Assume a constant difficulty.
Assume pool produces a new block every 30 seconds on average, for a particular coin and at the pools particular total hashrate.
Miner A has 0.5 megahash hashrate
Miner B has 5 megahash hashrate
Assume these hashrates translate to finding a share every 30 seconds, or 3 seconds respectively (again, on average).
Miner A will only find a share in time approx 50% of the time. So half the time he has 1 share, half the time he has 0 shares. He will have worked an average of 15 seconds for nothing when the block changes.
Miner B will find an average of 10 shares. He, as well, would have been working towards another share when the block changes. However, on average, he will have only been doing so for 1.5 seconds.
So the difference for Miner A is the difference between all or nothing.
The difference for Miner B is between, say, 9 and 10 shares... or maybe 10 and 11 shares...
Do you see it yet?
The bolded part is not correct. Sometimes the miner will have 0 shares, sometimes 1, sometimes
more than 1. On average, 1.
I stated he finds a share on average every 30 seconds of work. If he finds it in 29 seconds, great he gets a share. 31 Seconds? Nothing.
For every time he grabs one in 15 seconds, an equal number of times it will take 45 seconds.
Therefore on average he gets 0.5 shares per block.
It is of course possible that he could get 2, 3, 4 shares with some extreme luck. This is balanced by the fact that the pool, as well, could go on a streak and get 2, 3, 4 blocks quickly with the same level of luck.