What marks get boosted?
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Title Power 3 adds 3 rolls to the odds of finding a Mark available on wild Pokemon. Thus:
Rare Mark: 4 in 1000Any Personality Mark: 4 in 100Specific Personality Mark: 4 in 2800Weather Mark: 4 in 50Time Mark: 4 in 50
These odds assume you don’t have the Mark Charm.
Marks (Serebii)
Here is a useful resource for the base odds.
I have found that each level gives you an extra roll on each check. It is suprisingly straightforward, actually. I tested this in Blizzard conditions for confirmation, and that seems to be exactly what is happening, and it occurs at the time the Pokémon spawns, not when it is captured.