Ethereum's Dencun Upgrade: Part Two

Implications

The Dencun upgrade intends to change the way that gas is used and paid for on the network. The specifics of its implementation have implications on the base fee, the amount of ETH earned by stakers, and the amount of ether supply burned in each block.

Current gas market

Recall that the base fee adjusts dynamically to target gas usage per block of 15M units. If the amount of gas within the previous block is below this target, the base fee of the current block will decrease. The opposite is true if the amount of gas within the previous block is above the target. The maximum amount the base fee can change between consecutive blocks is 12.5%. For example, say the base fee per unit of gas is 1B Wei. If block 1 contains 28.5M units of gas, then the base fee for block 2 is calculated as follows:

A lower demand for gas usage will lead to a lower base fee, making gas usage cheaper and “unlocking” existing demand at a lower price. This brings the gas usage back to the target equilibrium price of 15M.

The variable base fee keeps the amount of gas used per block very close to the target level, as the green line in the chart above shows. Overall, this keeps the amount of computation within each block at a stable level. In periods where non-L2 activity drops (resulting in gas used per block falling below the target, and subsequently base fee dropping), L2 activity picks up due to a cheaper base fee, keeping the ecosystem in equilibrium. 

During periods of significant network activity, the base fee can change drastically – see below, where the base fee increases significantly over the period of 15 minutes.

We observe significant network congestion between 6:30am - 6:45am. On multiple occasions, the amount of gas within consecutive blocks is at the maximum of 30M gas units, resulting in the base fee in the following block increasing by the maximum of 12.5%. Over this period, the base fee increased from ~20 billion Wei (per unit of gas), to ~100 billion Wei (per unit of gas). This highlights how sensitive the base fee is to the amount of gas used per block. 

One of the modelling assumptions made is that post upgrade, all L2 activity will move to the new blob space, thus we have modelled the removal of all gas related to L2 activity. In practice, blob transactions must still pay to live on the execution layer. The amount they pay will be negligible, since each blob transaction will include a maximum of 6 hashes (one for each blob). Therefore, this does not affect the conclusions drawn from this section.

Directly after the upgrade, we would expect L2 activity to move very quickly to the new “blob” gas market. This will create an immediate shortfall in the amount of gas within each block, falling below the target (see Figure 2). If activity does not recover in a timely manner, the block-to-block update function would cause the base fee to go to zero, making block space incredibly cheap. Users would in effect, only be paying the priority fee that is collected by block proposers.

Figure 4 illustrates just how quickly the base fee can fall if activity does not recover to the 15M equilibrium level. This, of course, is an extreme example. 

A more realistic example is as follows: L2 activity instantaneously moves to the new “blob” gas market post upgrade, creating a shortfall in gas usage. Initially, the lower block usage results in a drop in the base fee, unlocking new levels of demand at a lower base fee price. Since it will be cheaper to use the network, intuitively, this should incentivise non-L2 activity to pick up and the base fee to stabilise at a lower level than before the upgrade. 

The time period over which we expect this to take place is important. In Figure 3, we saw how 10 minutes of above-target gas usage can lead to a five-fold increase in the base fee. Therefore, we expect to see significant movement in non-L2 activity in the hour (at most) following the upgrade.

Monte Carlo Simulations

To better understand the effect of the length of time taken for non-L2 gas usage to make up the shortfall, we modelled the evolution of the base fee in several cases: 15 minutes, 30 minutes, and 45 minutes.

For each situation, we run 1,000 simulations, and plot a distribution of the terminal base fee. We do not consider situations in which non-L2 activity stays around the current levels, since the amount of gas used per block will simply fall below the target, resulting in the base fee tending to zero. 

To simulate how we expect non-L2 activity to change post upgrade, we construct a random walk from the last known datapoint before the upgrade (which we have assumed to be ~23:25pm on October 16th 2023), to 15M units of gas (we have chosen 15M since that is where we expect activity to remain, in order to keep the network in equilibrium). To build this stochastic model, we have taken into account the underlying drift and standard deviation of known non-L2 activity. For a discussion on the mathematics behind this model, we ask the reader to reach out to us on the following email address: research@blockscholes.com.

For the 15, 30, and 45 minute simulations, the mean terminal base fee (per unit of gas, measured in Wei), is 2.53 x 10^9, 1.488 x 10^9, and 2.831 x 10^9 respectively. Furthermore, the modal bins are:

• 1.875 - 2 x 10^9
• 2.75 - 2.875 x 10^8
• 0 - 99.9 x 10^6.

This indicates that as the time taken for the network to recover post upgrade increases, there is a greater chance of the base fee approaching zero. Should it take longer than 45 minutes for network activity to pick up, we would expect the base fee to tend to zero.

Therefore, we expect non-L2 activity to pick up within minutes of the upgrade due to an initial fall in the base fee, subsequently unlocking new levels of demand. If not, the network runs the risk of having consecutive blocks below the target gas limit for a prolonged period of time, resulting in the base fee tending to zero.

How will ETH burnt change?

A lower base fee will also have implications on the amount of ETH burnt. Recall from the “Gas Mechanics” report [here] that the base fee paid for each unit of gas is burnt from the supply of ETH in order to offset the issuance of new ETH to validators. In the period following the upgrade, we expect the amount of ETH burnt from supply to fall in tandem with the lower equilibrium base fee. Should the base fee stabilise at a lower level post upgrade, we expect the amount of ETH burnt from circulation to fall thereon.

Above, it is evident that as the time taken for the network to recover post upgrade increases, less ETH will be burnt from the supply. This is directly related to the evolution of the base fee post upgrade, since we previously argued that the base fee will tend to zero as the time taken for the network to recover increases.

Blob Gas Market

Modelling the evolution of the base fee in the new “blob” gas market is slightly more difficult, and will require heavier assumptions. Recall that L2 solutions must pay for a full blob of gas, even if the storage they require is below a blob’s capacity. Immediately after the upgrade, L2’s cannot share blobs, but future upgrades could include blob sharing protocols.

Since there are six blobs per block and the blob base fee increases if the running total of excess blob gas is above the target of three blobs worth of gas, we could see blob base fee increase sharply as L2 solutions compete for blob space. How L2 solutions will compete for blob space is more difficult to model as each rollup submits chain data for storage at different frequencies. However, we can analyse how much data each L2 solution is currently storing onchain.

In the current market, 16 units of gas = 1 byte of data stored. In the new blob gas market, 1 unit of gas = 1 bytes of data stored. Post upgrade, each block will be able to store ~0.75MB of data, which is equivalent to ~0.125MB of data per blob. Therefore, assuming blocks are validated ~12 seconds, we can calculate the amount of data L2 solutions can store onchain per day. From this, we can calculate the amount of data currently stored by L2s, as a proportion of the amount of data they will have available in the new blobspace.

Although we do not know exactly how L2 solutions will compete for blobspace post upgrade, it is evident in the figure above that there is enough space available for L2 solutions to use the new blobspace, despite each blob only being able to host a single rollups’ data. Therefore, we would not expect L2s to actively compete for blobspace in each block, preventing a situation where the new blob gas market becomes congested, leading to a significant increase in the blob base fee. As L2 activity grows, we expect the Ethereum foundation to increase the amount of data each blob can store.

Conclusion

We believe that gas usage will recover very quickly from the loss of L2 usage immediately post the fork to the upgraded chain. Otherwise, the base fee per unit gas will fall to near-zero, making transactions incredibly cheap and encouraging more activity.

The recovery of gas usage implies that the base fee will stabilise at a lower level post-fork. While less gas usage in each block and a lower base fee means less ETH burnt per block, we do not expect this to have a material effect on the daily net supply change.

We expect L2 activity to move quickly to the cheaper blob gas market post-fork. While eventually L2s are intended to share blob space, at present they must use an entire blob for their own purposes. We expect that the space made available to L2s will be sufficient for current data storage levels, and that the new blob space will not become congested.