Which spell is the better use of concentration for a ranged Valor bard with the Elven Accuracy feat: Greater Invisibility or Swift Quiver?

Question

Assumptions:

• ranged College of Valor bard
• the bard has 20 Dex
• the bard is shooting with a longbow
• another player can consistently provide the Help action for 1 attack with advantage every turn
• the bard has the Elven Accuracy feat

The bard is level 10, so a +4 proficiency bonus. The bonus action would generally be used to either cast Healing Word on allies or give them bardic inspiration. For the sake of this question, we can just look at raw damage.

So the comparison as I understand it is:

• Greater Invisibility: 2 attacks with Elven Accuracy advantage, bonus action available
• Swift Quiver: 4 attacks, 1 with Elven Accuracy advantage, no bonus action available

Which is the better use of concentration?

Answer 1

For the sake of argument, we're going to assume that the way this character uses Elven Accuracy (which, when a creature has Advantage, allows one of the Advantage dice to be swapped with a new die, at the user's whim—XGE 74), is that this character will always swap their lowest rolled die with the new one, which is the mathematically optimal way to use it.

Swift Quiver is always going to offer greater damage output

Unfortunately, while having Advantage, especially Advantage with Elven Accuracy, is a pretty decent boost to damage output, it's just not going to compare to having two additional attacks.

Below, I've constructed a table representing the statistically average damage output per round of this character, assuming no other buffs or expended resources than what you have specified, and assuming that with using Swift Quiver, one attack gains Advantage (and thus Elven Accuracy), and with Greater Invisibility, both attacks gain Advantage (and thus Elven Accuracy). I've also included single attacks with a longbow, using a normal roll and an EA-Advantage roll.

\begin{array}{|l|r|r|r|r|r|r|r|} \hline \text{Name} & \text{AC 0} & \text{AC 11} & \text{AC 13} & \text{AC 15} & \text{AC 17} & \text{AC 20} & \text{AC 25}\\ \hline \text{Swift Quiver x4} & 37.891 & 37.891 & 35.010 & 32.043 & 28.935 & 23.879 & 13.934\\ \hline \text{Greater Invisibility x2} & 20.281 & 20.281 & 20.220 & 19.987 & 19.469 & 17.909 & 12.268\\ \hline \text{Longbow x1} & 9.250 & 9.250 & 8.300 & 7.350 & 6.400 & 4.975 & 2.600\\ \hline \text{Longbow W/Elven Accuracy x1} & 10.141 & 10.141 & 10.110 & 9.993 & 9.735 & 8.954 & 6.134\\ \hline \end{array}

We can see that having Advantage is producing a modest, ~9.6% improvement in overall damage for an individual attack, but it's just not going to compare to a direct, +100% improvement in damage when using Swift Quiver.

Note an important fact however: this improvement becomes far less pronounced at higher ACs on the target. Indeed, I extended the array to calculate for AC 29+, and found that at that point, the difference becomes less than 1%. However, there is no point where mathematically, Swift Quiver deals less damage, no matter how high the AC goes, and no published creature in 5th Edition D&D has an AC higher than 25, which is the AC of the Tarrasque.

So ultimately, the choice this character needs to make is whether the 50-20% improvement in damage is worth losing their Bonus Action used for other purposes, like healing allies or providing Inspiration. If so, they should use Swift Quiver. If not, they should use Greater Invisibility.

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^{Full stats for this analysis were posted here, for anyone curious.}

Answer 2

Under these circumstances, Swift Quiver is always better or equal for pure damage. Since both situations involve at least one attack that has Elven Accuracy, we just need to compare the 3 normal attacks that remain in the case of using Swift Quiver to a single Elven Accuracy advantage attack for Greater Invisibility.

Having Elven Accuracy means you roll 3 d20 and take the best result. The attack then hits if the best result is enough for a hit. Doing 3 attacks is also rolling 3 d20 but then any roll that is good enough for a hit will deal damage. This is naturally strictly better than the previous case.

Let me explain what this means in more detail. Let's call the Elven Accuracy case EA and the Swift Quiver case SQ. In both situations, you are rolling 3 d20. Let's take these 3 d20 results and order them from higher to lower: let's call them r1, r2 and r3, where r1 >= r2 >= r3. In order to hit a certain target, we need a certain d20 roll result, let's call this rt. We have the following possibilities:

• If rt > r1, then 0 attacks hit for both EA and SQ, a tie
• If r1 >= rt > r2 >= r3, then the EA attack hits and exactly 1 of the SQ attacks hits, another tie
• If r2 >= rt > r3, then the EA attack still hits but now 2 SQ attacks hit so SQ is clearly better
• If r3 >= rt, then the EA attack still hits but 3 SQ attacks hit so SQ is clearly better

Even factoring in criticals, it's easy to see that the EA attack is a crit if at least one of the d20 rolls is a 20. However, when this happens, then at least one of the SQ attacks would also crit (and the other ones may or may not hit)

Of course, Swift Quiver is expending your bonus action but in terms of just looking at the damage done, Swift Quiver always wins.