Item discovery is a hidden stat in Dark Souls 2 that represents the rate at which you discover items. It was a normal stat displayed on your character screen in Dark Souls that was adjusted due to different factors like items you wore and whether you were human or hollow. In Dark Souls II, the amount of item discovery you have is hidden from view, but there are certain items that display that they increase your item discovery.
Update: See full-scale test results here.
The actual amount each item increases item discovery is:
Prisoner's Hood= 10
Traveling Merchant Hat = 25
Jester's Cap= 50
Symbol of Avarice = 100 (also increases soul absorption, but you gradually lose health
(5 per second, can be reduced with the Ring of Restoration and Charred Loyce Shields))
Prisoner's Tatters = 15
Watchdragon Parma= 50 as of patch 1.10
Covetous Gold Serpent Ring = 50
Covetous Gold Serpent Ring+1 = 75
Covetous Gold Serpent Ring+2 = 100
Rusted Coin = 100
Burning Bonfire Ascetic will increase item discovery on enemies in that area. The increase begins at +150 for bonfire intensity 2 and caps at +375 for bonfire intensity 8.
They all stack. These are just base points that are used in item discovery calculation. They do not represent percent of item discovery increase.
So best stack is Symbol of Avarice + Covetous Gold Serpent Ring+2 + Prisoner's Tatters + Watchdragon Parma + Rusted Coin + Bonfire Intensity 8 = 740.
Nearly all enemies in game (except bosses, and also known - hollows in Things Betwixt) can have up to 10 possible drop items. It looks like item discovery only affects whether you will get a drop or not. The higher your item discovery, the more chance you will get a drop.
All items have the same rate of drop (no different specified). Just a random number is used to select a drop item from the list of drop items assigned to enemy.
If this random number is higher than your item discovery then you don't get any drop at all.
Random number can be between 0 and 10000.
Total item discovery is calculated as follows in 10 maximum steps (they also equal to drop tiers):
Let's call your additional item discovery from equipped items "addition."
Formula is tested on Hollow Infantry. If your addition = 100 like from Symbol of Avarice:
1: 150 + addition +
2: 150 + addition +
3: 150 + addition +
4: 150 + addition +
5: 150 + addition +
6: 150 + addition +
7: 700 + addition +
8: 500 + addition,
then you will get 2900 in total.
If your addition is 265 (all from items) then you will get 4220.
Sometimes it is:
1: 150 + addition +
2: 150 + addition +
3: 150 + addition +
4: 150 + addition +
5: 100 + addition +
6: 400 + addition +
7: 100 + addition,
and so on.
It seems that the formula is based on the enemy you kill. If enemy drop rate should be more rare then formula addition steps are lowered and base numbers at the end are lowered too. But your "addition" is always the same as you have from equipped items.
Now let's say your random number generated as 1000.
Then (150 + 100) + (150 + 100) + (150 + 100) + (150 + 100) = 1000
Once sum of tiers becomes higher or equal to random number then addition stops. And you get the index of your drop that can be from 0 to 9 (10 total).
In our example you will get 3 (+1 +1 +1 then stop before 4th +1).
Index 3 is 4th item in drop items list (counting from 0).
If it is first Infantry in the Forest o Fallen Giants that has these drops:
Hollow Infantry Helm
Hollow Infantry Armor
Hollow Infantry Gloves
Hollow Infantry Boots
Bandit's Knife
Lifegem
Throwing Knife
then you will get Hollow Infantry Boots as drop.
Some items will only be dropped by an enemy once. For example if you kill a falconer and it drops the falconer gloves that falconer will never drop the falconer gloves again until you enter a new NG cycle either by beating the game or using a Bonfire Ascetic. This will increase the drop rate of the other items when killing this individual falconer.
Soul memory and currently collected souls do not affect item discovery calculation / drop.
Human/hollow form does not affect item discovery.
It looks like item discovery is lowered for enemy after you kill same enemy multiple times (after respawn). (Tried to kill enemy, then die, then kill respawned, then die ... and item discovery is lowered - human/hollow does not affect). ( I can too confirm this, in SOTFS. I was farming the respawning heide knight's and got less drops over time. Over a timespan of about 6~ hours.)
All tested on Forest of the Fallen Giants.
Have not checked but believe being sinner or not does not affect item discovery.
