BASE_REWARD Formula Enquiry

Question

Reading about Ethereum 2.0, I note the formula for the BASE_REWARD, which is

"the base unit that other rewards are calculated from"

is given as following:

base_reward = effective_balance * (base_reward_factor / (base_rewards_per_epoch * sqrt(sum(active_balance))))

where

"base_reward_factor is 64, base_rewards_per_epoch is 4 and sum(active balance) is the total staked ether across all active validators"

So a validator that doesn't propose a block in that epoch and is not part of the sync committee (ignoring the inclusion_delay_reward for simplicity) should get (6.75/8 * BASE_REWARD) per epoch.

Given an active validator set of 747,846, assuming a given validator's effective stake of 32 ETH and Ether staked per validator of 32 ETH (I know average balance is quoted as 32.14 ETH but presumably the excess is not counted as 'staked'), this gives:

base_reward = 32 * (64 / (4 * sqrt(32*747846))) ~ 0.10466 ETH

And for non-sync committee, non-proposer:

Epoch reward = base_reward * (6.75/8) ~ 0.08831 ETH

However this is of course not correct, but if I omit the square root from the above calculation, the epoch reward per validator is:

Epoch reward = 21394 Gwei * (6.75/8) ~ 18,051 Gwei

This result is much more in line with reality, where currently the reward for same assumptions is about 11,000 Gwei.

So this is a long way of asking was the square root removed from BASE_REWARD formula? All docs I read refer to the first formula I gave, so not sure where the discrepancy is. If it's been updated, where can I find most updated and comprehensive docs?

Sources: Ethereum.org 1 beaconcha.in 2

Answer 1

Here are the values to calculate the base reward:

base_reward = 1,000,000,000*64/(sqrt(32,000,000,000*747846)) ~ 413 Gwei (value in Gwei!)

Then the reward R for an attestation is :

R = base_reward * 32 * (14+26+14) / 64 ~ 11,151 Gwei

The result is, as you said, much closer to 11,000 Gwei. If you want to know how I picked the values for the equation, I suggest you look at the best documentation of ETH2 out there : eth2book.

There's a lot of documentation with detailed explanations each time. You will find everything you need!