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I don't think difficulty increasing would affect pool luck.
that's your error - finding a block is a Poisson process. Variance (actually sqrt of variance, but that's semantics) is proportional to the square root of expected blocks. Percentage variance is thus 1/sqrt(number_of_blocks)
If you normally get 100 blocks in a given week, you should expect +/- 10 blocks variance (i.e., 10%).
If difficulty rises and you now get 9 blocks a week, you should expect +/-3 (i.e., 33%)
Difficulty stepped up around the same time as I notice the pool luck decrease. My concern that difficulty would not affect pool luck came from the equation Luck = exp(-total_shares / difficulty). While I did not keep a historical account of the previous difficulty block share total, I assume shares per block did go up with difficulty. Since the increase in both shares (assumed) and difficulty- would this not normalize pool luck percent? Does Poisson process apply to luck? The increase in block time by its self would account for difficulty, but a decrease in pool luck suggests someone else is still finding the blocks. Even though total bitcoin hash rate is fluctuating, the last few days it still averages around the same.
I suppose the word luck is just that. Luck. While it can be mathematically explicit, it still is just luck in its purest form.
Though, something is still not connecting for me.
