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So I've been noodling on it for a minute and I think I'm starting to see it better. The way I'm thinking about it is correct, payout is only based on your hashpower relative to the rest of the network, BUT only at the moment that difficulty changes. From there, the pool hashrate rules the variation. The effect of every pool in the world increasing hashrate would just increase block production speed, and then difficulty would adjust up after the 2016 blocks. So if you tracked the % change in pool rate from when difficulty changed and applied that to what you calculate from payout at moment of difficulty change, it should correlate with reward.
Difficulty is what decides your expected reward per THs per time period.
Expected reward is typically called 100% PPS
It changes each 2016 blocks.
Your block reward depends on the pool hash rate.
If the pool hash rate 'expects' us to find a block every 2 days, then your Reward per block, at 100% PSS, and no Txn Fees, will be twice your expected daily 100% PPS ... since you only expect a block every 2nd day.
On top of that 'expected' 100% PPS you add transaction fees and subtract pool fees.
So e.g. if we find 2 blocks in a day when we expect one block every 2 days, that day you'd expect to be Rewarded 400% PPS + TxnFees - Pool Fees ... due to "400% luck" (for that day)
i.e. 'expect' 0.5 blocks a day, got 2 blocks = 2 / 0.5 = 4
That's also what the PAPPS% number is on the web site: MeanTx% * Luck% - pool fee