What is the break point for using a level 1 spell slot for Divine Favor rather than for Divine Smite?

Question

Divine Favor (from a level 1 spell slot) lasts for up to 10 rounds, and on a hit does 1d4 radiant damage.
On a critical hit it adds 2d4 radiant damage.
Divine Smite (from a level 1 spell slot) is good for 1 hit, but does 2d8 radiant damage.
If the hit was critical it does 4d8 radiant damage.

Assumption 1: Combat lasts from 3-6 rounds

Why?
a. That's how long combat tends to last with this group
b. For a two round fight divine smite is without question the better choice.

Case 1: hit Armor Class 14
Case 2: hit Armor Class 16

While I can see Divine Favor being a decent use of a level 1 spell slot once the Paladin has two attacks per Attack Action at level 5, I am trying to nail down (in tier 1 play) how many rounds the combat needs to last for Divine Favor to be the better choice for a level one spell slot.

Assumption 2: paladin makes concentration save if hit during combat.

That assumption is to keep the question within a tight scope. As I discuss this with my paladin player, a separate risk assessment needs to be made vis a vis loss of concentration.

Assumption 3: single class paladin, level 2, 3 or 4.

My back-of-the-napkin-math says "4 rounds" but I may not be setting the problem up correctly. If every attack hits, 4d4 is slightly more damage than 2d8 on average: 10 versus 9. But every attack does not hit.

How many rounds does combat have to last to make divine favor the better choice?

My instinct is that against one big monster, use divine smite to nova the monster down; against a mob of small creatures use divine favor to whittle down a lot of targets - but that is a separate question/problem.

Note: I am the DM in this case, not the player. The Paladin is Dragonborn, and does not have the Sentinel feat. Strength is 18 (Rolled stats). Paladin is sword and board. An answer for a strength 16 paladin (point buy) is acceptable.

Lastly: if you believe that the answer is "It's never the better choice, and here is why" - demonstrating the "why" answers the question. (For example, if the "why" shows that it's not better until the seventh round, it meets the question/problem constraints).

Answer 1

It varies with enemies' hit points, up to turn 8

The actual damage dealt is usually not the thing we are interested in. A often more useful metric is how many (more) things will this let us kill reduce to 0 hit points. A major point here is that dealing 2d8 extra damage to something that would die to an extra 1d4 is wasteful. The problem is that how quickly something will die depends on how many hit points it has, so our result is going depend on that.

So we need to compare how many enemies with a given hit point total and AC we can kill on average over a number of turns using each of two methods: an extra 1d4 on each attack or dealing an extra 2d8 on the first hit. For each of these methods we're ignoring other attacks being made etc., but that would make the modelling completely unfeasible.

Trying to do this analytically makes by brain hurt, so instead I'll be using simulation. The basic idea is to simulate the given scenario, note how many kills we get, and average across many, many runs of the simulation. My Python code here. A couple of notes:

• I simulated crits, but not the paladin waiting on a crit to use their Divine Smite. The Smite is always used on the first hit.

• The last enemy attacked is counted as a partial kill, with the fraction being their fraction of lost hit points.

• I've run this with 1M tries for each data point (yes, this gives quite long run times), effective AC 8 (equivalent to AC 14 with +6 to hit), and using a d8 damage weapon (longsword, warhammer, etc.). Hit points were chosen with a scaling resolution from 5 to 120. (5, 6, 7, 8, 9, 10, 12, 15, 18, 22, 26, 30, 35, 40, 50, 60, 70, 80, 90, 100, 120.)

This can we generate two tables for the average killrate of each method as a function of number of turns and enemy hitpoints. From this we can obtain the relative difference between the two as a function of the two variables. In the below table a positive value (green) means using divine favor has a higher killrate, and a negative (red) means using Divine Smite is better. The plot of the relative rates can be viewed at one's own leisure, it's a bit messy.

There are a few things to observe from the above results. As enemy hit points become very high, the turnover point becomes 6 which agrees with considerations of damage only. This makes sense as little to no damage is lost as a result of the target dying.

At 15 enemy hit points divine favor becomes particularly poor, being more efficient only after 8 rounds. This is presumably because the enemy is just left at very few hit points quite often. Below 15 hit points favor becomes better earlier. This is presumably because the added d4 is often sufficient to kill of enemies where the normal post-Smite attacks do not. At 6 hit points favor is always better (assuming more than one turn) as any hit is guaranteed to kill with favor, but has a chance not to post-Smite. For 5 hit points either method does nothing, because a normal hit is guaranteed to kill the target. Whether the result is positive or negative for 5 hit points is down to noise/chance.

The above method only considers the paladin attacking the enemies. Trying to factor in party members makes the simulation both trickier (more things to calculate) and more specific (need to set attack options for each party member). In general when also considering the enemies potentially being attacked by others, each hit point would have contributions from lower hit points of the paladin only consideration.

Answer 2

6 rounds depending on your hit bonus

against AC 14 with only one attack per round

If the paladin has a hit bonus of 5 (+3 STR, +2 Proficiency) then they will hit AC 14 60% of the time. Divine Favor adds an additional 1d4 to each hit for an average of 2.5 per hit. Adjusting for the chance of missing (2.5 * 0.6 = 1.5) gives an average damage increase of 1.5 per attack.

Assuming you hit at least once during the combat then Divine Smite does a guaranteed 2d8 damage for an average of 9 damage.

Assuming 1 attack per round (not dual wielding or a polearm fighter and no opportunity attack) then it will take exactly 6 rounds for Divine Favor to equal the additional damage of Divine Smite (9 / 1.5 = 6)

Using AC 16 the chance to hit with a +5 bonus is 50%. Divine Favor adds an average of 1.25 damage per round and so it will take 8 rounds for Divine Favor to exceed Divine Smite

Two factors should be considered in addition to average damage increase, however:

1. Frontloaded damage is generally more useful. If you can take down the Grimlock on the 1st round then there are fewer rounds when it can attack you.

2. Extra damage is useless once the target is at 0 hp. If you are fighting a bunch of goblins and you have a greatsword and +3 STR you will have an average damage of 10. Adding 2d8 to a hit on a goblin is probably overkill, even more so if you waited for a critical hit. Adding 1d4 is likely still overkill (it only changes the chance of slaying a 7 hp goblin by 10%) but it will be more efficient than Divine Strike.

So when does Divine Favor become more useful than Divine Smite?

• You expect a longer combat (6+ rounds) and the enemies have AC less than or equal to 14.

• There are many enemies with low hp. Depending on how low even Divine Favor might be a waste but can at least make slaying them slightly more reliable.

• You expect to have more than one attack per round. If you are a polearm fighter and/or expect to have many opportunity attacks Divine Favor will produce gains faster. Divine Smite still is better for frontloading damage but if you just want to increase average damage over the encounter Divine Favor might now be better. Do note, however, that if you only have 2 attacks per round it will still take 4 rounds to equal the damage of Divine Smite with +5 to hit against an AC 16 opponent.

Answer 3

The issue is concentration, not damage

Paladins have limited spell slots and figuring what to use for concentration and which to save for Divine Smites is one of the larger aspects of managing paladin resources.

Divine Favor offers one option for increasing damage, but there are other spells that Paladins have they must also consider to use their concentration. If they go all-in on damage increase, then your question can be answered by others mathematically.

But the real issue for the player is what spell do they want to be concentrating on for other effects. Spells like Shield of Faith, Bless, Protection from Good and Evil, and even Heroism present some very good options that they should be considering.

If they are also using Divine Favor, they have also removed the option of using any of their smite spells which also require concentration. This same issue is still present no matter what concentration spell they choose, but it is something else to consider.

Answer 4

It's messier than that.

Well, of course it is. There's a few things that the "simple math" answer can't taking into account.

• Timing in the fight: taking out the first of five goblins a round early is worth a lot more than taking out the last of those goblins a round early. Smites let you front-load your damage, which means that you can burn through the dangerous, early parts of the fight (when all the foes are still on the battlefield) that much earlier.

• Hits and Crits: Divine Smite is picked after you successfully hit. That means that to compare damage from the two spells, you have to compare it to number of successful hits, rather than number of attacks. Further, since it's done after the hit is rolled, you can actually save your smite for when you happen to roll a crit. Now, it's not possible to get crits on schedule. You might get one late int eh fight or not at all. Things like this make "when do I use my smites" one of the more significant bits of tactical decisionmaking for the paladin. Still, it's a distinct advantage, if you can exploit it.

• total damage: a d8 has an average damage of 4.5 vs a d4's average of 2.5.

/***********/

Basically, for early game (one attack per round) and a 3-6 round fight, it's almost always going to be better to use smites, just because you'll generally miss about half the time, and so you won't get enough hits to make up the damage. If your enemies are individually weak enough that a single hit with smite is significant overkill, then that's less likely to be the case. If it's not overkill, though, then smites are actually better for numerous mid-range foes, as burning through the first enemy or two quickly can make the fight a lot easier. Otherwise, Divine Favor is going to be best for single large foes with low AC but lots and lots of hit points (so you'll generally not miss, and early HP vs late HP won't matter much, but the fight will go on long enough for you to rack up a decent number of attacks). Divine Favor improves significantly once you hit level 5 and get your second attack, especially since at that point you have enough spell slots to consider using both, and they do stack.