D&D General Reducing incoming damage: +1 =/= +5%

[clearstream]

Something I wanted to briefly investigate is the impact of +1 on AC. Sometimes it is discussed as 5% better. My interpretation differs. The model I suggest is that of reduction to incoming damage. Suppose 20 feeble skeletons are attacking a fighter, hitting on 16+ and dealing 5 damage on a hit. For the sake of argument assume perfect distribution: each round, five skeletons hit and deal 25 damage. What does +1 AC do for the fighter?

1. Continuing for the sake of argument to assume perfect distribution: each round four skeletons hit dealing 20 damage. Four skeletons, instead of five.
2. In abstraction 4/5 = 0.8 so the incoming damage is 80% of what it had been.
3. That means that the benefit of +1 AC to the fighter was to reduce the damage by 20% (the one out of five hitting skeletons that no longer hits.)
4. +1 AC is only a 5% improvement when all twenty skeletons are hitting (on 1+), so that +1 AC reduces that to nineteen instead: 19/20 = 0.95 for a 5% reduction in incoming damage.

That is why defense fighting style, at a meagre +1, is at least as good as archery and dueling, which both offer +2. They're all solid styles, but defense is sometimes evaluated as being much worse than it is. Additionally, AC is something that the more you have, the more additional points count. As can be seen by considering if only two feeble skeletons were hitting (on 19+) so that the change took incoming from two hitting each turn to one hitting each turn. 1/2 = 50% or an incredible 50% reduction in incoming damage.

 

[Charlaquin]

I think part of the reason AC is often undervalued is that the rules don’t always treat it consistently. In weapons, for example, +1 AC seems to be treated as “worth” 1 damage per round - switching from a 2-handed weapon or dual-wielding light weapons (1d12 or 2d6) to a versatile weapon (1d8) and a shield (+2 AC) is trading 2 DPR for 2 AC. Taking the defense fighting style over the dueling fighting style is trading 2 DPR for 1 AC. So it makes the latter look like a worse trade.

 

[Mordhau]

It also means by taking it, an attack that would have hit you does so 5% less often. If I'm hit on 11+ then 50% of attacks will hit. If I'm hit on 12+ then 45% will hit.

If I'm hit on a 19 or 20 (10% of the time) then increasing AC +1 will mean I am hit 5% of the time. However the range of numbers that I'm hit on will halve (2 to 1). So from another perspective, I've improved my defence by 50%.

It's a matter of perspective and it's worth keeping both in mind. In the case above if I'm only being hit 10% of the time, then I get a massive improvement and manage to increase that, but that improvement only applies within the 10% of the time I would already actually get hit. In fact raising your AC so you only get hit on a 20 is probably not worthwhile, as your AC is already so good that you're not getting hit most combats.

So if you're only usually getting hit for one attack in a combat, reducing that by 50% isn't going to do much. (You're party is still going to be resting because other people are taking damage and you won't run out of hit dice). If the GM is regularly reducing you to 0 by peppering you with hordes of goblin archers a 50% reduction is going to be huge.

I don't think defence style is bad per se, but it's probably best taken in lieu of Great Weapon Style.

The issues are:

• There's not a lot of punishment potential for enemies who ignore you. Having great defences doesn't help you a lot if the enemy just attack someone else instead.
• The punishment you can get (say from Sentinel) is highly affected by your ability to put out damage. If your punishment attack is weak, it can be ignored (and single melee attacks get increasingly weak over the course of the game)
• It's hard to get your AC so high that you can really feel confident of weathering a storm of attacks like you could in 4e. (Defence style just doesn't get you there).
• A fighting style generally affects almost all your damage. +1 AC does nothing against things that affect saving throws. At a certain point Resilient (Wisdom) becomes the best thing you can do for your defences.

 

[Mordhau]

Defence Style is better on a Paladin then a Fighter.

• They don't have Con proficiency and they may want to cast Bless - in which case, it's better they don't get hit at all.
• They can smite on their opportunity attacks
• The weapon damage is not the sole element of their damage.

 

[Ancalagon]

What this is about is essentially "relative" vs "absolute". One has to think about both when doing these kind of analysis.

Suppose your fighter has a poor AC and is getting hit by half the skeletons, and is taking 50 damage a round. +1 AC is now 45 hp damage per round... Is the difference between taking 50 and 45 hp damage per round really significant? No, you are in trouble either way!

Now suppose the fighter has a great AC and is getting hit by only 2 skeleton per round, taking 10 dmg per round, and with a +1 AC is only getting hit once for 5 damage (we'll ignore crits for now). That's reducing incoming damage by half - that's huge! Very helpful

BUUUT

If you are a high level fighter with 150 hp, does it really matter? It's going to take 30 rounds instead of 15 rounds to die... but surely the skeletons will be defeated long before then. Also, if the skeletons already only hit the fighter on a 20, even more AC won't help at all....

 

[Staffan]

I recall that in the early days of World of Warcraft, the concept of "effective health" for tanks was floating around. Basically, the idea was that if you had 1,000 health and 50% damage reduction, your effective health was 2,000 (1,000/50%).

Using the same metric but with the more stochastic way armor works in D&D, we can see that a 12th level fighter with Con 14 will have 100 hp (assuming fixed hp). Looking over the first page of results when searching D&D Beyond for CR 12 creatures (yes, I know 5e is unlike 3e and Pathfinder in that it doesn't assume fights against roughly "on-par" creatures, but it's helpful to get a baseline) shows that most have an attack bonus of +7 to +9 with occasional outliers, so I'm going to simplify to +8. If the fighter has full plate, that's an AC of 18, meaning the monsters hit on 10+ and miss on 9-, which means the fighter only takes 55% of incoming damage. So the fighter has an effective health of 100/0.55 = 182 hp.

Adding a +2 AC bonus (e.g. a shield) to the fighter lowers that to 45%, so they now have 222 effective hp, a 22% increase. Adding a second +2 bonus (e.g. shield of faith) lowers it even more to 35%, for 286 effective hp, which is a 57% increase over the baseline or a 29% increase over a single +2 bonus.

This is of course a simplification. For one thing, I've ignored crits, because the extra damage from one varies in 5e. I've also ignored damage that bypass AC, which is fairly common. But it shows a tendency that boosting AC has accelerating returns (or whatever the opposite of diminishing returns is).

 

[Mordhau]

In practical terms boosting AC is somewhat relative to your capacity to get the monsters to attack you other than the other PCs.

If your AC is 15 and the Wizard's is 15 and you get attacked equally it's a loss for the party (the wizard has less hitpoints and will go down faster. If you can position yourself so that you take more hits than the wizard, than it's a win for the party, but if you take too many hits so that you go down that turns into a loss. So you want to boost your AC so that you can take a higher proportion of hits and it not turn into a loss to the party.

Really it's all about getting that right. The more you can get the enemies to attack you rather than someone else (and this is only partly mechanical, tactical play and positioning can affect this too) the more you benefit from boosting your AC.

You don't really benefit from having your AC so high that noone attacks you until the rest of the party goes down and everyone gangs up on you (unless you're AC is so high that you still win even by being the last man standing - which still doesn't sound like an ideal situation for a fun game).

 

[FrogReaver]

What this is about is essentially "relative" vs "absolute". One has to think about both when doing these kind of analysis.

Suppose your fighter has a poor AC and is getting hit by half the skeletons, and is taking 50 damage a round. +1 AC is now 45 hp damage per round... Is the difference between taking 50 and 45 hp damage per round really significant? No, you are in trouble either way!

Now suppose the fighter has a great AC and is getting hit by only 2 skeleton per round, taking 10 dmg per round, and with a +1 AC is only getting hit once for 5 damage (we'll ignore crits for now). That's reducing incoming damage by half - that's huge! Very helpful

BUUUT

If you are a high level fighter with 150 hp, does it really matter? It's going to take 30 rounds instead of 15 rounds to die... but surely the skeletons will be defeated long before then. Also, if the skeletons already only hit the fighter on a 20, even more AC won't help at all....

Exactly this. I used to push hard for the relative view just as Clearstream and it does have its place… But for the most part a character is going to be attacked no more than 60 times per day. +1 ac means he will get hit maybe 3 times less. And on more back line characters they probably take even fewer attacks.

A persons initial reaction on importance drastically changes when viewed from the perspective of being hit 3 more times an adventuring day.

 

[clearstream]

It also means by taking it, an attack that would have hit you does so 5% less often. If I'm hit on 11+ then 50% of attacks will hit. If I'm hit on 12+ then 45% will hit.

If I'm hit on a 19 or 20 (10% of the time) then increasing AC +1 will mean I am hit 5% of the time. However the range of numbers that I'm hit on will halve (2 to 1). So from another perspective, I've improved my defence by 50%.

It's a matter of perspective and it's worth keeping both in mind. In the case above if I'm only being hit 10% of the time, then I get a massive improvement and manage to increase that, but that improvement only applies within the 10% of the time I would already actually get hit. In fact raising your AC so you only get hit on a 20 is probably not worthwhile, as your AC is already so good that you're not getting hit most combats.

So if you're only usually getting hit for one attack in a combat, reducing that by 50% isn't going to do much. (You're party is still going to be resting because other people are taking damage and you won't run out of hit dice). If the GM is regularly reducing you to 0 by peppering you with hordes of goblin archers a 50% reduction is going to be huge.

I don't think defence style is bad per se, but it's probably best taken in lieu of Great Weapon Style.

GWF is fairly bad. I think the main comparators are archery, defense, dueling and perhaps now interception. Blindfighting is probably too conditional.

The issues are:

• There's not a lot of punishment potential for enemies who ignore you. Having great defences doesn't help you a lot if the enemy just attack someone else instead.
• The punishment you can get (say from Sentinel) is highly affected by your ability to put out damage. If your punishment attack is weak, it can be ignored (and single melee attacks get increasingly weak over the course of the game)

I agree that 5th doesn't offer so many ways to establish relevancy as a defender. Tar pits like Trip. Fear effects like Menacing and some Paladin abilities. Casters can work to force attackers back too, of course. Repelling blast and such like.

• It's hard to get your AC so high that you can really feel confident of weathering a storm of attacks like you could in 4e. (Defence style just doesn't get you there).

None of the fighting styles alone get a character far. It's what they are taken in conjunction with. SnB with plate and defense gives AC 21. A lot also depends on whether a party is aware of how to use buffs effectively. Treantmonk's god-wizard covers that well.

• A fighting style generally affects almost all your damage. +1 AC does nothing against things that affect saving throws. At a certain point Resilient (Wisdom) becomes the best thing you can do for your defences.

The choice isn't between defense and resilience, but defense and other fighting styles. Were the campaign one in which hostile NPC casters played a large role, then archery might be the best choice. Generally speaking, I think it is better for characters in a party to strongly counter one dimension of attack each, then for all characters to weakly counter multiple dimensions.

 

[clearstream]

Exactly this. I used to push hard for the relative view just as Clearstream and it does have its place… But for the most part a character is going to be attacked no more than 60 times per day. +1 ac means he will get hit maybe 3 times less. And on more back line characters they probably take even fewer attacks.

A persons initial reaction on importance drastically changes when viewed from the perspective of being hit 3 more times an adventuring day.

I run long adventuring days, and your experience does not chime at all with mine. It likely comes down to nuances in what campaigns focus on and overall context at the table. What are other party members doing? What are they facing? For the last couple of years for us that has been OOTA and then ToA. Fighters (typically battle masters), warlocks, paladins, bards and clerics have featured highly.

However, be wary of thinking of it as +1 AC in isolation: I certainly wouldn't advocate that. Defense is much less valuable on characters with low AC, who might well benefit more from other tactics.