They don't even depend that much on luck, if you're training a player long term. Yes, if you roll a single die, there's a lot of luck in that. But if you roll 50 dice, you're pretty much certain to get some 6's, some 3's, some 1's. Yes, you'll get more of some numbers than others, but it's very unlikely that you'll get 20 of one number, and 1 of one. Rolling lots of dice in games produces less luck than rolling the die once, by far. It'll even out.
Remember that "pops" are not what training does. Training raises sublevels. When that hits thresholds, it produces visible pops, but that's just the visible manifestation of a process. It's like birthdays. Just because today isn't my birthday, doesn't mean I'm not getting older.
*sob*