With Variable Damage, as the name implies, your damage will vary each time it is dealt.  Even weapons with multiple projectiles like shotguns will each have a chance to deviate from base damage.  This is done script-free through a single perk, and currently damage can vary anywhere between -25% and +25% of the stated damage found in the pip-boy, though the max and min damage are unlikely to occur.

At the moment, the damage variation is rather subtle, especially when shooting with low damaging weapons, but I can add additional types of variations though MCM.

The perk has to be added for any entity to deal variable damage.  While I like to have added the perk to anyone you meet dynamically, my attempts were successful, but the game would inadvertently freeze after 2 minutes of gameplay.  So until I find a stable way of doing this, here how it goes.

Installation

There are 4 options that you can pick from when installing the mod.

Player-Only Adds the perk only to the player.  Should be compatible with anything as no vanilla records were touched.

Humanoids-Only Adds the perk to humanoids by editing their race to add the perk.  Namely other Humans, Super Mutants, (non-feral) Ghouls, and all forms of Synths are affected.

All-Enemies Adds the perk to most entities in the base game.  Nearly every race entry is edited to accomplish this.

All-Enemies+DLC Adds the perk to nearly every entity including those found in the major DLC



Besides the Player-Only option, all other options will edit the race entry.  If you use a mod (typically an overhaul) that edits these, I suggest you place this mod ABOVE them and let them override.