This topic resurfaces every once in a while.
I had a hypothesis, that hasn't been confirmed nor rejected yet: Praying changes your luck.
Let's say you did the job "Ambush" for 50 hours. On average these should drop 9 fancy jewelries. Let's say you notice that you've got way fewer products than expected. Try praying once, then do another batch of the job.
Or you're harvesting chili peppers for days, and the key to Henry's house still hasn't dropped. Pray once, then go back to the pepper field.
Or you notice you barely land a hit during duels, despite wearing dueling clothes and having a good allocation of skills. Try praying once, then go back to dueling.
Or during fort fights, you seem to miss more shots than ever. Visit the church for a praying, then join the next battle.
However, if you notice you're on a roll, don't go praying. If my hypothesis is correct, praying can either increase or decrease your luck, or increase your luck for an activity and decrease it for another.
I noticed something like that, never gave itmuch thought till i read this. While i was searching for valuable drops in GR, if i prayed for no reason while things were going smoothly i wouldn't get item drop for ages.