I want to know if you can make an attack roll with one stat, but deal the damage with another. As a monk, can you make a melee attack roll using your Strength modifier, but roll damage with your Dexterity modifier?
I was thinking of making a multiclassed monk/barbarian. I was hoping to use Reckless Attack to gain advantage on the attack roll, but that requires attacking using Strength, so I was wondering if I could attack using Strength but use my Dexterity modifier for the damage rolls.
You must use the same ability modifier for damage and attack.
Basic Rules, Damage and Healing
When attacking with a weapon, you add your ability modifier--the same modifier used for the attack roll--to the damage.
It makes certain multiclasses more powerful and makes the already-powerful DEX ability score even more powerful.
For example, consider a multiclassed Barbarian/Monk. Allowing the player to use STR for attack and DEX for damage means they can Rage and use Monk features in the same attack. Rather than having to make a choice with consequences, the player can have the best of both features with no consequences.
Attack rolls have the following general rule:
Ability Modifier. The ability modifier used for a melee weapon attack is Strength, and the ability modifier used for a ranged weapon attack is Dexterity.
Damage rolls also have a general rule:
When attacking with a weapon, you add your ability modifier--the same modifier used for the attack roll--to the damage.
Because these are general rules, there can be exceptions to them. Finesse weapons, for example, are exceptions to the rule about using Strength for melee attacks, but are not exceptions to the rule about using the same modifier for attack and damage rolls:
Finesse: When making an attack with a finesse weapon, you use your choice of your Strength or Dexterity modifier for the attack and damage rolls. You must use the same modifier for both rolls.
The monk's martial arts ability is an exception to both the general rule about melee weapons using strength and the general rule about having to use the same modifier for attack and damage rolls:
You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.
It is easy to see the exception to the melee-Strength rule. That martial arts is also an exception to the same-mod rule is harder to see. There is some weak support in that, unlike finesse, martial arts does not explicitly call out the need for the same modifiers to be used.
But the stronger reason is the specific use of 'can + and'. Whenever a class ability includes "can", we are to understand that it is generating possibilities under the player's control; using "can" with "and" implies that each possibility may be taken separately and independently.
For example, consider the text of unseen servant:
Once on each of your turns as a bonus action, you can mentally command the servant to move up to 15 feet and interact with an object.
We understand this to mean that as a bonus action you can command the servant to move, or you can command it to interact, or you can command it to do both - but it is not required that it do both. If 'can + and' meant 'either both or neither', it would mean you could have the servant move only when it also interacted with an object. By itself, the servant could not move across an empty room!
Another example of this distributive 'can + and' is the wood elf's:
Mask of the Wild. You can attempt to hide even when you are only lightly obscured by foliage, heavy rain, falling snow, mist, and other natural phenomena.
Grammatically, "or" might be a more natural choice here rather than "and". But the specific way the PHB uses 'can + and' is to indicate that any and all selections from a list are possible; you can take some without the obligation to take others. So, my wood elf can attempt to hide with just foliage and nothing else, with just heavy rain, with foliage and heavy rain, etc., without implying anything about whether there has to be mist or not.
Returning to martial arts:
You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.
This means that you can use Dex instead of Str for attack rolls, or for damage rolls, or for both. Because martial arts uses "can + and", and because it doesn't explicitly prevent you from using one and not the other like finesse, you can make each choice independently as an exception to the same-mod rule.
Thus your barbarian / monk makes their first attack, and chooses to use their reckless attack feature. For the remainder of their turn, all of their Strength-based attack rolls will have advantage. They make their attack roll using Strength, and do not choose to replace the Strength modifier with Dexterity (because if they did, they would lose reckless advantage on the attack). If they hit, they then choose to use their martial arts feature to replace the Strength damage modifier with Dexterity.
