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:
Traveling Merchant Hat = 25
Covetous Gold Serpent Ring = 50
Covetous Gold Serpent Ring+1 = 75
Covetous Gold Serpent Ring+2 = 100
Jester's Cap = 50
Prisoner's Hood = 10
Prisoner's Tatters = 15
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))
Watchdragon Parma = 50 as of patch 1.10
Rusted Coin = 100
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 = 365
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 as "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 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 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
Throwing Knife
then you will get Hollow Infantry Boots as drop.

Soul memory and currently collected souls do not affect item discovery calculation / drop.
Human/hollow form does not affect item discovery.
Burning Bonfire Ascetic does not affect item discovery or drop lists.
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 Giants
Have not checked but believe being sinner or not does not affect item discovery.

    • Anonymous

      10 Jan 2017 12:06  

      I also found from farming bonfire astetics that you lose a lot of your percentage of loot drop if you are lower on health. Tried with the symbol and compared with the jester and found a much higher drop rate with the jester cap so check your facts a little better n get out into the world of Dark Souls

      • Anonymous

        10 Jan 2017 11:57  

        Being a sinner has no effect on item discovery anywhere in the world plus two parmas is extremely unconventional and would make the farming task a lot more tedious

        • Anonymous

          Higher Max?29 Aug 2016 11:02  

          It might not be very efficient, but if you daul-wielded 2 Dragon Parmas with the other max discovery items wouldn't that make it the potentially highest discov. set?

          • Proof of numbers29 Aug 2016 11:02  

            I'm sorry but can you post up info how you came up with this info etc. allot of people are going to be EXTREMLY skeptical of all your info period without backing of the codes and work you're doing.

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