More, your Luck stat apparently does NOT factor into ANY of this.
I put on gear to max my Luck during this run, hoping for more drops, Lucky Ring, Lucky Charm, even found a Rare Ring which also often wore, and so on. I thought I was getting Critical Hits fairly often because I had upped my Luck by a lot, but no, I was just getting those because I was getting them.

Wanna know what the Luck stat does in HoD? It does ONE single thing, increasing the odds that the Rare Ghost spawns in some places, one of those running away enemies you need to hurry to kill. He has a rare chance to drop a second Lucky Ring for you, which, uh, apparently you would then need to find him more often, and nothing else?
He might also drop a necklace which boosts Int, but there's so many much better ways to boost Int which don't require soulcrushing grind.

The Rare Ring apparently DOES make it more likely for Rare Drops to happen, but that's the only way you can help your odds if you want to get more drops, nothing else matters. People have the fucking gall to call the Luck busted in AoS or DoS.
To anyone interested in HoD, it's a fun game and I'll still recommend it, but you can completely ignore Luck as a stat, you don't need it for anything at all that matters.