How to scientifically measure the distribution of blockchain assets such as Bitcoin?

The distribution of cryptocurrency assets has been a controversial topic. The focus of debate is whether the cryptocurrency assets are too concentrated. Does this prevent people from adopting it?

(In the eyes of laymen, 2% of Bitcoin addresses control 80% of Bitcoin wealth)

Although this is a very important issue, before we can answer it, we have to figure out a question. What metrics do we use to measure it?

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In this week's analysis, we will discuss how to define and measure the distribution of cryptocurrency assets and view data for some head assets.

First, it is important to distinguish between wealth distribution and income distribution. The wealth distribution is different from the income distribution. In all national economies, the distribution of wealth is significantly lower than the income distribution.

According to the 2018 World Economic Forum (WEF) Inclusive Development Index, “in recent years, this problem has hardly improved and wealth inequality has increased in 49 economies.”

The table below highlights the differences between the five most productive national economies in the study sample and the most evenly distributed (Iceland) and least distributed (Namibia) economies. In the United States, the distribution of wealth is 2.3 times less than the income distribution, as measured by the Gini coefficient. The Gini coefficient is a statistical measure of distribution with coefficients between 0 (or 0%) and 1 (or 100%), with 0% indicating complete equality and 100% indicating maximum inequality.

Table 1: Distribution of wealth and income in selected countries in the 2018 World Economic Forum Inclusive Development Index

Before we turn to cryptocurrency, there is another key point worth mentioning: the definition of “wealth” in the WEF index report refers to the value of all financial assets plus the family’s actual assets (mainly housing) minus liabilities. Therefore, the wealthy Gini index measures the distribution of multiple assets, which measure the distribution at the household rather than the individual level.

When comparing these metrics to cryptocurrencies or other asset classes, it is important to extract the differences.

Measuring the distribution of crypto assets wealth: address issues

Since the crypto assets are not the national economy, and we are unable to obtain the exact number of individuals or households participating in the crypto-asset network, we (1) cannot measure the income distribution, and (2) we can only use the metrics such as addresses to measure the wealth distribution (the address is encrypted) An identifier consisting of the letters and numbers of the asset account). And this creates two problems:

1. The address can be owned by individuals and businesses (or other individual groups) ;
2. An entity can have multiple addresses ;

Addresses are not only about individuals, but also about businesses and other groups. To complicate matters, since any individual or group can have multiple addresses, it is impossible to determine the number of individuals represented by the encrypted asset address. On the one hand, an exchange address can represent millions of individual users. On the other hand, a person can have millions of addresses.

Therefore, in order to measure the distribution of cryptocurrency assets by address, we need to use a unique approach and should not compare it with traditional methods for other asset classes.

With this in mind, let's look at some useful indicators for measuring the allocation of cryptocurrency assets.

Cryptographic currency wealth Gini coefficient

The wealth Gini coefficient of crypto assets is often used as a means of emphasizing the assumed inequalities in cryptographic assets. Many people have cited some previous attempts, such as this article by Balaji S. Srinivasan. (For a description of how to calculate the Gini coefficient, see Balaji's article)

Calculating the wealth of the Gini coefficient through various cryptographic assets requires considerable effort, which is a measure that Coin Metrics is trying to add. In the meantime, it is necessary to reiterate the following challenges: (1) calculate the indicator; (2) use the indicator to compare the cryptographic assets with external networks such as the national economy.

The first is the choice of sampling unit. As mentioned above, for national economies, the sampling unit is usually a family. For cryptographic assets, we can't measure individuals or families, so we have to use addresses to measure (it's difficult to choose a subset of addresses to sample).

Not only in the sampling unit, but here we also measure the distribution of individual cryptocurrency assets, rather than when calculating the wealth Gini coefficient in the national economy (calculating all assets of the family minus liabilities).

Other wealth distribution indicators

In addition to the Fortune Gini index, we can also look at several other metrics to gain insight into the distribution of cryptographic assets. The following is the distribution of the top five encryption assets before August 17, 2019.

Table 2: Distribution of wealth of the top 5 crypto assets by market capitalization

BTC is by far the oldest cryptographic asset, and its most widely distributed metric is the number of addresses with a valid balance (defined as an address with at least one billionth of a supply). However, the (average/intermediate) address balance of the bitcoin address is the highest, and in addition, the value of the address balance is more than one million dollars, and bitcoin is the most.

In addition to BCH (BTC forks), ETH ranks second in these data, although it is the youngest. ETH not only has a large number of meaningful balance addresses, but also has a low average address balance. However, the comparison between different networks is not straightforward. Ethereum's gas charging mechanism tends to leave more dust addresses (dust, which means accounts with less than the cost of the transaction). This can make the distribution of ETH more uniform by lowering the average account balance. On the other hand, Ethereum is also an account-based protocol. Compared to UTXO-based protocols, users based on account agreements often reuse addresses, which makes account-based protocols appear less evenly distributed when using address-based metrics.

In this asset sample, the distribution of XRP is the most uneven .

Keep in mind that many of the above metrics are affected by the market value of assets. Since BTC has the highest market value, it seems to have a higher concentration of wealth. If we expand the size of non-BTC assets to the same market value as BTC and multiply all the indicators by this multiple, an interesting picture will appear. But we also have to be careful to emphasize these data, because the BCH forks are somewhat different.

Table 3: Distribution of wealth after the top 5 crypto assets are extended to the BTC market value

Finally, an important consideration in the distribution of asset wealth is time. The BTC, the oldest asset in the table below, clearly demonstrates this. The current distribution rate can be seen from the slope of these trend lines. For example, using the trend line slope at the time of chain release, we would expect 218 new addresses to hold at least 1 BTC per day. However, since the early release of the Bitcoin network is unlikely to represent today's distribution model, it may make more sense to adopt the most recent slope.

Figure 1. Number of addresses with at least X BTC units

Table 4: BTC distribution band curve slope

Below are the distribution maps for several other assets.

Figure 2. Number of addresses with at least X XRP units

Figure 3. Number of addresses with at least X ETH units

Figure 4. Number of addresses with at least X BCH units (starting from the fork date)

Figure 5. Number of addresses with at least X LTC units

In summary, measuring the distribution of crypto assets wealth requires a new approach. It requires the use of addresses that do not correspond exactly to individuals or households, and measures only the wealth of a single asset (not all household assets minus liabilities), so it cannot be directly compared to traditional wealth distribution measurement methods in national economies. In the coming months, Coin Metrics will continue to publish more research on this topic.

Network data summary

For the mainstream encryption assets, last week was a tough week. The market value of BTC fell by more than 10% last week, and the market capitalization of ETH, XRP and LTC also fell by at least 10%. However, the realized market value of these five assets has remained relatively stable .

In terms of the number of transactions, adjusted transfer value and daily expenses, the above assets have also declined. Both LTC and XRP suffered a particularly severe blow. The transfer value of XRP adjustment decreased by 31.5%, and the daily cost of LTC decreased by 39.6%.

In terms of computing power, the LTC decline is very obvious, which is 11.3% lower than last week, BTC's computing power is reduced by 4.6%, ETH is relatively stable, and BCH is up 5.7%.

The correlation between mainstream cryptographic assets has remained high for the past week.

The synchronization of the three major encryption assets is even more obvious.

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