What does purity do?

I'm guessing it effects the priest's eligibility to become cardinal or pope, but I can't see much effect of the eligibility trait itself either.

Doesn't show many stats for the priests, but they seem to affect the priest if they become Pope. Anyone else notice that violent Popes seem far more likely to order crusades and excommunicate factions?

Purity/Violence influence the piety of Inquisitors spawned if the priest becomes a pope.
High Violence = Higher Piety
High Purity = Lower Piety