The reason gas prices have been declining for the past 4 quarters despite having over 100% gas usage

The Enigma

One interesting curiosity I've noticed is that Ethereum gas prices have been falling 20-40% each quarter since EIP-1559 initiated DESPITE gas usage being over the 100% 15M target gas usage.

This is surprising because normally under EIP-1559, if each block stays exactly at the 100% gas target, gas price will also stay exactly the same.

So why is this happening?

This counter-intuitive phenomenon can be explained by simple math. After EIP-1559, gas price changes whenever the previous block's gas usage deviates from 15M gas. It increases by 12.5% at 30M gas, and decreases by 12.5% at 0M gas. Any value between the 2 limits affects price proportionally up to 12.5%.

So what happens if a 30M-gas block were followed by a 0M-gas block?

(x+a) * (x-a) = x^2 - a^2 (1 + 0.125) * (1 - 0.125) = 98.4% => 2.6% price decrease 

Thus if a 30M-gas block were followed by a 0M-gas block, the gas price would still fall 2.6% even though the average gas usage stays at 15M gas. The larger the volatility from the 15M-gas target, the larger the negative price pressure.

In fact, in an extreme theoretical case where there were one full day of 30M-gas blocks followed by another full day of 0M-gas blocks, the gas price on the 3rd day would be 10⁵⁰ times smaller despite that the average usage between the 2 days was still 15M gas. Obviously, validators will not magically be able to process transactions 10⁵⁰ times cheaper, so this is completely theoretical.

Nevertheless, the effect is there, and we have been experiencing a 20-40% decrease in gas prices quarterly since EIP-1559 was introduced in Aug 2021. Though the decrease has slowed down since The Merge.

A mix of these 2 cases will continue happening until a dynamic market equilibrium is reached:

1. Gas price keeps falling every quarter
2. Daily gas usage rises noticeably above its current 102% average.