Mining and lumberjacking are handled via “harvest banks”. Every harvest bank is filled with a dice rolled resource.
For Skinning, the hides type are rolled when first selecting/targeting the corpse with a skinning knife.

Depending on the region where the crafter is located, the dice roll chances are as following:

Mining/Lumberjacking only:
Additionally on every mine attempt a 50%/50% chance is given to aquire the resource type of the vein or, in dungeons, the fallback resource which is one type below the vein type. So if a player gets a Bronze mining vein, he will get (on average) 50% copper and 50% bronze ore out of it.
Outside of dungeons, the fallback resource is always iron.

Also on every mine attempt, a skill check has to be passed to get resources (against the resource type - what defines the min and max skill for the skill check - see the table below). Here the resource type of the used tool provides a bonus (a valorite pickaxe gives 25% mining skill bonus as an example)

Luck can upgrade a harvest bank to the next better resource. The more luck a player has, the higher the chances that a harvest bank will upgraded to a higher resource. With 100 luck, the player has the doubled chance to upgrade the vein (relative to the chance the resource he tries to update to has).

Example: The player mines the first time on a fresh spot and gets a shadow vein. The chance for copper in a dungeon level 2 is 30.2%. So with 100 luck he has a 60.4% chance to upgrade the vein to copper. With 10 luck, he has a 6.4% chance to get the upgraded vein. This upgrade possibility is only given when the vein gets filled (so on the first mine attempt - not on every single mine attempt on an existing vein.)

See Stealth

For gathering skills, a few weapon types benefit from their associated gathering profession. All damage increases are calculated as an additive bonus.