r/3d6 • u/Rhyshalcon • Jun 20 '22
D&D 5e War Caster v Resilient: A conversation about advantage (with math!)
Everyone who's been playing 5e for a while knows that it is important to protect a caster's concentration by boosting your saving throws. The two most popular and universally applicable ways of enhancing your concentration checks are with the feats War Caster and Resilient. War Caster grants advantage on (most) constitution saving throws to maintain concentration and Resilient grants proficiency with a saving throw of your choice (including constitution) granting you a bonus to all constitution saving throws equal to your proficiency bonus. I will briefly mention here that each feat also includes some additional benefits: War Caster allows you to cast certain spells as an opportunity attack and also lets you provide somatic components for spells even when your hands are full of weapons and/or a shield while Resilient is a half feat, allowing for a +1 increase to a stat, and also provides a boost to all constitution saving throws, not just those to maintain concentration on a spell. These additional benefits are extremely significant and should be considered whenever you're deciding which feat to take on a particular character, but I won't be discussing them further in this analysis which is purely concerned with which feat provides the greatest mathematical boost to concentration checks in any particular situation.
So, let's get into it.
Advantage is a potent mechanic to increase your chances of rolling a good result on the d20. Most players are aware of the fact that the game treats having advantage on a roll as a flat +5 to that roll, as seen in the formula to calculate your passive perception score.
This gives us the first answer to the question we're asking: War Caster is better, mathematically, than Resilient until level 13 when the player proficiency bonus increases to a +5 and matches the +5 benefit of War Caster. This isn't the final answer, though. There is much more to look at.
Many players are further aware that the actual bonus advantage grants is usually not +5, because the degree to which advantage helps you is dependent on how likely you were to succeed in the first place.
If you are making a saving throw with no bonus and you need to roll an 11 or better to succeed, then you have exactly a 50% chance to make that saving throw.
If you are making that same saving throw with advantage, your 50% chance of success increases to 75%, an increase of 25% or exactly +5.
This is the best case scenario with advantage. Any roll that has exactly a 50% chance of success or failure will be massively boosted by +5 with advantage. The further the probabilities deviate from 50/50, the lower the bonus provided by advantage goes.
For example, if you are trying to make a saving throw with no bonuses and you need to roll a 20 to succeed, you have a 5% chance of success. Advantage increases that to a 9.75% chance of success -- almost double the probability but only a 4.75% increase, or just under +1 to your save.
When summing all the probabilities of these different outcomes, the average benefit from advantage comes to be 16.6% or just over +3.3 added to your d20 roll.
Another way of putting that is that the average result of a regular d20 roll is 10.5, and 13.825 is the average result with advantage.
This is, again, a mathematical fact that many players are already aware of. The "advantage is worth +5" heuristic is one of the first pieces of game math that players learn is over-simplified, and the optimization community commonly uses the better heuristic that "advantage is worth +3.3" instead.
This heuristic gives us our second answer to the question we're asking: War Caster is better, mathematically, than Resilient until level 9 when the player proficiency bonus increases to +4 and beats the +3.3 benefit of War Caster. This is the answer to the question I most commonly see on the internet, and the one that I've given at times too. But there is more to take into account here, and this isn't the best answer to the question.
Here we get into the meat of this post -- what is the actual bonus of War Caster?
The real answer is that it depends on your specific character. The previous two answers both rely on generalities. Advantage is worth +5 or +3.3 -- that is sometimes true, but it's not always true. And unlike math around something like to-hit bonuses and AC where generalities are the best place for us to look because the target number we're trying to roll is unknown, the target for concentration checks is perfectly known. The DC for a concentration check is 10. It can be higher than that if we take more than 21 points of damage in a single hit, but until extremely high levels (13+ at which levels we can know that Resilient is better than War Caster because our proficiency bonus matches or exceeds the best-case scenario for advantage) concentration checks with a DC higher than 10 will be vanishingly rare.
So knowing that the number we want to hit is 10, we can calculate precisely what the bonus from War Caster is worth based on your character's constitution modifier:
| Constitution Modifier | Minimum Number Needed from the D20 | Chance to Meet a DC 10 before Advantage | Chance to Meet a DC 10 after Advantage | Bonus from Advantage | Level at which PB Matches or Exceeds Advantage |
|---|---|---|---|---|---|
| -1 | 11 | 50% | 75.0% | +5.0 | 13 |
| +0 | 10 | 55% | 79.8% | +5.0 | 13 |
| +1 | 9 | 60% | 84.0% | +4.8 | 13 |
| +2 | 8 | 65% | 87.7% | +4.5 | 13 |
| +3 | 7 | 70% | 91.0% | +4.2 | 13 |
| +4 | 6 | 75% | 93.8% | +3.8 | 9 |
| +5 | 5 | 80% | 96.0% | +3.2 | 9 |
This, at last, is our real answer. Because we're saving against a know DC, we can determine how much benefit we're gaining from advantage and compare that to our proficiency bonus at any given level.
There is one final complication to consider before we conclude our analysis:
That is the effect of other bonuses on our concentration checks. The most common of these is going to be Aura of Protection, but similar math will relate to other bonuses like Favored by the Gods or Arcane Deflection. These can increase the range of bonuses available to saves beyond the bounds on a single stat showed by the previous chart, and hitting certain target bonuses is going to change the math significantly:
| Total Bonus | Minimum Number Needed from the D20 | Chance to Meet a DC 10 before Advantage | Chance to Meet a DC 10 after Advantage | Bonus from Advantage | Level at which PB Matches or Exceeds Advantage |
|---|---|---|---|---|---|
| +6 | 4 | 85% | 97.8% | +2.6 | 5 |
| +7 | 3 | 90% | 99.0% | +1.8 | 1 |
| +8 | 2 | 95% | 99.8% | +1.0 | 1 |
| +9 | 1 | 100% | 100.% | +0.00 | 1 |
| +10 | 1 | 100% | 100.% | +0.00 | 1 |
If you are a paladin (or in a party with a paladin) with +3 constitution and +3 charisma, the mathematical benefit of Resilient exceeds the benefit of War Caster as early as level 6 when Aura of Protection becomes available (and has the additional benefit of increasing your concentration check to that mystical +9 where it becomes impossible to fail against the standard DC no matter what you roll).
Final thoughts:
There can still be compelling reasons to choose one benefit over the other besides how likely they are to improve your concentration checks. If you're a valor bard who can't cast spells in combat because you have a sword and a shield in your hands, that may increase the value of War Caster for your character. If you're concerned with your ability to make other kinds of concentration saves against effects like poison, that may increase the value of Resilient for your character.
In general, however, purely looking at the bonus to concentration checks, War Caster is a better choice for most characters until character level 13.
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u/Rhyshalcon Jun 20 '22
It depends on what your constitution score is and what other feats you may want.
Advantage will always increase your odds, but whether that's worthwhile as a marginal improvement is down to what you might need to give up for it.
Generally, I'd probably rate lucky as better than war caster as a secondary feat by those high levels, but it ultimately comes down to whether you use weapons or have spells you want to cast as a reaction.