# Are you in the Bitcoin 1% ? A New Model of the Distribution of Bitcoin Wealth

Sep 9, 2017 · 10 min read

# Introduction

Previous models of the distribution of Bitcoin wealth all depended on an analysis of Bitcoin wallets and Bitcoin addresses. That approach fails inevitably because of the unknowable relationship between people owning Bitcoin, Bitcoin wallets, and Bitcoin addresses. This is a description of a new model of the distribution of Bitcoin wealth built on the assumption that a universal Power Law applies, and that it mirrors the distribution of global financial wealth as reported in the Credit Suisse Global Wealth Report 2016. The Bitcoin distribution that results is tweaked manually to reflect the great mining rewards paid out in the early years to a few people, making it still less equitable than the highly inequitable financial wealth distribution. An estimate of the Bitcoin-owning population is derived from a survey of traffic to Bitcoin-related websites as reported by Alexa.com in comparison to traffic to sites of popular financial corporations that publish their user numbers.

There are two parts to this essay — a) why former models based on address analysis failed, and b) the new model. Scroll halfway down if you are uninterested in the first part.

# A. Models of Distribution of Bitcoin Wealth Analyse Wallets & Addresses Data Always Fail

Previous models of the Distribution of Bitcoin Wealth have depended on an analysis of Bitcoin wallets and Bitcoin addresses. They have all been based on the Bitcoin Rich List.

The usual way to calculate the distribution is to say that 1% of 19,562,222 Bitcoin addresses is 195,622 addresses and, looking at the table, the 195,622'th wealthiest address is placed in the 1–10 Balance bracket, much closer to 10 than to 1. To make this clearer I have re-jigged the data in a Sheet:

So, the address which is the 149,238'th richest contains exactly 10 Bitcoins. That address is at 0.76% in the distribution. The address at 1% is in the 1–10 bracket and will contain a little less than 10 Bitcoins.

Some people then jump wrongly from addresses to Bitcoin holders without thinking:

Coinbase stats at September 2017:

I pointed out this error to Ari David Paul on Twitter. He did not acknowledge his mistake so it is fair to publish his fatuous Tweets. Addresses is not the same as people.

Update:

Tom Lee of Fundstrat Global Advisors, makes the same mistake. He says there are only 300,000 holders of at least \$5,000 of Bitcoin.

This is another, better attempt to describe the Distribution of Bitcoin Wealth. It is produced by Dennis Porto based based on surveys and was published in Business Insider in February 2014: How Much Wealth The Top 1% Of Bitcoin Owners Have.

This is a logarithmic chart, so it’s a little hard to read. The blue curve meets 1% at the 50 BTC mark. (In the red circle.) Is 50 Bitcoins the mean wealth of those Top 1%, or median wealth, or the minimum wealth to qualify for the 1%? It’s not clear.

The Relationship Between People, Wallets, Addresses

The problem with most estimates is that they fail to account for the fact that the relationship between Person Holding Bitcoin, Wallet, and Address is a little complicated. It is not necessarily 1 : 1 : 1. That is to say, it is not true by definition that one Person has one Wallet that uses a single Bitcoin Address.

For a start, a Person may hold many Bitcoin Wallets. And a Wallet can make use of many Bitcoin Addresses. (Indeed it is advisable to generate a new Address every time you use your Wallet for reasons of anonymity.) So the relationship can be 1 : Many : Many.

Exchange ‘Wallets’ are not real Wallets

When you hold Bitcoin at an exchange such as Bitfinex you do not actually own a genuine Bitcoin Wallet as you do not own the private keys. The security for this pseudo-wallet is provided by the exchange, not by your private keys. Sending Bitcoin to an exchange, you immediately give up ownership of it. You own nothing except a non-contractual IOU from the owners of the exchange to pay you Bitcoin. It is non-contractual because you cannot have a contract with an unknown counterparty. What is Bitfinex’s Company Registration id? Who owns it? Where are its accounts published?

The owners of the exchange will own several genuine Wallets — wallets for cold storage and hot wallets for when clients request withdrawals— containing the Bitcoins of its many clients.

Anyway, let us pretend the clients of the exchange own the Bitcoins which they sent to the exchange, and are now stored in the exchange’s Cold Wallet. We then have this relationship — Many People (millions of Bitfinex clients) : 1 Wallet (the Exchange’s cold storage Wallet) : 1 Address. We can actually see that Wallet on the blockchain:

Bitcoin Address 3D2oetdNuZUqQHPJmcMDDHYoqkyNVsFk9r is the richest Bitcoin Address in the Bitcoin Rich List. It is the only Address in the Bitfinex Cold Wallet. It contains about 120,000 Bitcoin valued at \$525 million, or 0.72% of all Bitcoins.

The owner of Bitfinex owns the Private Keys to that Wallet so he owns the Bitcoins in the Wallet. So in fact we have the nice simple relationship 1 Person (Owner of Bitfinex ) : 1 Wallet : 1 Address (with 120,000 Bitcoin).

In conclusion, the previous model of Bitcoin distribution fails because of the fundamental flaw that there is no clear-cut and predictable relationship between Persons Owning Bitcoin, Bitcoin Wallets, and Bitcoin Addresses.

# B. The New Model of Bitcoin Distribution

I have modelled the distribution of Bitcoin Wealth in a way that disregards Wallet and Address data entirely.

Assumptions

1. Power Law applies to Distribution of Bitcoin Wealth.
2. Distribution of Bitcoin Wealth exactly mirrors that of Global Wealth.
3. 25 million Bitcoin Owners.
4. No lost Bitcoins.

Model Assumption 1: Power Law Distribution Applies
A Power Law is a functional relationship between two quantities, where a change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another.

The economist Pareto devoted attention to this and conceived the 80/20 rule. Pareto showed that 80% of the land in Italy was owned by 20% of the population; he observed that about 20% of the peapods in his garden contained 80% of the peas.

Our model assumes the Power Law because it applies to so much natural life. The Power Law applies to the distribution of financial income, and of financial wealth, and of sexual wealth measured in number of partners (whether that be of Alpha lions in the African Savannah or Alpha human males in metropolitan cities), and of attention wealth measured in Twitter Followers.

From Wikipedia:

The distributions of a wide variety of physical, biological, and man-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, the foraging pattern of various species,the sizes of activity patterns of neuronal populations,the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms,the sizes of power outages, criminal charges per convict, volcanic eruptions,and many other quantities. Few empirical distributions fit a power law for all their values, but rather follow a power law in the tail.

Power law distributions look like this:

Model Assumption 2: Distribution of Bitcoin Wealth mirrors that of Global Wealth, but with adjustment for concentrated mining rewards 2009–2011

We use this assumption because, actually, why would one not make this assumption? There is one valid objection:

A a result I manhandled the model slightly to skew more ownership to the richest owners of Bitcoin than was implied by the financial wealth distribution.

Thankfully there is an excellent source of data on the distribution of global wealth: The Credit Suisse Research Institute (CSRI) Global Wealth Report 2016 pages 22–27. And CSRI Global Wealth Databook 2016, Table 2–4 p. 94.

I derived a Distribution of Global Wealth from that data.

To be in Top 1% in Global (Fiat) Wealth, you need \$770,000 Net Wealth (Gross Wealth minus Debt).

Model Assumption 3. There are 25 million Bitcoin Owners (January 2017)

I arrived at an estimate of 25 million owners (many owning Dust-like amounts) from analysis of traffic to Bitcoin-related websites, and comparing that traffic to non-crypto business sites who publish their number of users. This analysis was done in January 2017. Traffic to Bitcoin sites is much greater now (September 2017) and so there are now more Bitcoin owners than 25 million. But I don’t have the time or inclination to check all those Alexa rankings again.

Bitcoin sites get enough traffic to imply 25 m. owners of BTC. For example, in January 2017 Blockchain.info was getting similar traffic to webmoney.ru which claimed 31 m. users.

Most popular Bitcoin sites (September 2017):

1. Coinmarketcap
2. Coinbase
3. Poloniex
4. Bittrex
5. FreeBitco.in
6. Blockchain.info

To get an idea of the volume of traffic to these Bitcoin sites, let’s look at the site of Santander.co.uk, which is a (Spanish-owned) British bank which has reported that it has 14 million customers, nearly all of whom use online banking.

Model Assumption 4: No Lost Bitcoins

I made this assumption purely to simplify the model. It would be simply to augment the model with an assumption of Lost coins being equal to a certain positive amount.

# The Distribution of Ownership of Bitcoin

Having derived the distribution of Global Wealth, and the Global Ownership of Bitcoins numbers, I mapped the Wealth Distribution to derive a Bitcoin Distribution. I then skewed it a bit to make Bitcoin wealth distribution even less equitable than fiat wealth distribution to reflect rewards from early days of mining. (See how the ratio of Mean/Median is greater for the Bitcoin Distn. than the financial Distn.)

70% of Bitcoin Owners Own 2% of all Bitcoin. Who are they?

Examining the Bitcoin cumulative distribution, the richest 30% of all Bitcoin owners own 98.3% of all Bitcoins. So the poorest 70% of Bitcoin owners own less than 1.7 % of all Bitcoin. It takes merely 0.153 Bitcoins to be placed in the Top 30% richest Bitcoin owners. So who are these 17.5 million people who own less than 0.153 Bitcoin? (That is about \$665 at current prices.)

I cannot be sure, but I suspect they are people use Bitcoin faucets. (Faucet is the American English word for tap.) They might gain them from Bitcoin Faucets like Bitco.in (.IN is the Indian state domain).This site claims to have more than 7 million registered users.

The Alexa rating for Bitco.in is consistent with this claim. Indeed the traffic to this site is greater than to any other Bitcoin site excluding Coinmarketcap, Coinbase, Poloniex and Bittrex.

Bitco.in is just one of thousands of such faucets. A Google search for Bitcoin faucet comes up with 473,000 results.

#12 May 2018 Exchange Registrations

The exchanges often close the doors to new Registrations under the pressure of excessive demand. Advice is to register with these exchanges immediately while you still can:

Binance: Number 1 exchange by trading volume

Coinexchange: Low-cap alts specialist

HitBTC: Top-5 exchange with large volumes

Altcoin: Revolutionary decentralized exchange operating atomic swaps

Bitfinex: Second largest global exchange.

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