Size has nothing to do with Luck. If someone is having bad Luck, it does not imply that someone else is having good Luck. Luck does not balance out, it just averages out over time. Luck is just that, Luck.
I'm confused. If two people flip a coin six times an hour, and each time the winner gets 25 bitcoins - doesn't ones person's luck affect the other persons luck? In this analogy, I understand the "size of the player" doesn't matter because they have the same chance of winning (the exact same pool size), but one player's luck seems to affect the other player.
I also understand how a smaller pool's share of the total bitcoin rewards will eventually equal its percent of the total network hashrate; however, even taking this into consideration, one pool's luck should impact other pools (in the short term).