Modeling Ethereum node MEV: How much do nodes earn?

Original title: "Post-Merge MEV: Modeling Validator Returns"

Original author: pintail

Original compilation: Kxp, BlockBeats

To commemorate the merger (also known as the Paris hard fork), a giant Ethereum logo has been erected at the Louvre the central.

Summary

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After the proof-of-work mining era ends, execution layer transaction fees will be paid to proof-of-stake validators. Due to the EIP-1559 fee burn, the vast majority of the remaining fees actually paid to validators is "Maximum Extractable Value" (MEV).

After the merger, Ethereum will have a fixed 12-second block interval instead of a variable block interval of 13.5 seconds on average. However, this change may not have much impact on MEV instability.

From March 2022 to August 2022, the level of MEV reaching miners has been relatively stable, albeit low.

A model based on paying the same level of MEV to validators after the merger shows that the median return for validators is 6.1% APR (including MEV and consensus layer rewards) , the lower quartile is 5.3%, and the upper quartile is 7.3%. This is based on data from the past 6 months (March 2022 to August 2022).

Users who run multiple validators or share revenue with other validators (e.g. via liquid staking providers) will experience lower levels of volatility in their earnings .

Introduction

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As Ethereum continues to transition to the Proof-of-Stake (PoS) beacon chain as the mainnet's consensus engine, many media outlets are focusing on the end of the proof-of-work mining era , and the attendant energy usage issues and reduced ether issuance (PoS is more secure and resistant to centralization). However, another consequence of the beacon chain taking over transaction inclusion and ordering responsibilities is that transaction inclusion fees currently paid to miners will instead be paid to block producers. That is, any randomly picked validator will publish a block every 12 seconds.

The way of selecting validators and producing blocks has not changed from the existing procedures, just as I As mentioned in the first post on validator rewards, even if validators fully participate, this process will generate some random variation in income. So, for this article, the question is to what extent validator earnings will be affected by the fees they receive for including transactions into the Ethereum execution layer.

The specific meaning of MEV

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In the title, I referred to the fees for these execution layers as "MEV", but this may cause some confusion as the term MEV can mean both "miner Extractable value", which can also mean "maximum extractable value" - neither of these terms seems to accurately describe the rewards validators get for including or ordering transactions in the merged Ethereum block. To reduce ambiguity, the Flashbots team introduced the term "realized extractable value" to describe the value actually achieved, rather than the theoretical maximum. However, this naming method can also cause some misunderstandings, and we still can't clarify whether the value is the value "realized" by the searcher, or the actual amount paid to the miner/validator. So, for the sake of simplicity, since the term "MEV" is already widely used, I will use it here to refer to the revenue earned by miners/validators.

So if we can use such direct words as transaction fees, why choose What about a fancy term - MEV? The main reasons are as follows: Since Flashbots introduced the fork of Ethereum’s mainstream execution client geth, the income of transaction recording and sorting has undergone tremendous changes. As of August 2022, about 74% of Ethereum's hash rate is running mev-geth, so that miners can receive more time-sensitive transaction bundles to obtain income, and get rewarded with direct payments (previously the money was It was consumed during the Gas fee auction).

Furthermore, mev-boost, developed in collaboration between Flashbots, the Ethereum Foundation and the client team, enables Validators profit from the same combined revenue stream. In fact, regardless of whether validators choose to run mev-boost, the block fees they receive still belong to MEV in a broad sense. More importantly, since the London hard fork introduced EIP-1559, the congestion fee in the transaction fee is no longer paid to miners, but is burned. What this means is that the vast majority of miners’ revenue now consists of transactions that pay a special premium for their captured value, or MEV, since those less time-sensitive transactions pay miners a nominal fee.

Early model

In my previous article on validator rewards, I only focused on the rewards validators get for participating in the beacon chain (i.e. the consensus layer). Building on this, in July 2021 Flashbots' Alex Obadia and Taarush Vemulapalli presented their early results on the impact of introducing MEV for validator rewards. To this end, they exclusively obtained Flashbots transaction bundle data from a sample of approximately 100,000 blocks. First, they averaged across blocks and applied a fixed value of MEV to each block. They then looked at the 1st and 99th percentiles in this dataset to determine the income range of the validators (which turned out to be significantly different).

In this article, I will further improve this method by:

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1. Observe the overall picture of the fee income (not just the Flashbots bundle), because from execution All miner fee income of the layer can be identified as some kind of MEV

2. Use a larger-scale data set and consider the change of MEV level over time

3. Yes Model the distribution of the entire result

4. Calculate the change of the result distribution of running multi-verifier users

One observation in the above article is that it is difficult for us to infer how EIP-1559 has affected the fees paid to miners (at the time of writing, the introduction of EIP-1559's London hard fork is not live yet). However, we now have a lot of data on this. In the image below we can see that the portion of the fee that was originally paid to the miners was wiped from the ether supply after the London hard fork. Obviously, the data before and after the London hard fork are not comparable. For this reason, in this post, we will only be dealing with the post-London hard fork data.

# imports / definitions / db connection

# get block summary data from db as pandas dataframe

# plot daily fees/coinbase transfers

Select data set

In this article, we will use historical data to make predictions about the future (this method is used in financial event is not reliable). As I explained in my previous post, the transaction fee market has undergone major changes in August 2021 due to the implementation of EIP-1559 in the London hard fork, which went live at block 12,965,000, Therefore, data prior to this point are not comparable to recent data. The hard fork after this was Gray Glacier which went live at block height 15,050,000 , and pushed back Ethereum's difficulty bomb. But before that, the average block interval has already started to change. The block interval will change later, but it seems to have a limited impact on usable MEV, so we don't have to worry about it Gray Glacier previously had issues with a slight increase in the average block interval.

So we have over a year of usable data since the London hard fork. In fact, we might as well use exactly one year of data to allow time for the fee market to settle. We will focus on blocks in the range from block 13,136,427 (first block mined on September 1, 2021) to block 15,449,617 (last block mined on August 31, 2022). These blocks contain a full year's worth of data, totaling approximately 2.3 million blocks.

After choosing this block range, we need to determine how many miners are in each block income. To do this, we'll use Flashbots' mev-inspect-py tool, which is used to scrape blocks of "Coinbase Transfer" transactions, and aggregate fees. This is because there are currently two main ways to pay miners, including Flashbots bundle transactions with MEV - either setting a sufficiently high transaction fee, or paying miners directly as part of the transaction. Seekers have been preferring to pay miners with gas fees rather than Coinbase transfers due to the more efficient gas fees. Nonetheless, we would like to include both in our dataset for a more comprehensive picture.

In order to determine the MEV amount of each block, we have to do more work. First, we must exclude transactions in which miners pay themselves, since these transactions do not make economic sense. Therefore, we need to identify multiple addresses controlled by a mining pool (this involves some manual reconnaissance on Etherscan), then label each transaction based on whether the sender address is in a pool group, and based on the Transaction pools to annotate each block. Once this is done, we have the opportunity to generate a per-block MEV digest, minus EIP-1559 burnt ether and pool transfers, and save the result as an extra in the Postgres database populated by mev-inspect-py sheet.

Finally, it turns out that one of the transactions had a higher transaction fee than any other much (7676 ETH). In fact, this transaction fee alone was worth about $23 million, a large percentage of all MEV withdrawn during this period. In this case, the high fees were the result of a mistake, and the vast majority of fees have already been refunded by miners. With this in mind, I chose to remove this transaction from the dataset.

Block Interval

Before we start looking at the distribution of miner revenue across blocks in more detail, we should pause to consider another post-merge change, namely that the block interval changed from Random (about 13.5 seconds between blocks on average) becomes a fixed 12 second block interval. Intuitively, we might think that a longer block interval would give miners more opportunities to harvest MEV from incoming transactions, and thus more block profits. We might also think that a change in the block interval greatly affects miners' income.

I also address this issue in the appendix. Now, suffice it to say that, on the face of it, variable block intervals seem to have very little impact on miner revenue. In the following, I will show that the average frequency of blocks increases slightly, from an average interval of 13.5 seconds to 12 seconds, by inversely scaling all miner revenues by this ratio. However, I won't be modeling what happens when going from variable intervals to fixed intervals.

Historical MEV levels

Let's take a look at the two graphs below to see how much MEV a miner can expect to earn in a typical block. From the histogram we can see that the miner income per block tends to be very low. The second graph may be slightly less intuitive, but it's actually more informative. We can see that the median miner income is 0.07 ETH. Several other points are also marked in the graph, with the lowest 1% of blocks paying miners no fees at all, and the highest 1% of blocks paying miners over 1.8 ETH in fees. As shown in the table below (but not on the graph, as this would distort the axis too much), the top 0.1% of blocks paid miners 12.5 ETH or more in fees.

# plot block revenue histogram and empirical cumulative density function (ecdf)

MEV Trend

The histogram and ECDF above are based on our entire year of data and plotted as a static distribution. However, we might argue that the level of miner income will change over time, and that the distribution of miner income will depend on various factors, such as the level of on-chain activity, trends in the proportion of available MEV paid to miners, or the relationship between L2 The MEV value available on the base chain compared to the blockchain.

To make this clear, the graph below shows the median block reward for each week in the dataset number, the population median we saw earlier is represented by the dashed red line. The reason for using weeks as a unit is that we found that the activities on the chain will have certain periodic changes every week, for example, there are relatively few activities on weekends. Therefore, by grouping these data and extracting the median, we remove the periodic noise. Obviously, in this chart, the median weekly level of miners' income is on the decline as a whole, and the fluctuations are gradually easing. If we bisect the icon with the dotted orange line, then we can see the two halves as two separate parts representing the level of MEV paid to miners under different network/market conditions. What we need to take away from this, however, is that we cannot place a great deal of confidence in any estimates of future revenues based on historical data (keep this in mind, as this is what I Content).

# Look at variation across the dataset

Since miner income levels in our year-long dataset are not stable, we can compare the before and after parts of the dataset in a more granular way. The figure below shows the ECDF of the two parts of the dataset, where the blue line represents the first half of the dataset, the orange line represents the second half, and the blue line is significantly lower than the orange line. The x-axis shows income data, and at each quartile, miner income levels are higher in the first half of the dataset. The ECDF for the entire dataset shown in the previous graph would fall between these two lines. As shown in the table below, the median MEV of each block in the subsequent six months is roughly half that of the previous six months.

# Generate ECDFs for the first half of the dataset versus the second

Simulation of the rate of return of MEV after the merger

So, combining what we know about miners' historical block revenues, let's simulate a validator's MEV revenue over the course of a year. Since we are now considering validators and not miners, I will express the result in terms of a percentage return of 32 ETH. We haven't come up with a specific analytical expression for the distribution of revenue per block (it's hard for me to come up with a reasonable expression with the help of Pareto distribution). This complicates the modeling a bit, so in this case we will use a Monte Carlo simulation.

The principle of this method is very simple: generate a uniform distribution between 0 and 1 random number, and use this number to do a lookup from the ECDF we calculated earlier (the ECDF is scaled to account for the change in average block interval from 13.5 seconds to 12 seconds); then, distribute the revenue from that block to a Randomly selected validators; finally, the process is repeated until we have a year's worth of simulated blocks (2,629,746 blocks in total). We will perform three such calculations, using the ECDF for the full year dataset, and the ECDF for splitting the dataset into two parts.

We will assume validator behavior is good (no missing block proposals). We will also use a validator set size of 420,000, which is close to the size of the August 2022 validator set. This number of validators can also be divided into exactly 32 groups, which will be very useful when we study validator groups later.

# simulate a year's worth of block proposals

# plot ECDF and histogram for single validator return

Therefore, using the median as a basis, when based on the "high MEV" period (i.e. September 2021 MEV appears to add about 3 percentage points to a validator's APR when we use data from the "low MEV" period (March 2022 to August 2022) About 1.5 percentage points. However, some validators earn almost nothing in MEV over the course of a year, while a lucky few can earn more than 100%.

Build a complete validator reward model

Now that we can see approximate validator MEV payoffs, let's complete the simulation by introducing proofs and synchronizing committee rewards. Since beaconcha.in often shows a participation rate of over 99% on the beacon chain, we are here to Simplification can default to all participation. In practice, if the situation we see on mainnet today persists post-merge, the main reason for changes in validator rewards will be due to randomly assigned block producer responsibilities, sync committees, and MEV, not due to validator Performance.

Therefore, in the simulation below, all verifiers will get the same rewards, but every 256 epochs a committee of 512 validators is randomly selected, and that committee is then rewarded with full sync committee rewards for their full participation in the subsequent 256 epochs. The selection of MEV per block is the same as before, but validators now receive beacon chain block rewards, as well as execution layer transaction fees (MEV).

# model full validator returns using previously calculated MEV ECDFs

# plot simulated full validator returns

So, based on our full year historical MEV dataset, and taking into account the reduction in the mean interval, we have The simulated returns for the “middle 50%” of validators are roughly between 5.7% and 8.5%. At the same time, the “luckiest 1%” of validators will have an annual return of 30%, while the “unluckiest 1%” will only have 4.2%. The least profitable validator in the entire system still made a return of 3.8%, while the most profitable validator returned more than 4500% (or 45 times) during the year. However, the rate of return in this model does not include compound interest. In a real-world scenario, operators earning such large rewards may choose to set up new validators and earn even more as a result.

Run Multiple Validators

The last question we want to consider is what distribution of rewards there will be for stakers running multiple validators. In the chart below, validators in our simulated set (based on block revenue data for an entire year) are divided into groups of 2, 4, 8, 16, and 32 validators to compare ECDFs for different group sizes annual rate of return. The dashed red line in the figure represents the average reward rate for the entire validator set (i.e., the reward each validator would receive if all MEV and beacon chain rewards were shared equally). We expect the average rate of return to be what a large group of validators (such as Lido, or very large institutional stakers) earns before any fees are deducted.

# calculate ECDFs for 1, 2, 4, 8, 16, 32 validators

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From the table we can see that the larger the verifier is, the steeper the ECDF line will become. This is equivalent to the narrowing of the peak of the histogram, indicating that as the size of the verifier increases, the volatility of the return will continue to decrease. Not only that, but we can also observe that while running a single validator has an interquartile range (i.e. the difference in APR percentage between the 25th and 75th percentile) of about 2.8 percentage points, for 32 validators For the group, the interquartile range was only 1.2 percentage points.

This is what we expect to see - by running multiple validators, we Fluctuations in rewards from the consensus layer and the execution layer can be smoothed out. To my surprise, the return volatility (measured in the interquartile range) of a group of 32 validators is only about 2.3 times lower than the return volatility of a single validator. This is quite a good result for some, because they want their returns to be more stable and predictable, and this will also make the data distribution more concentrated (in this case, if the return level is positive If the distribution is dynamic, then increasing the pledge by 32 times will reduce the return volatility by 325.8 times). Barnab Monnot (Head of the Robust Incentives Group at the Ethereum Foundation) has done some initial work on this. He found that the tendency toward concentration of wealth may be the result of an uneven distribution of rewards, though this remains an open question.

Conclusion

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In this post, we attempt to use past data to model the effect of merged executive layer fees on validator returns. We found that MEV increased returns to validators by about 3 percentage points when we used data from a period of high MEV (September 2021 to February 2022), but when using data from a period of low MEV (2022 March This figure drops to 1.5 percentage points when data are available for the period from August to August 2022. In both cases, the level of rewards was rather volatile, with some validators receiving almost no MEV over the course of a year, and some earning far more than 100% annual returns. When we added consensus layer rewards, we found that well-behaved validators would earn at least 3.8% APR, with a median annual return of roughly 6.1% (on a low MEV dataset) to 7.6% (on a high ). We found that groups of validators have smoother returns than a single validator, although (at least to me) this effect is less pronounced than expected, with a group of 32 validators showing more volatility than a single validator. The volatility is about 2.3 times lower.

However, past performance is no guarantee of future returns. We do not yet know the extent to which MEV will be used by validators in the future, and what proportion will be ultimately obtained by other actors (applications, users, L2 sequencers, builders, relayers...). Therefore, the modeling results in this paper are not predictions of the future, but merely suggest several possible scenarios.

< p>At the end of the article, I haven't talked about such a problem: after the merger, we can know the identity of the block producer of a certain slot in advance. As things stand, this change on proof-of-stake blockchains opens up new possibilities for atomic cross-chain transactions as well as multi-block MEV (since validators with a significant percentage of stake may be deployed on multiple blockchains synchronized block proposal). However, how these functions will be implemented is still a big unknown. Nonetheless, I hope this post gives validators some ideas about where they are going in Ethereum post-merger and how they should think about their own benefits, and maybe this will help Proof of Stake in the coming weeks and months as well. And a few years to build their own ecology.

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