You can make a simple melee attack is an attack with a natural weapon, melee weapon, improvised weapon or an unarmed strike. When making a simple melee attack, roll 1d20 and add your strength, plus any proficiency bonus (if applicable), against the target's AC. The damage it deals varies.
When making a simple melee attack with an improvised weapon, the DM may state that feats, properties or abilities or proficiencies that work with melee weapons may apply if the improvised weapon is sufficiently similar. For example, the DM may decide that a chair leg functions enough like a club when making an improvised weapon attack, and allow a fighter to apply her duelist fighting style and add proficiency to the attack roll. Otherwise, it deals 1d4+strength bonus damage and most characters and creatures are not proficient in improvised weapon attacks.
Sometimes you can use a ranged weapon as an improvised weapon. If you do so, its properties as a ranged weapon do not apply to the attack.
When making an unarmed strike, your attack deals 1 point of damage (2 on a crit), plus your strength bonus. Most creatures and characters are proficient in unarmed strikes.
When making an simple melee attack with a melee weapon, use the weapon's damage dice plus your strength modifier for damage. If you are proficient in the melee weapon, you get to add proficiency to your to-hit roll.
Most creatures are proficient with any natural weapon they have. Damage is determined by the natural weapon, and typically adds your strength bonus. Some natural weapons use dexterity for attack and damage instead of strength.
Simple ranged attacks can be with a ranged weapon, a melee weapon with the thrown property, an improvised weapon, or a natural weapon. Ranged attacks involve rolling 1d20 plus your dexterity modifier plus your proficiency bonus against the target's AC. The damage it deals varies.
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