When is casting Blade Ward better than taking the Dodge action?

Question

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?

Or, to put it more mathematically, when will the Dodge action reduce the number of successful attacks by more than 50%?

---

FOLLOW-UP

For those of you saying Blade Ward isn't worth taking because offense is typically better than defense, I understand. However, this character already has 2 offensive cantrips -- a ranged attack and a saving throw debuff with some damage -- plus 3 utility cantrips.

He will learn 2 more as he levels up. I'll probably choose multi-target damage for one of them. Beyond that, I don't see the value in yet another offensive selection, and none of the remaining utility options seemed a good fit for this character. Thus my consideration of Blade Ward.

I was trying to figure out exactly what value Blade Ward added, especially in light of the available Dodge action. (Thank you, all, for your help on that.) Depending on what we conclude here, I'll decide if I should go ahead and take Blade Ward or try to make a 4th utility option fit this guy's themes instead.

---

Answer 1

Usually, these options break even when your enemies need to roll a natural 11 or better to hit you

Ultimately, which action is better comes down to how easy it is for your enemies to hit you and exactly how much damage they do. When considering statistical questions like this I like to use Anydice to figure them out.

For the case of attacks, I created this anydice script:

function: attack ROLL:n TARGET:n DAM:d CRIT:d {
  if ROLL = 1 { result: 0 }
  if ROLL >= 20 { result: DAM + CRIT }
  if ROLL >= TARGET { result: DAM }
  result: 0
}

DAM: 1d10+3
CRIT: 1d10
loop AC over {1..20} {
  output [attack 1d20 AC DAM CRIT] named "Attack against AC [AC]"
  output [attack 1d20 AC DAM CRIT]/2 named "Attack against AC [AC] with resistance"
  output [attack 2@2d20 AC DAM CRIT] named "Attack against AC [AC] with disadvantage"
}

The function attack calculates the expected damage when making an attack (simply feed in a d20 roll for to hit, the d20 roll needed to hit, and the damage done plus additional damage on a crit). In this example I used a fairly typical longsword attack to set the damage (1d10+3, with an extra d10 on a crit). Resistance is applied by halving the resulting damage, and disadvantage is applied by using the roll 2@2d20 (an expression which selects the second highest die from a 2d20 roll).

You can eyeball the results in Anydice (I suggest using the "Table" and "Summary" view modes to make the most visual sense of it), but I went ahead and exported the results to do a bit more analysis. Below is a table showing the relative benefits of resistance and disadvantage against a 1d10+3 longsword attack.

Min. to-hit	Av. Damage	Resistance	Res. Reduction	Disadvantage	Disadv. Reduction
1	8.35	3.9375	52.84%	7.685	7.96%
2	8.35	3.9375	52.84%	7.685	7.96%
3	7.925	3.7375	52.84%	6.89875	12.95%
4	7.5	3.5375	52.83%	6.155	17.93%
5	7.075	3.3375	52.83%	5.45375	22.92%
6	6.65	3.1375	52.82%	4.795	27.89%
7	6.225	2.9375	52.81%	4.17875	32.87%
8	5.8	2.7375	52.80%	3.605	37.84%
9	5.375	2.5375	52.79%	3.07375	42.81%
10	4.95	2.3375	52.78%	2.585	47.78%
11	4.525	2.1375	52.76%	2.13875	52.73%
12	4.1	1.9375	52.74%	1.735	57.68%
13	3.675	1.7375	52.72%	1.37375	62.62%
14	3.25	1.5375	52.69%	1.055	67.54%
15	2.825	1.3375	52.65%	0.77875	72.43%
16	2.4	1.1375	52.60%	0.545	77.29%
17	1.975	0.9375	52.53%	0.35375	82.09%
18	1.55	0.7375	52.42%	0.205	86.77%
19	1.125	0.5375	52.22%	0.09875	91.22%
20	0.7	0.3375	51.79%	0.035	95.00%

The results show that the break-even point between resistance to damage and disadvantage on the incoming attack is when the enemy needs to roll ~11 or better hit you. It also shows that though the value of resistance varies very little, the value of disadvantage swings dramatically from very low to very high as the attacker's hit chance decreases.

This makes sense mathematically; if the enemy has a 50% chance to hit, then disadvantage on the attack roll reduces that to 25%, so exactly halves the number of attacks that hit. Above a 50% hit chance, disadvantage becomes proportionally less effective, so the flat 50% of resistance is better; below a 50% hit chance, disadvantage becomes more effective, and so the increasingly reduced chance of being hit overtakes the flat reduction of resistance.

However, the values in the table don't quite perfectly correspond to what we'd naively expect. Because you round down the fraction when halving damage, resistance actually grants slightly better than 50% damage reduction when the original damage is odd; however, disadvantage not only reduces the chance of a hit but even more significantly reduces the chance of a crit, and so also reduces the expected damage by a slightly greater proportion than it reduces hit chance. The exact determination of which is better depends on how much damage the enemy does normally and how much extra damage they do on a crit. In this case, using a typical 1d10+3 damage attack, resistance is ever so slightly better when requiring an 11, but disadvantage is clearly superior on a required 12+.

Resistance becomes a stronger option as the individual attack damage decreases, because when the damage values are already very low, rounding down those fractions is proportionally stronger. In the most extreme case of an attack that only ever does 1 damage or 2 on a crit, such as a rat's bite, then resistance is better all the way up until you're hit on a 17+. Conversely, when the attack damage is very high on average, the effect of rounding fractions is proportionally less; if you're being bitten by a Tarrasque for 4d12+10 damage, then resistance is a better option only up to a required 10, and disadvantage gains the edge on a required 11+.

If an attack has unusually vicious critical damage, the effect of reduced critical hit chance becomes stronger. Taking the 1d10+3 example, if the critical hit instead does an extra 2d10 damage (for instance, as a result of a Half-Orc's Savage Attacks feature), then disadvantage is better on a required 11. If that crit did an extra 4d10 damage (e.g. as delivered by a high-level barbarian half-orc) then disadvantage would be better on a required 10+.

Taken altogether, the general rule of thumb we can derive here is that if the enemy needs to roll an 11 to hit you, resistance and disadvantage will be nearly equivalent; below that, resistance is superior, and above that, disadvantage wins out, except in quite extreme edge cases. For the attacks of most monsters an adventurer is likely to encounter, this rule holds. You could experiment with changing the values in the script I used if you want to figure out the exact break point in different circumstances.

Are they worth it?

In practical terms, the value of either action is somewhat dubious in most situations.

When you're already hard to hit, Dodge is relatively better than blade ward, but the absolute value of Dodging is ultimately quite trivial. If an enemy hits you on a 16+ with a 1d10+3 attack, Dodging saves you just under 2hp per attack. Even for a much deadlier attack, such as the Tarrasque's 4d12+10 bite, at the same hit chance, Dodging saves you only ~8hp per attack.

When you're getting hit half the time, the two actions are roughly equivalent to each other. 1d10+3 on an 11+ loses ~2.4hp to either. If the Tarrasque's 4d12+10 hits on 11+, blade ward saves ~9.1hp, and Dodging saves ~10.2hp.

When you're easy to hit, blade ward is better than Dodge, and the absolute value of the action is greater than when you're harder to hit - but still relatively low. A 1d10+3 attack that hits on a 6+ loses ~3.5hp per attack to a blade ward. A 4d12+10 attack that hits on a 6+ loses ~14.33hp.

Contrast this to using your action to, for instance, cast a 1st level magic missile. That spell will do 10.5hp damage on average, and is likely at the low end of the expected damage output available to your character by the use of their action. That's more damage dealt than is saved in almost all of the examples above, even when accounting for being attacked multiple times!

Unless you expect to be attacked multiple times by enemies that do a lot of damage and will hit you easily, your action would very likely be better spent doing something else. If you are in that circumstance, though, blade ward is a much better option for mitigating your incoming damage than the Dodge action.

As a general rule, as well, you're almost always better off to take damage in a few smaller chunks than in one big chunk. For example, if you're trying to maintain concentration on a clutch spell, you're better off taking two hits that do 25 damage each and making two achievable DC12 concentration saves than one hit that does 50 damage and requires a quite unlikely DC25 save. So, for practical purposes, I judge that blade ward is better than Dodge, damning with faint praise though that may be.

Bonus saving throws tangent: when you can save for none on a natural 10 or less

Blade Ward isn't actually useful against saving throw effects since it only applies to weapon attacks, but the original version of the question did ask and so I figured it out. For the sake of argument, if you were in a situation where you could choose between getting advantage on a saving throw or resistance to the resulting damage, the math basically works out inversely to that of attacks. I used this anydice script in order to calculate the consequences for saving throws:

function: save ROLL:n TARGET:n FULLDAM:n HALF:n {
  if ROLL >= TARGET {
    if HALF { result: FULLDAM/2 }
    result: 0
  }
  result: FULLDAM
}

DAM: 3d6
loop DC over {1..20} {
  output [save 1d20 DC DAM 1]/2 named "Save for half against [DC] with resistance"
  output [save 1@2d20 DC DAM 1] named "Save for half against [DC] with advantage"
}

loop DC over {1..20} {
  output [save 1d20 DC DAM 0]/2 named "Save for none against [DC] with resistance"
  output [save 1@2d20 DC DAM 0] named "Save for none against [DC] with advantage"
}

The results depend on whether or not you save for half damage or no damage, so I split those two out into different sections. The save function takes a d20 roll, a target number, a damage expression and a flag for whether or not it saves for half; then it calculates the expected damage given those values. As above, I recommend table and summary view.

These results show us that when you can save for no damage, advantage on the save is better than resistance if your required number is 10 or less; if you need to roll an 11 or better to save, resistance is superior. Basically, this is the inverse of the result for attacking - on a required 11, advantage will make the save exactly twice as often as a regular roll, but resistance works out slightly better because it rounds down that fractional damage, and this time there are no critical hits to skew it back the other way.

However, if you can only save for half damage, resistance is always better than advantage on the saving throw; there is no required roll where advantage on the save won't reduce your expected damage more than giving yourself resistance will. The chance to halve your incoming damage twice - both with a save and with resistance - simply skews the results strongly in favour of resistance.

Answer 2

As shown in the numbers analysis by Thomas Markov, when it comes down purely to the numbers, Blade Ward is likely to be better if the opponent is pretty likely to hit.

There's a few additional reasons why you'd want to use one over the other, so I'm giving some edge cases here.

You might want to use Dodge if:

• The damage isn't what scares you. Dodge, if it works, also lets you avoid any other effects from being hit, like becoming poisoned, paralyzed, pushed, grappled, etc

• Half damage is still going to drop you. If you're at 1 hp then taking half damage won't make a big difference (unless you die outright; but see below)

• Only part of the damage is physical. IE; poison bite, flaming sword, that kind of thing.

• Your enemy has really nasty crits (or Divine Smite). The odds of taking a crit when attacked with Disadvantage are very low.

• Your enemy can Sneak Attack you with Advantage so you need to cancel it.

You might want to use Blade Ward if:

• Taking full damage is going to be fatal, but half is not. If you have 1 hp and 10 max hp, then being hit for 15 damage means you die. Being hit for 7 damage means you are dying. 10% chance of outright death is scarier than 20% chance of being down and taking death saves.

• You have regenerating temp HP. Odd case, but if you have 5 temp HP per turn then taking 5 damage every turn will never harm you, but taking 10 damage every other turn will eventually kill you.

• When you want to get hit but not die from it too quickly. Armor of Agathys, Hellish Rebuke, Fire Shield, etc all benefit from triggering more often without killing you.

• Your enemy already has Disadvantage, so you're just stacking on more defenses.

And then one more, due to the lack of "half a point of damage". If you are taking very small and odd amounts of damage, the numbers in the table might skew a bit because 3 damage goes down to 1, not 1.5. That means that Blade Ward blocks 66% of 3 points of damage instead of 50%.

It becomes less visible with bigger amounts of damage; 21 damage goes to 10, which is just 52% and it limits down to 50% anyway.

However it does mean that in the most extreme edge case, taking a single point of damage, Blade Ward reduces damage by 100%. Dodge won't top that. This probably won't come up very often, except for one very important thing: it means your Wizard will survive that battle with the common house cat for as long as he can stay awake to cast Blade Ward ;)

Answer 3

As a player, this is impossible to really know.

The probability that a particular attack hits you is a function of two things: your armor class, and the attacker's bonus to hit. As a player, you do not know what an attacking creature's bonus to hit is, so you can't know for sure if Dodge will be better than blade ward.

That said, we can make some estimates based on our own armor class and where we think a creatures bonus might be, but we should realign our approach to the math here.

We should compare the relative average reduction in damage.

We could check the Dodge action for when it makes an attack 50% or more likely to miss, but we can get more information by analyzing the average damage reduction. For simplicity, suppose a single attack deals 10 damage. We will check the damage reduction from both Dodge and Blade ward at different ACs and Hit bonuses.

So there are going to be several tables here, and eventually we will get to a table that shows exactly which combinations of AC and attacker hit bonus are better for Dodge or blade ward.

First, we have a basic expected damage table. Assume an attack deals 10 damage on a hit. For further simplicity, I am not considering critical hits or misses. We can still get close enough to what we need here without crits complicating things. Then the expected damage for the attack given an AC and hit bonus is:

When the attacks are made at disadvantage, our table looks like this:

So the average reduction in damage of the Dodge action is:

Finally, we subtract the blade ward numbers (the first table halved) from this table, and it well tell us when Dodge is better than blade ward:

The green cells indicate where Dodge is better than blade ward against an attack. So to use this table, you have to consider how many attack you expect to receive, what your own AC is, and where you think the attackers' hit bonus is at. As I stated in my first section, you can't know for sure, but if you think you;re going to fall in the green range, the Dodge action is probably better.

I know, I didn't address saving throws, but it was already complicated enough, and lots of saving throws you will encounter will be for more than just bludgeoning, piercing, or slashing, so if you're anticipating fireballs, obviously just Dodge.

Blade ward has its place when you suspect that a creature's attacks are especially likely to hit, either because your AC is terrible, or you suspect they have a very high bonus to hit.

Answer 4

Neither

Because they are both crappy uses of your one and only Action.

The point of D&D combat is to reduce your opponent to 0hp before they do the same to you. Except in extremely niche and vanishingly rare cases neither of these options advance that goal. The pertinent question for action choice is “which action best assists me to win this combat.” Neither of these do that. At best they delay you losing.

Attack is a better choice. Cast a (better) Spell is a better choice. Dash and disengage are likely to be better choices. Hell, even Help is a better choice.

That said ...

Dodge is better

From an opportunity cost perspective.

Anyone can Dodge so it has no opportunity cost. Blade Ward takes up a rare and irreplaceable cantrip slot and there are so many better cantrips to put there.

That said ...

The mathematics is straightforward

1. If you aren't going to be targeted by an attack, Dodge doesn't help.
2. If you aren't at risk of suffering Bludgeoning, Piecing or Slashing damage, from weapons Blade Ward doesn't help.
3. Otherwise ...

Dodge is as good or better than Blade Ward if:

$$ \sum_{i=1}^n(1-(1-h_i)^2)(B_i+b_i+O_i+o_i)+c_i^2(2B_i+b_i+2O_i+o_i)\ge\sum_{i=1}^n\lfloor{h_i(B_i+b_i+O_i+o_i)+c_i(2B_i+b_i+2O_i+o_i)}\rfloor $$

where $$ \begin{align} i&=\text{the }i\text{th attack}\\ n&=\text{the total number of attacks}\\ h_i&=\text{the chance of the }i\text{th attack hitting normally}\\ c_i&=\text{the chance of the }i\text{th attack hitting critically}\\ B_i&=\text{a random variable representing the rolled Bludgeoning, Piercing or Slashing weapon damage from the }i\text{th attack}\\ b_i&=\text{the bonus Bludgeoning, Piercing or Slashing weapon damage from the }i\text{th attack}\\ O_i&=\text{a random variable representing the rolled Other damage from the }i\text{th attack}\\ o_i&=\text{the bonus Other damage from the }i\text{th attack}\\ \end{align} $$

Once you know the variables, the computation is straightforward.

However, in practice, you will rarely if ever know any of the variables in enough detail to make more than an educated guess.

Answer 5

Other answers have covered the general case really well but there are several situational factors that greatly influence the choice between Dodge and Blade Ward:

Several subclass features synergize with Blade Ward

In particular the Eldrich Knight has access to War Magic feature that states the following:

Beginning at 7th level, when you use your action to cast a cantrip, you can make one weapon attack as a bonus action.

The Valor Bard gains similar feature (Battle Magic) at level 14, that works with all bard spells.

These features in particular make Blade Ward almost always the superior choice because you can retain part of your offensive capability.

---

If you happen to be a Beastmaster Ranger of at least 15th level - casting blade ward will also affect your animal companion. Similarly Blade ward will also apply to any mount summoned by Find Steed or Find Greater Steed.

Blade Ward stacks with other sources of disadvantage

Having disadvantage on attacks is not uncommon and as a spellcaster there are plenty of tools how to inflict it upon your enemies (e.g. anything that causes them to be poisoned or frightened). If your enemy would already have disadvantage on the attack Dodge has no effect while Blade Ward still functions normally.

This also means that Blade Ward might be more effective based on subclass choice of your other party members. E.g. Cavalier Fighter or Path of the Ancestral Guardian Barbarian can consistently grant disadvantage to enemies targeting other party members.

Dodge stacks with other sources of resistance

Resistance to appropriate damage types is much rarer than disadvantage, but if you happen to have it it is worth remembering that Blade Ward is useless in this case. So if you happen to have Stoneskin in effect or you are a Warlock of Fiend that has chosen the appropriate damage type for Fiendish Resilience - remember to use Dodge.

You can do both as Sorcerer with Quickened spell

Quickened spell metamagic option allows you to cast Blade Ward as bonus action. If you really want to avoid being damaged you both doge and cast Blade Ward on the same turn.

Answer 6

You shouldn't plan to do either.

"The best defense is a good offense." Do you know who said that? Mel, the cook on Alice.

It's very rare that you would rather use an action to defend than to make an attack, even if it's just a cantrip. Dead enemies don't deal damage, and passing time against a powerful opponent by going defensive is rarely a good strategy.

There are exceptions; if you've gotten cornered and don't have any useful melee attacks, or you've been blinded, or something like that, defending is probably better than making an attack at disadvantage. If you've just cast a big concentration spell, you may want to defend to prevent losing it (though using your action on mirror image or invisibility would be vastly more effective than either Dodge or blade ward, if you have the spell slots for them). But those scenarios are very rare, in my experience. In many years of playing 5th edition, I think I might've used the Dodge action two or three times; there's almost always something more useful to do.

And then when it does seem like a good idea to take a defensive stance, the blade ward cantrip is better primarily when the enemy already has advantage on you or your defense is poor so you have little chance of escaping the hit even with disadvantage; Dodge is better against enemies that deal non-weapon damage or have a relatively low chance to hit. Still, in most cases they seem pretty close to identical in terms of average effect on survival.

In the aforementioned "keep my concentration" scenario, halving the incoming damage may be superior to dodging, but only if you're pretty sure of taking only one or two hits. Sooner or later, you'll roll low, and it won't matter whether the incoming damage was 2 or 22.

Situationally, Dash can be as good or better as a defensive option -- putting a wall between you and the enemy or just getting a long way down-field can often be all it takes to prevent even getting targeted.

In other words, defending doesn't tend to be a good strategy anyway, and like true strike, blade ward is not vastly superior to your innate actions in most cases. It seems unlikely that blade ward is worth the cantrip slot.