Plenty of people have done the math on this and the percentages ARE correct. When you take everyone who's doing these, over a period of time, the chance to gather is correct.

Every single time you gather, you have a chance to fail. And a 20% chance to fail each and every swing is actually pretty big. Having an 80% success rate doesn't mean you'll do 10 swings and only 2 of them will fail.

Streaking/clumping does happen on occasion even with the best RNG systems, but it's not some sign that the gathering percentages are incorrect. I would say that on the whole, for the 2 years I've been playing and gathering, I've never felt the percentages were incorrect.