Summary
Chaos Labs has performed a comprehensive data-driven analysis of the likely implications of increasing the Arbitrum minimum base fee.
The major takeaways can be summarized as follows:
Arbitrum gas usage
These findings cover the utilization level of Arbitrum blocks and details around how this proposal could impact gas prices on Arbitrum in all scenarios.
- 80%-90% of Arbitrum transactions pay the minimum base fee.
- Arbitrum blocks use approximately 5% of their maximum utilization since the Dencun upgrade on Ethereum. There is a lot of room to grow revenues by increasing usage.
- Increasing the minimum gas price increases the gas price at all utilization levels due to the Arbitrum fee mechanism being set as a multiplicative function of the minimum fee.
- This is compounded by the convexity in the Arbitrum gas price mechanism with respect to utilization.
- Simply put, increasing the minimum base fee by whatever factor will increase gas prices at all block utilization levels by at least that factor.
Arbitrum Gas Prices Relative to Other Rollups
These findings position Arbitrum gas prices relative to alternative rollups currently. To ensure apples-with-apples comparisons, only the most well-used rollups are included in the analysis.
- Arbitrum transaction costs are currently approximately in the middle of the range of L2s. They are cheaper than Linea and Optimism, but more expensive than Base and Blast.
- Perpetual futures trading uses up almost half of Arbitrum gas. This is a gas price-sensitive use case that could be forced to migrate should fees increase.
- Other high-frequency use cases, such as gaming and SocialFi, require cheap transactions to compete as products. Factors like composability are also less critical for these use cases. The decision where to deploy apps in these categories depends on Arbitrum gas prices relative to alternative rollups.
- The decision around setting the minimum base fee on Arbitrum will affect the type of applications it can support and, therefore, its DeFi ecosystem.
Impact on Arbitrum Sequencer Revenue
These findings discuss the potential impact on Arbitrum sequencer revenues.
- It is important to remember that $Revenue = baseFee \times gasUsed$. This is more important over longer time periods where growth in the amount of gas used plays a larger role in revenue. The finance analogy is growth companies that derive most of their value from their future earnings.
- Increases in base fees that inhibit growth in gas used can result in lower long-term sequencer revenues.
- Arbitrum blocks have significant spare capacity.
- Increasing Arbitrum’s minimum base fee will likely immediately lead to a short increase in revenue. However, the magnitude of the increase in base fee will be offset by a decrease in activity.
- Data from the reaction to the Dencun upgrade can provide an upper bound on the activity impact over the short term. This implies that a 4x minimum fee increase will reduce activity and gas use by at most 50%. In reality, though, we expect the reaction to be more muted.
- The exact reaction is impossible to determine as past events have affected multiple factors, such as increasing chain throughput and prices on other chains.
- The Dencun upgrade, which reduced the amount of gas required to post a transaction to Ethereum and, therefore, made transacting on Arbitrum cheaper, led to a doubling in the number of Arbitrum transactions per day.
- We conclude that even over short time periods, there is positive gas price elasticity, and therefore, a change in the gas price will affect the amount of activity on Arbitrum.
Conclusion
Chaos Labs does not support an increase in the minimum base fee on Arbitrum with the intention of increasing sequencer revenues. The likely short-term increase in revenues from the increase will come at the expense of growth in gas usage. Growth in gas usage will have a significantly larger effect on revenues over the medium to long term, and it does not make sense to put this at risk while blockchains are still so early in their development cycle.
We point to perpetual futures trading, the use case on Arbitrum that currently pays the most gas to the sequencer, as an at-risk category should this proposal pass. Perps protocols considering where to deploy will likely need to choose alternative chains to compete. Existing protocols could also migrate in time to compete on fees.
Context and Analysis
The primary risk that increasing the minimum base introduces is that activity on Arbitrum could suffer as a result. The minimum base fee is an administered price and therefore there is the risk that the market for block space might not be willing to pay it.
This risk analysis’s framing is focused on answering whether an increase in the minimum base fee could cause activity to suffer and, if so, how much.
Arbitrum Base Fee Mechanism
Arbitrum employs a modified version of the EIP-1559 transaction fee mechanism seen on Ethereum. It uses a parameter called speedLimitPerSecond (denoted as S) that dictates the target gas usage and thus influences the block sizes. The mechanism works by aggregating all gas (G) accrued since the genesis block, formally denoted as the GasBacklog (B).
Approximately every fourth block (given Arbitrum’s 250 millisecond block times), the speedLimitPerSecond parameter is updated. Specifically, 7 million gas units are subtracted from the GasBacklog during each update cycle, aiming to reach an equilibrium.
The Gas Backlog at a given block n can be mathematically represented by the following function:
In parallel, the Base Fee F(B) follows the following formula:
The dynamics of this mechanism can be observed in the plot below. The
GasBacklog naturally grows in a staggered fashion due to the periodic updates. Approximately every fourth block, the speedLimitPerSecond (7 million gas) is subtracted from the GasBacklog. As a result, if the gas used in the fourth block is below this speed limit, the GasBacklog will decrease, resulting in a negative Gas Backlog Delta for that block. This pattern causes the GasBacklog to exhibit a sawtooth-like growth pattern. As the GasBacklog exceeds the target of 7 million gas, the BaseFee starts to increase in response, reflecting the higher demand and usage of the network.
As a result, the implications of changing the minimum base fee are complex and multi-dimensional. This complexity arises because the function determining the base fee is exponentially multiplicative with respect to the GasBacklog. Consequently, the growth in the BaseFee is significantly exponentially amplified for all GasBacklog values.
In the plot below, we depict a snippet of 3000 blocks on Arbitrum, where the GasBacklog jumped to as much as 140 million. Assuming all other parameters remain constant, we overlay theoretical minimum base fees of 0.03 and 0.05 to compare the growth in the base fee during a spike. This comparison highlights how even slight changes in the minimum base fee can lead to substantial differences in the base fee growth during periods of high network usage.
This means that under the assumption of similar peak congestion, as seen in the plot with a GasBacklog of 140 million gas units, the BaseFee, assuming a minimum value of 0.05, will rise by nearly 6 times compared to the current BaseFee, resulting in a 0.23 Gwei difference. Consequently, raising the minimum BaseFee would lead to further increases in the BaseFee relative to the GasBacklog. In other words, a spike to 0.05 Gwei from a minimum of 0.01 Gwei would be equivalent to a spike to 0.28 Gwei from a minimum base fee of 0.05 Gwei.
We observe that due to the multiplicative nature of the base fee function, coupled with the exponentiation driven by congestion, the dollar cost of a transaction can increase substantially, irrespective of the GasBacklog. As the GasBacklog scales, this delta naturally deviates further, leading to even more significant increases in transaction costs.
Users of Arbitrum Block Space
Gas use on Arbitrum between 15 March and 15 May shows that perpetual futures exchanges and DEXs have the highest demand for Arbitrum block space. Together, they accounted for over 70% of total Arbitrum gas over the period.
In the largest category, 46.6% of Arbitrum gas was used by perpetual futures contracts. This use case is dependent on low transaction costs as traders transact with a high frequency, and low trade fees mean gas makes up a proportionally higher share of total transaction costs. Low gas costs are important for a good user experience on the chain.
It can also be assumed that developers’ decisions on where to deploy their perpetual futures exchange will factor in gas costs, and higher costs could dissuade them from using Arbitrum.
Historical Base Fees
Historically, Arbitrum transactions have been priced at the minimum base fee 80%-100% of the time. This is not because blocks do not contain much activity individually, but because in most 1-second cycles, gas seldom exceeds the 7m speed limit gas*.*
The top chart below shows the daily percentage of blocks where the base fee equals the minimum base fee.
The lower chart below shows the percentage of the maximum gas limit that is currently consumed daily. This has mostly hovered around 5% since early April, with the exception of the Layer Zero airdrop day when utilization increased to 45%.
We conclude that there is significant capacity for Arbitrum to grow gas usage.
Revenue Driver Analysis
Determining the likely change in revenue required a detailed analysis of the two factors affecting it: the base fee of a transaction, and the amount of gas used.
The analysis that follows investigates the impact that changes in the base fee will likely have on gas usage. This will inform estimates of changes in revenue when the minimum base fee is increased.
Ethereum’s Dencun upgrade on 15 March 2024 introduced proto-danksharding which reduced the gas needed to post transaction data. This reduced the cost of transacting on arbitrum by approximately 80%.
To see how this decrease in ETH transaction costs affected the amount of activity, we need to look at the number of daily transactions. This is because gas needed per transaction dropped significantly, making before and after gas usage comparisons impossible.
We observe an approximate doubling in daily Arbitrum transactions around Dencun. Although the effective increase in supply of blockspace through lower gas per transaction would have had a significant impact in enabling this increase, we come to the conclusion that the economic driver of this increase was related to users paying 80% lower base fees.
This data point of an 80% drop in transaction costs leading to a 100% increase in activity provides one data point to estimate the likely elasticity with respect to gas price on Arbitrum. Unfortunately, this is overly simplistic, and we need to account for other factors that likely mean that the effect will not be exactly the same in the other direction, especially over the short term.
Dencun Increased the Amount of Transactions that Could Fit into a Block
The observed behavior in the analyzed data showed that in one-second cycles, the last block usually exceeded the equivalent per block speed limit gas, but not to the extent that it exceeded the cycles 7m gas speed limit, which would increase the base fee. This means that the available supply of block space is very relevant in determining the likely impact on gas usage.
The most recent 7d average gas used per cycle is 5.6m, relative to the 7m speed limit where base fees increase according to utilization.
Dencun decreased the amount of gas per transaction and, therefore, increased the amount of transactions possible before gas increased.
Dencun Decreased Fees for all L2s
The competitive environment for block space pricing amongst L2s was left relatively unchanged by Dencun. This limits our ability to forecast activity migrating to alternative chains.
Elasticity is Use Case Dependent
It is reasonable to assume that more frequent use cases, like perpetual futures trading and DEX swapping, will be more gas price sensitive than less frequent activities like interacting with lending protocols.
There is also likely an inertia in the amount of activity over short time periods, meaning that the initial negative reaction to a base fee increase will likely be less than the initial positive reaction to a fee reduction.
Another implication is that the minimum base fee level will have an impact on Arbitrum’s DeFi landscape. A higher minimum base fee will lead to less high frequency and fee-sensitive protocols deploying and focusing on Arbitrum.
Utilization Leading to Higher Average Base Fees
Arbitrum base fees have mostly been set by the minimum base fee because over most 1-second windows, the total gas used has not exceeded the 7m speed limit parameter. Increasing block space utilization beyond this point more consistently would lead to an increase in realized base fees, as pricing would then be set by usage and block space demand through the mechanism described above.
This could increase base fee pricing to the same point, but at higher gas utilization, driven by demand rather than externally administered. This would be a less risky means to increase the base fee as the increase would be driven by actual demand and, therefore, has less potential to cause users to leave.
Increasing the Minimum Base Fee Impacts Base Fees at All Utilization Levels
The multiplicative nature of Arbitrum base fees means that increasing the minimum base fee increases base fees proportionally at all utilization levels. This change affects more than just the gas price floor; it will affect gas prices at all times on Arbitrum.
Arbitrum Transaction Costs Relative to Alternative Chains
The analysis thus far has focused on Arbitrum activity without considering the external environment. In reality the transaction cost on alternative chains will have a large impact on the fee sensitivity of Arbitrum activity.
On this measure, Arbitrum base fees appear approximately in line with alternative chains. Last week, the median Arbitrum transaction fee was 59% higher than Base, 138% higher than Blast, 76% lower than Linea, and 16% lower than Optimism.
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