Does Proficiency Add to Damage?

Proficiency is generally not added to damage rolls unless some feature expressly says it should. Additionally, it is important to remember that with Finesse weapons, the fighter has the choice of which modifier to use, but they have to use the same modifier for both attack and defense.

Do you add your proficiency bonus to your damage?

Don't Add a Proficiency Bonus to Damage or Healing Throws

While the bonus can be added to attacks, saves, and ability checks, it cannot be added to damage or healing throws. ... It does not add to the damage done in an attack or to the amount of HP restored when healing.

Do you add ability modifier to Damage?

When attacking with a weapon, you add your ability modifier—the same modifier used for the Attack roll—to the damage. A spell tells you which dice to roll for damage and whether to add any modifiers.