The chance to hit an opponent is the same as with a closed ranged weapon.
Means your attack rating multiplied by 10 minus the defence of the monster multiplied by 10.
(Modified by your items and active spells)
The chance to do a critical hit is: Dexterity+Luck in Percent (modified by used bow and arrows).
The amount of damage you cause is: 2-12 (modified by used bow and arrows)