I read Chance of Zero Blocks Per Epoch - thanks for that.
It is true that smaller pools have a higher chance of not winning a block in any given epoch. Even worse, every time they don’t win a block their chance to win a block in the next epoch is slightly less because the total stake is increased by the reward from the previous epoch (i.e. 15m). If I’m not mistaken it is a Bernoulli distribution.
We have 23.06b lots in the jar. A pool with 10m active stake has 10m lots that win. For every block per epoch (i.e. 21600) we reach into the jar and draw a lot. The chance of not winning a block is, according to Bernoulli, the probability that none of those 21600 draws is one of our 10m lots.
However, let’s assume Bob owns a pool and his dad is paying/running it for him - the cost for Bob is zero. No one is delegating to Bob’s pool and he is putting 100k into the pool. He can reasonably expect to win 7 blocks per year. Because he gets all of the rewards (“cost per block” is zero) every time he wins a block, his ROA would be exactly the same as if he delegated to a large pool that also had zero cost.
Bob rarely gets rewards, but he does not need to share them. By delegating to a large pool, he would get rewards more regular, but they would only be a fraction of epoch reward.
The total reward per epoch is proportionally distributed to all participating pools. Each participating pool distributes rewards proportionally to its delegators, but only after the pool reward is subtracted (i.e. cost to the delegator)
I’d say effective cost per block matters, not how often a pool wins a block.