How do "Divine Orbs" really work?

Thanks hammer, appreciate it.

Edited to show the improvement, extra damage, extra attack speed. Not much but for my end game bow it was worth it. Still room for improvement, but it is quite costly so we'll see. Would love to get 129/13% on it.

Seems like everyone else explained it perfectly.

Basically my bow had the cruel mod and the conquerors mod. Looking at the item data page under prefixes you can determine the min/max a new roll with a divine will yield.

In my case the min i could have rolled is 195%. The max is 223%. I was at 210% and already planned to sell my bow. Wanted to gamble just for fun. Ending up at 211% was pretty laughable but at least it went up and not down.

For reference:
Cruel is 130% -149% ipd.
Conquerors is 65%-74% ipd

When i made that bow it was at 136%ipd. When I exalted it, it went to 210%. Due to this I knew the exact values each mod was contributing.

Just curious: are there any items higher than 211%ipd in this league/reset? Ive yet to see one. Also, my bow is officially sold - will be out of my posession when i get home tonight.