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 change of winning (the exact same pool size), but one player's luck seems to affect the other player.
Mining is more like continually flipping coins until you get X in a row.
Both players can be unlucky and take much longer than expected.
You aren't competing directly against each other, but both racing to be the first to hit a random target. Me being slow doesn't make you any faster.
There is not a fixed rate of Bitcoin generation, on average it should be 25 every 10 minutes, but it could be 25 in 10 seconds or 25 in 2 hours.