23 030
4 10 - 22 14 300 4 276
3 5 - 10 7 120 794
2 2 - 5 3 36 111
1 1 - 2 1 11 15
Largest holdings:
1. 280,000 XMR
2. 147,000 XMR
3. 80,000 XMR
4. 65,000 XMR
5. 50,000 XMR
top holding: 280,000 XMR
top 10: 22,500 XMR
top 100: 2,200 XMR
top 1000: 285 XMR
# of holders: 5,188
avg holding: 427 XMR
== 1.92 BTC
== 1,211 USD
median holding: 100 XMR
half of the coins belong to 43 people
Case B - 13,200 holders:
Code:
min max avg #ppl tot.xmr
17
16 100 000 - 215 443 142 600 1,2 165 745
15 46 416 - 100 000 66 189 2,5 165 745
14 21 544 - 46 416 30 722 5,4 165 745
13 10 000 - 21 544 14 260 12 165 745
12 4 642 - 10 000 6 619 25 165 745
11 2 154 - 4 642 3 072 54 165 745
10 1 000 - 2 154 1 426 116 165 745
9 464 - 1 000 662 291 192 329
8 215 - 464 307 726 223 179
7 100 - 215 143 1 816 258 976
6 46 - 100 66 3 632 240 412
5 22 - 46 31 3 632 111 589
4 10 - 22 14 1 816 25 898
3 4,6 - 10,0 6,6 726 4 808
2 2,2 - 4,6 3,1 291 893
1 1,0 - 2,2 1,4 87 124
17
16 100 000 - 215 443 142 600 1,2 165 745
15 46 416 - 100 000 66 189 2,5 165 745
14 21 544 - 46 416 30 722 5,4 165 745
13 10 000 - 21 544 14 260 12 165 745
12 4 642 - 10 000 6 619 25 165 745
11 2 154 - 4 642 3 072 54 165 745
10 1 000 - 2 154 1 426 116 165 745
9 464 - 1 000 662 291 192 329
8 215 - 464 307 726 223 179
7 100 - 215 143 1 816 258 976
6 46 - 100 66 3 632 240 412
5 22 - 46 31 3 632 111 589
4 10 - 22 14 1 816 25 898
3 4,6 - 10,0 6,6 726 4 808
2 2,2 - 4,6 3,1 291 893
1 1,0 - 2,2 1,4 87 124
Largest holdings:
1. 137,000 XMR
2. 80,000 XMR
3. 65,000 XMR
4. 50,000 XMR
top holding: 137,000 XMR
top 10: 20,500 XMR
top 100: 2,150 XMR
top 1000: 270 XMR
# of holders: 13,234
avg holding: 167 XMR
== 0.75 BTC
== 473 USD
median holding: 46 XMR
half of the coins belong to 150 people.
