Dear NOs, LDO holders, and stakers  more than one and a half years have passed since The Merge and a lot has changed in our space, not only with Dencun, but also the launch of Lido V2, onboarding wave 5 of the curated set, the longawaited release of the Simple DVT module to mainnet, etc.
We have seen the protocols develop and new findings, dashboards, and tools being published with regard to MEVBoost, the block builder and relay markets, the Lido on Ethereum relay lists [a, b], timing games around bid size maximization, and on the validity of the assumptions made right after the merge [c, d]  e.g. about the opportunity costs of minbid based censorship resistance in proposer/builder separation (PBS) [e, f] as well as the adoption of respective optional configurations by Lido’s curated NOs [g, h].
This has prompted fellow DAO contributor @Greg_S and myself to revisit the topic of minbid to, collaboratively with you, identify the best possible approach for it on Lido on Ethereum today.
Status quo
In contrast to the original assumption of around 60% optins, up to and including VaNOM Q1/2024, only 5/37 ≈ 13.5% of the curated NOs selfreported that they had configured some form of minbid. Furthermore  checking the Lido Fees Dashboard  only about 8026/58246 ≈ 13.8% of all blocks proposed by validators run by the curated NO set in the last month had an unknown payload source  which, for the sake of simplicity, can be equated with nonrelayed, locally built (“vanilla”) blocks. Taking those 13.8% as a rough differentiator between NOs using minbid (those with a higher percentage of blocks proposed with unknown PS than the reference) and those who do not (lower percentage), within the last month 6/37 ≈ 16.2% of them seem to have had minbid configured at least temporarily or to a limited degree.
Questions
Before we dive into the methods that Greg used to calculate possible outcomes in terms of vanilla blocks proposed and APR lost for various combinations of minbid settings and adoption rates of curated Lido on Ethereum NOs based on historical data, let me first share the questions we would like to discuss with you based on said findings:

Between the maximization of the staking APR  crucial for the competitiveness of the Lido protocol and the security of the Ethereum network  and the resistance to transaction censoring by block builders and/or relays with the help of minbid, taking the opportunity cost of unrealized MEV rewards into account, what percentage of vanilla blocks do you consider reasonable for Lido on Ethereum?

Given the importance of the share of optins to the percentage of blocks locally built by the curated set, the dynamics of this metric i.a. due to bid sizes changing over time, the easy adaptability of the minbid setting and difficult monitorability of the configuration for the DAO, as well as the circumstance that currently fewer NOs use minbid than originally anticipated: should individual NOs be allowed to configure higher values than specified in the Block Proposer Rewards Policy at a given time to bring the overall vanilla block rate closer to, for example, the 28% initially targeted? Practically turning the policy’s minbid requirement into an interpretable reference point conditional on the percentage of blocks locally built by the entire set?

If you do not consider this approach feasible, given the constraints that prevent some of the NOs from configuring minbid entirely, what else do you propose to ensure Lido on Ethereum’s censorship resistance?

Irrespective of whether we agree on a tolerable share of APR to be sacrificed, vanilla block rate or minbid setting as the independent lead variable to achieve satisfactory censorship resistance  in your opinion, how often should this parameter be reviewed to provide a helpful and enforceable reference and at the same time keep the effort required within reasonable limits?
Relation between minbid and APR
Before diving into the numbers, it is crucial to again highlight the following relation between minbid and APR: If part of the Lido on Ethereum NOs do not use minbid, those who do need to produce (significantly) more vanilla blocks for the entire set to reach the targeted rate.
For example, with 10 NOs, a targeted share of 30% vanilla blocks, and 6 NOs not configuring minbid, the remaining 4 NOs need to produce 75% of blocks locally to achieve a share of 30% (4/10*0.75=0.3). We call this the ‘adjusted percentage’share of blocks which need to be produced locally by NOs that use minbid to reach the desired total percentage of vanilla blocks.
The equation is simple:
\text{Adjusted percentage}=\dfrac {\text{Desired total percentage}} {\text{Share of NOs that uses minbid}}
Now, let us dive into numbers. The full table can be found here and since it is pretty large, we will only use the most relevant parts of it in this post.
Protocol’s POV
From Lido’s point of view, it is important to look at the whole structure of the validator set and take into account both NOs who use and those who do not use minbid. For each combination of a percentage of NOs who configure minbid and a range of possible minbid values, we created a table showing the respective rates of vanilla blocks produced and the APR decrease in percentage points  following, e.g., for minbid values of 0.03, 0.05, and 0.08 ETH:
How to read this table
If the DAO agrees to set minbid to 0.03 ETH and 40% of the NOs optin, Lido’s curated set produces 9.4% of blocks locally while the APR decreases by 0.06%. Therefore, instead of an APR of 3.4% it generates 3.34%.
Accordingly, if minbid is set to 0.05 ETH and 60% of NOs use it, Lido produces 28.8% of blocks locally, but the APR decreases more drastically, by 0.2%.
It is also important to note that these tables generally tend to overstate losses since the percentage of vanilla blocks due to minbid is considered as part of the expected value, while in reality, not each locally built block would necessarily be lower in value than a relayed one, for example in times of low bid sizes during which builders are not able to bundle blocks more valuable than validators with minbid configured.
How to make a decision
Using the above table, NOs can decide which decrease in rewards is acceptable to them for a certain level of expected censorship resistance, while also understanding how many vanilla blocks will be produced by Lido if other NOs optin to minbid as well.
Methodology and calculations
All calculations are based on historical data of all blocks produced by Lido on Ethereum’s curated set from the merge until 20240423. The calculations consist of several steps:
Step 1. Minbid values by vanilla block percentages
First, we solve the task of finding the minbid values required by various predefined vanilla block percentages. For that, we take a targeted share of vanilla blocks, e.g. 30%, and then calculate the adjusted vanilla percentages based on the amount of NOs who configure minbid.
As a result, we get the following table:
If every NO uses minbid, each needs to produce 30% of blocks locally to achieve 30% of vanilla blocks. If 60% of NOs optin, they need to produce 50% locally for the total share of vanilla blocks to remain 30%. Accordingly, a situation in which only 20% of NOs configure minbid to achieve a total share of 30% vanilla blocks is impossible (we assume that block proposals are split equally among NOs), which is why the adjusted percentage for this scenario was left empty.
Then, we determine the minbid values that satisfy the condition of being the limit below which the targeted adjusted percentages of locally built blocks have historically fallen. This means that, e.g., for the adjusted percentage of 37.5% we search the minbid setting below which 37.5% of proposed blocks have fallen (basically the 37.5th quantile), which is 0.04 ETH.
The complete table for 30% looks like this:
Value 691.96 ETH was the highest ever recorded MEV reward until the time of writing, and practically means that all blocks with a lower bid will be produced locally. For the full table, please go to the ‘Minbid values’ tab in this spreadsheet.
Step 2. Vanilla block percentages by minbid values
Next, we solve the opposite task, predefine various possible minbid values and find which share of vanilla blocks they result in, depending on the amount of NOs who optin. From the previous step, we learned that most of the relevant minbid settings lie in the range of 0.03 to 0.2 ETH, therefore the chosen values for minbid are [0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.1,0.12,0.14,0.16,0.2].
We then rank the initial dataset and look for the share of blocks which lies below each minbid setting, and as a result, get the following table (this is an example of minbid 0.06, the full table can be found on the ‘APR decrease’ tab of this spreadsheet):
Step 3. APR decrease
The third step is to calculate how the APR is affected by changes to the minbid setting. For this, we determine the average rewards for relayed and nonrelayed blocks since the merge, which are 0.13 and 0.015 ETH, respectively. We subsequently solve for the expected value of a proposed block by using the shares of vanilla and relayed blocks. For example, if we produce 33.8% vanilla blocks, the expected value is:
0.338 * 0.015 + (1  0.338) * 0.13 = 0.09 \; \text {ETH per proposed block}
We then divide this value by the average reward per relayed block, to find the ratio of the reward we would earn compared to a relayed block:
\dfrac{0.09}{0.13} = 0.7 \; \text{or 70%}
Therefore, the expected value per block with a minbid setting of 0.06 and 60% of optins is 70% of the expected value per block if we would only produce relayed blocks. In other words, we would lose 30% of the expected value of each proposed block under these conditions.
Furthermore, we need to find the share of EL rewards in the total structure of Lido earnings, depending on different combinations of minbid values and NO optins. For doing so, we take the 30days averages of the CL and EL APRs. For example, under the above mentioned conditions and for the last month of data, the average CL and EL APRs equaled 2.86% and 0.78% respectively:
2.86\% + 0.78\% * 70\% = 3.41\%
By knowing this value we can finally determine the APR decrease suffered from configuring minbid by subtracting the result from the current 30days average APR of 3.64%:
3.64\%  3.41\% = 0.23\%
The outlined approach is based on several strong assumptions:

To achieve the highest possible APR, it is assumed that no NO is optin to minbid. This is an inaccurate representation, since currently between 13.5% and 16.2% of NOs seem to have minbid configured. Therefore, the real decrease of APR would be lower than calculated.

The expected values are based on averages, but in reality the EL rewards for proposed blocks could be higher than the configured minbid value for most of the blocks and therefore the overall rewards decrease would again be lower than determined.

Since 30days averages are taken, if the market conditions change, the real results could deviate to either side.
Taking into account these assumptions, we suggest that the numbers presented should be considered as maximal possible rather than expected decrease of APR.
PS: Edited to fix equation formatting & an incorrectly referenced value