Unarmed Damage

Unarmed Damage is a derived statistic in Fallout 3 and Fallout: New Vegas.

Fallout 3
Unarmed Damage affects only damage done with Unarmed weapons and fists. This damage is added to the damage value of unarmed weapons, in the case of using fists this is the only damage inflicted on an opponent.

For Melee weapons there is a separate statistic called Melee Damage. Strength does not influence Unarmed damage; it only influences melee damage.

Unarmed Damage is governed directly by the Unarmed skill.
 * $$\text{Initial level}=\left\lceil\frac{\text{Unarmed skill}}{20}+0.5\right\rceil$$

Unarmed skill itself can be expanded in terms of Fallout 3 SPECIAL attributes, giving the following:
 * $$\text{Initial level}=\left\lceil\frac{2+(2\times\text{Endurance})+\left\lceil\frac{\text{Luck}}{2}\right\rceil}{20}+0.5\right\rceil$$

Example: An Unarmed skill of 90.
 * $$\left\lceil\frac{90}{20}+0.5\right\rceil=5$$

Example: A starting Endurance of 5 and Luck of 5.
 * $$\left\lceil\frac{2+(2\times5)+\left\lceil\frac{5}{2}\right\rceil}{20}+0.5\right\rceil=\left\lceil\frac{15}{20}+0.5\right\rceil=2$$

Fallout: New Vegas

 * The equation from Fallout 3 is used.
 * The official Prima strategy guide incorrectly gives the Unarmed Damage value as one quarter of the Unarmed Skill.
 * Similar to Melee Damage, unarmed attacks in V.A.T.S double weapons' base damage. Bonus damage from the player's Unarmed skill is not doubled, though.

Behind the scenes
In the original Fallout games, Unarmed Damage was to be another statistic used to measure bonus damage done. It went unused in-game, however.