I’m considering Blade Ward for a character’s cantrip selection. It takes an action to cast, resulting in the following effect:
Until the end of your next turn, you have resistance against bludgeoning, piercing, and slashing damage dealt by weapon attacks. (PHB pg. 219)
Where “resistance” means:
If a creature or an object has resistance to a damage type, damage of that type is halved against it. (PHB pg. 197)
Importantly, this character could make a different defensive choice, using its action to Dodge instead of casting the cantrip. The Dodge action results in the following:
Until the start of your next turn, any attack roll made against you has disadvantage if you can see the attacker, and you make Dexterity saving throws with advantage. You lose this benefit if you are incapacitated (as explained in appendix A) or if your speed drops to 0. (PHB pg. 192)
Because Blade Ward lasts until the end of your next turn while Dodge ends at its start, Blade Ward is clearly better at protecting you from opportunity attacks that happen on the turn after you cast it. Similarly, if you’re not facing weapon attacks that deal bludgeoning, piercing, or slashing damage, the Dodge action is clearly the better choice.
However, if you’re only considering bludgeoning, piercing, and slashing weapon attacks dealt in the time when Dodge would be active, when is casting Blade Ward the better option? When is taking half-damage from attacks that hit a better choice than reducing those hits through disadvantaged attacks and advantaged Dexterity saving throws?
Or, to put it more mathematically, when will the Dodge action reduce the number of successful attacks and failed Dexterity saving throws by more than 50%?