This blog was posted on our Medium page by Takens Theorem.

The Beacon chain, the backbone of Ethereum’s move to proof of stake, went live in late 2020. Interested participants could deposit ETH into the Eth2 deposit contract, enabling them to participate as validators in the Beacon chain, which fused with mainnet in the celebrated Merge in late 2022.

A few weeks ago, the newest hard fork was activated: The Shapella upgrade now allows validators to withdraw their ETH back into regular mainnet circulation. Full withdrawals — through which validators exit Beacon — are significantly rate-limited. Partial withdrawals (such as staking rewards) are also limited but have higher bandwidth: 16 per block. At the time of writing, there have been over 2,500,000 withdrawals from Beacon, amounting to over 2,000,000 in ETH.

Since Shapella, there have also been plenty of fresh depositors. Last month saw the highest concentration of Beacon deposits so far. So even with millions of withdrawals, staking on Ethereum is an order of magnitude larger than current or pending withdrawals, at least for now (see a helpful survey of this in the Coin Metrics State of the Network #203).

From Etherscan’s deposits dashboard

It was widely discussed that initial deposits into Beacon were highly concentrated, including after The Merge (see prior post here). A few parties or pools control the vast majority of the deposited ETH, raising concerns that the network is insufficiently decentralized. Only a few parties could control the majority of block production.

We can measure this concentration with the Gini coefficient. It is a measurement of how unequally distributed a good is. A Gini of 0 means that there is no concentration, indicating equal distribution. A Gini of 1 means that a single entity has all the resources in a given distribution. We can show this by plotting the rank of depositors by their relative dominance in a cumulative distribution (from 0% to 100%, adding them up).

As you can see below, this is not a flat distribution. It shows that the first 500 depositors (in either regular or internal transactions) are responsible for over 80% Beacon inputs.

This distribution of depositors has a Gini coefficient greater than 0.85. This concentration is due in part to staking services such as Lido and Coinbase. An important note by Kyle Waters of Coin Metrics and others is that these staking services involve many participants who, in theory, represent a more decentralized potential as there are many hundreds or thousands of these depositors. So the debate is nuanced (including debate about metrics like the Gini), and also involves other aspects of the proof of stake consensus framework.

How about withdrawals? Have they been concentrated?

It appears they have been intensely concentrated, perhaps more so, with a Gini coefficient of about 0.98. This is likely due in part to the exit of Kraken, as just one of the withdrawing wallets, responsible for over 600,000 ETH, flows directly into a Kraken address. But it could also be due to the relative rewards accrued by these entities. Smaller validators may have to wait longer to justify withdrawal; larger validators may exit with a very regular stream of withdrawals as they receive more rewards. Indeed, wallet 0xB9D79 shows frequent, daily withdrawals. It has received withdrawals from Beacon over 1,000,000 times alone with an average of about 0.25 ETH. It seems to belong to Lido.

- Lido withdrawal manager

Concentration like this is very common across many networks, both in the digital world and in physical and biological systems. The tendency for resources to become concentrated has been argued to be an inevitable fact of reality — the vagaries of uneven distribution, preferential attachment, thermodynamics and more (hypotheses vary). Readers may recognize this as the famous “80/20” principle — 20% of the entities control 80% of the resources, work, etc. It’s a rough heuristic, a rule of thumb. But it expresses this concentration in a familiar way (though in the cases above, it is closer to “95/5”).

For Ethereum, this has been long under discussion. Vitalik addressed this concentration years ago, shortly after Beacon went live. He argued that focusing too much on the Gini coefficient and related measures of unequal distribution may oversimplify our understanding of important underlying relationships in a social or economic system. Such relationships may better express the nature of such “inequality,” its origins, architectural implications and risks. This seems reasonable, but one could argue that (i) other possible measures of underlying relationships may still yield strong indications of concentration and (ii) there’s simply obvious concentration at a glance. In any case, Ethereum is not the sole project subject to such discussion. Many, perhaps most, are. Even Bitcoiners debate mining concentration, too.

-Bitcoin pool ranking; https://mempool.space/graphs/mining/pools

In the design of protocols that decentralize responsibility, to ensure robustness to attack or manipulation, it is an uphill battle if this distribution is indeed an inevitability of nature’s principles. But we can try to vary the slope of this concentration to make sure that it doesn’t become too skewed.

There are movements afoot to promote this in Ethereum, such as facilitating a broader base of participants in block validation and block building. For example, Flashbots, despite fears of its dominance, has nobly taken on the challenge to open-source its tools and expand participation. Alongside these advances on Ethereum, developments such as EigenLayer allow depositors to restake their ETH into other services, such as to help secure an emerging project or protocol. This expands the potential utility of staked ETH, and could alter incentives around deposits and withdrawals in the future.

I wrote this for fun for Etherscan. I was not paid by anyone. I own various cryptocurrency things, sometimes ones that I mention in my writing. You can follow me on Twitter here.