Notes on the Bitcoin wealth distribution

We have received a few inquiries about the distribution of Bitcoin wealth as implied by our stats and richlist pages. Our site has also been used by some media outlets as a source for this kind of statistics. See, e.g.

We feel that we ought to give some qualifications about this kind of claim. Statistics about the distribution of bitcoin in addresses, or even in the kind of partial wallets we infer, are probably very misleading about the actual wealth distribution, because addresses are not people! This goes both ways: Neither do people just own one address (Most active bitcoin users would own at least hundreds and when they have been using best practices we do not associate these addresses as partial wallets), nor does every address just belong to one person (Consider the richest addresses, which are mostly exchange addresses. These can stand for millions of people!). Andreas has explained this most clearly here:

Before watching this video, I had always somehow assumed that the distribution in addresses can be used as an approximation of the true wealth distribution. But in fact this is highly dubious. Any given distribution (or Gini coefficient) on addresses could easily be transformed into an arbitrary wealth distribution by grouping or splitting addresses: Consider the edge cases where every address belongs to the same person or every address is shared by all users.

Jorge brought up an interesting view on this: The distribution we are measuring is really just the distribution of UTXO values, which could be seen analogously to banknote denominations in traditional money!

As an example, I tried calculating the Gini coefficient for the British Pound denominations given here. If my calculations (pen and paper!) are correct, it’s about 0.2654320. However, should this be read as an indication that British wealth is very evenly distributed? Hardly! It just means that their banknotes values don’t differ across multiple orders of magnitude.

Unlike the Bitcoin UTXO set, which clearly does. There are millions of outputs with just a few satoshis in them, as well as a few that have more than 100,000 BTC, which is about 10 trillion times as much! However, Bitcoin’s Gini coefficient means just that. Outputs vary very widely in value. This does NOT imply anything about the wealth distribution of Bitcoin hodlers.

Personally, the true wealth distribution remains an interesting question for me. In fact, it was what made me start this project. So how could we find more valid approximations? Well, exchanges might have a pretty good idea. Or web wallets. Have any of them published any statistics? Has the Mt.Gox leaked data been analyzed in this direction? If not, then maybe it’s time to do so!