When recruiting demons with the Stats Plugin App, a successful recruitment will always increase their stats. Less frequently, their stats will be increased "more", or "far more" than normal.

I started New Game+ and tried to recruit some lowbie demons with the app. After many tries, none saw their stats increase "more" or "far more" than normal, although it had seemed common towards the end of my previous game. Increasing my level to 20 and putting all points into Luck didn't seem to have any influence.

What influences the frequency of stats increasing "more" or "far more" than normal?

I know there are apps that will increase it, but otherwise nothing.

This might be a dumb thing to point out, but New Game + doesn't bring the apps you've bought over. I hope you haven't been leveling without going to buy apps.

Otherwise, I have no clue. I found myself getting new demons often, so I usually got other things with my app points.