Resistance is worth +7 AC. Approximately :)

[Skrum]

I was playing around with a DPR calculator, and noticed an interesting coincidence.

Example sets
8 attacks, each needing a 10 or better to hit, dealing 1d8+3 each: DPR 35
Same situation, but needing a 3 or better to hit (7 worse AC): DPR 56 (half is 28*)

3 attacks, each needing a 13 or better to hit, dealing 3d10+15 each: DPR 40
Same situation, but needing a 5 or better to hit (8 worse AC): DPR 78 (resistance to that damage would make it 39)

5 attacks, each needing a 14 or better to hit, dealing 1d6+6 each: DPR 17.5
Same situation, but needing a 7 or better to hit (7 worse AC): DPR 34 (half is 17)

10 attacks, each needing a 15 or better to hit, dealing 4d8 damage each: DPR 63
Same situation, but needing an 8 or better to hit (7 worse AC): DPR 126 (resistance to that damage would make it 63)

4 attacks, each needing a 17 or better to hit, dealing 2d10+8: DPR 17
Same situation, but needing a 12 or better to hit (5 worse AC): DPR 36 (half is 18*)

=================
I was just plugging numbers, so I used a whatever attack values came to my head. But I think there's something interesting in there - the AC/attack values that are the most "common" converge on resistance being worth about 7 AC.

Needing a 13 to hit is a monster with a +7 bonus attacking a plate/shield character (20 AC)
Needing a 14, well that's can be +6 against 20, or the same +7 against 21 (the character took defensive fighting style)
Needing a 15, that would be +6 against 21 (CR 5 wraiths for example have a +6 attack bonus, and deal 4d8+3 damage)

*The outliers - at very high armor class, armor becomes better. The chance to hit gets so low that reducing by half doesn't buy as much
At lower AC values, resistance is worth more - if the enemy is probably going to hit, better to be resistant
=================

While I know some people rebel against this statement, but in my experience, successful melee characters need 21+ AC by level 6. The strongest tanks in my group have static AC in the 23, 24 range (and reactions on top of that, but that's much harder to model).

This implies that a barbarian needs ~15 AC to match the "solid" range of defense. They'll need more like 18 or 19 AC to push them into elite level (assuming they're resistant to the damage...if they're not, they become quite squishy).

[stoutstien]

You can't really model the separately as they are part of the same mitigation subsystem and feed into each other. It's not resistance or AC its resistance AND AC.

[Skrum]

You can't really model the separately as they are part of the same mitigation subsystem and feed into each other. It's not resistance or AC its resistance AND AC.

I don't think I agree with that; yes they contribute to the same type of stat/defense, but they do so in different and mathematically measurable ways. "How much is resistance worth" is a findable value. I think this shows it's about 7 points of AC.

[stoutstien]

I don't think I agree with that; yes they contribute to the same type of stat/defense, but they do so in different and mathematically measurable ways. "How much is resistance worth" is a findable value. I think this shows it's about 7 points of AC.

Not really as avoidance (AC) and reduction (resistance) are active in two different parts of attack resolution. It's also why people are under the false impression that resistance gets weaker with higher AC rather than the opposite.
Nor does it factor in stuff like protecting concentration or avoiding on hit effects.

At most you can say at a single AC value resistance provides ~X AC value to EHP.

[Skrum]

Not really as avoidance (AC) and reduction (resistance) are active in two different parts of attack resolution. It's also why people are under the false impression that resistance gets weaker with higher AC rather than the opposite.
Nor does it factor in stuff like protecting concentration or avoiding on hit effects.

At most you can say at a single AC value resistance provides ~X AC value to EHP.

A melee character's primary defense is their AC

A melee character who wishes to succeed and not die generally needs a combination of good AC, resistance to damage, and good defensive reactions

An analysis of *how* valuable resistances are is perfectly possible, as the mechanical effects it provide are known

An analysis of *how* valuable AC is is perfectly possible, as the mechanical effects it provides are known

Since resistances and AC both contribute to the same output (how much damage will a character take), *comparing the two* is perfectly possible

Are there other factors? Yes - I excluded reaction-based abilities, for example. But none of that makes the AC vs Resistance comparisons useless

Seriously, if you don't find this useful, just move on. But that doesn't mean it's completely pointless, totally meaningless data. A character with 15 AC and resistance to the incoming damage should expect to take about the same amount of damage, round over round, as a character with 22 AC. I think that's quite interesting. I didn't say that was the be all, end all point on character defenses.

[Dr.Samurai]

A character with 15 AC and resistance to the incoming damage should expect to take about the same amount of damage, round over round, as a character with 22 AC.
That's interesting, and not intuitive to me. I would have guessed that the lower AC would mean that you'd take more damage over time despite having Resistance, as the damage would accumulate and overtake the 22 AC, which I would expect to get hit a lot less.

[Skrum]

That's interesting, and not intuitive to me. I would have guessed that the lower AC would mean that you'd take more damage over time despite having Resistance, as the damage would accumulate and overtake the 22 AC, which I would expect to get hit a lot less.

+6 to hit, 2d8+5 damage, 2 attacks
DPR vs 22: 7.9
DPR vs 15 w/ resist: 8.85

+7 to hit, 2d8+5 damage, 2 attacks
DPR vs 22: 9.3
DPR vs 15 w/ resist: 9.55

+8 to hit, 2d8+5 damage, 2 attacks
DPR vs 22: 10.7
DPR vs 15 w/ resist: 10.25

So, quite close in value overall.

However, it's worth nothing that this is completely normalized damage. In play, two +6 attacks against AC 22, there's a 56% chance that character takes *no* damage on any given round. There's also a 9.75% chance they get crit'd for 4d8+5, which they'd be eating every bit of. In contrast, the character with resistance is going to take damage most rounds, but it'll only be a little bit (and they'll be much more protected from crits, as they're no more likely to be crit'd but they still take only half).

[da newt]

very interesting and fun to think about but ...

there are many different damage types - how many are you resistant to?

there are many damaging spells etc that trigger off of saving throws so AC is not a concern, BUT resistance still applies ...





while some chase DPR, I do like to create a PC with some real survivability. I did just DM a few games w/ a higher level armored artificer satyr - his DPR wasn't impressive but his stupid high AC and very good saves made him very hard to target.

[No brains]

Does this mean that doubling any creature's hp is equivalent to giving it +7 AC?

[Skrum]

Does this mean that doubling any creature's hp is equivalent to giving it +7 AC?

Ohh interesting - and I would suspect yes, at least in terms of how many rounds it would be expected to survive. That's not usually something that's relevant for a PC, but it would def apply to monsters and encounter design.




there are many different damage types - how many are you resistant to?

there are many damaging spells etc that trigger off of saving throws so AC is not a concern, BUT resistance still applies ...


Yeah it gets very conditional, very quickly. I think the easiest way to think about it "my character has effectively +7 AC against enemies that are attacking with X damage type."

Resistances applying to things like spells (while AC only affects attacks) is an example of why AC and resistance aren't exchangeable (even if they're comparable in this way).

[Rukelnikov]

Does this mean that doubling any creature's hp is equivalent to giving it +7 AC?

Only if the PC were originally hitting on around a 7 initially AND they stick to just attack rolls AND the creature can't improve their AC any further.

EDIT: A lil clarification because it may be flying under the radar.

Resistance cuts damage in half, if a creature hits on a 7 that means there's 14 sides on a die where it deals damage (one of them is a bit more than regular damage but most of the times is less than double damage).

In order to bring expected damage down to half we need to remove half the hitting faces from the die, so we need 7 more AC to achieve this result.

If the creature was hitting on a 15 that'd be 6 sides hitting, so to cut this damage in half* we'd need 3 more AC.

*Crits would weigh heavier in this case since they'd be a higher percentage of the expected damage of an attack.

[Skrum]

Only if the PC were originally hitting on around a 7 initially AND they stick to just attack rolls AND the creature can't improve their AC any further.

These assumptions aren't as particular/excluding as it sounds.

Hitting on a 7, well the underlying game math assumes you hit with an 8 or better, so that's gonna be pretty close to a PC's hit chance against most foes. Also, the comparison doesn't fall apart the second it moves away from "midline;" it's only at the extremes, like needing a 17 to hit or a 5 to hit does it not apply as cleanly.

Most monsters can't change their AC. It's really just a few humanoids, or spellcasters if the DM gives them shield.

Attacking with spells, well, that def changes things. But most spells don't get used to burn through a single target's hit points. AoE is the most common spell damage, and it gets directed at creatures that usually have less hit points and no one would bother doing this kind of analysis for anyway.

The idea here isn't to perfectly model defenses in DnD. It was just a cool thing I found that I thought was interesting.

[Rukelnikov]

The idea here isn't to perfectly model defenses in DnD. It was just a cool thing I found that I thought was interesting.

It's perfectly fine, I just thought explaining what's happening under the hood might help people understand why this was the case.

[Atranen]

It's also why people are under the false impression that resistance gets weaker with higher AC rather than the opposite.

What do you mean by this? Certainly resistance will prevent more damage for someone with lower AC.

[JackPhoenix]

What do you mean by this? Certainly resistance will prevent more damage for someone with lower AC.

Sure, because someone with lower AC will take more damage, but it does the same thing no matter what: cuts the damage in half. Using the very first example from the OP without checking the numbers, the character with low AC and resistance will take 28 damage, while the character with high AC will only take 17.5 damage if he also gets resistance. The first character's resistance prevented more damage, but the 2nd character still took less damage overall.

[Amechra]

While I know some people rebel against this statement, but in my experience, successful melee characters need 21+ AC by level 6. The strongest tanks in my group have static AC in the 23, 24 range (and reactions on top of that, but that's much harder to model).

Don't you play in a group that only does hardcore deadly+ fights, or am I mixing you up with someone else?

...

In any case, I don't think that this is as interesting as you think it is. Or, rather, it's interesting, but more in the way it exposes your assumptions.



When comparing straightforward attacks like you are doing here, you can assume that they're basically just [Accuracy] * [Base Damage] (there are things that change this, like crits and conditional damage/accuracy boosts, but we're going to ignore those for simplicity here).
You make the claim that, roughly speaking, [Accuracy - 0.35] * [Base Damage] = [Accuracy] * [Base Damage/2]. If we simplify that, though, we get that [Accuracy - 0.35] * [Base Damage] = [Accuracy] * [Base Damage/2] → 2* [Accuracy - 0.35] * [Base Damage] = [Accuracy] * [Base Damage] → 2* [Accuracy - 0.35] = [Accuracy] → 2* [Accuracy] - 0.7 = [Accuracy] → [Accuracy] = 0.7. You're ultimately just assuming that base accuracy sits around 70%.


In fact, because both accuracy shifts and resistance are multiplicative changes to expected damage, you could set the "benefit" for resistance to any value between +1 AC and +9 AC as long as you assumed that most attacks hover around [effective AC bonus] * 10% accuracy. Enemies at your table have roughly 50% accuracy? Resistance is going to be roughly equal to +5 AC vs. normal attacks.

It also bears mentioning that this correspondence completely falls apart in situations where your damage can't be forced to vaguely correspond to [Accuracy] * [Damage], which includes stuff like "what if you have advantage on your attacks?" or "what if you get bonus damage on your first successful attack, and get multiple attacks per turn?"

[Rukelnikov]

Don't you play in a group that only does hardcore deadly+ fights, or am I mixing you up with someone else?

I play in such a group, and IMO it holds true.

[Skrum]

Don't you play in a group that only does hardcore deadly+ fights, or am I mixing you up with someone else?

Me, among others. But yes I've talked about that before.




In fact, because both accuracy shifts and resistance are multiplicative changes to expected damage, you could set the "benefit" for resistance to any value between +1 AC and +9 AC as long as you assumed that most attacks hover around [effective AC bonus] * 10% accuracy. Enemies at your table have roughly 50% accuracy? Resistance is going to be roughly equal to +5 AC vs. normal attacks.

I mean you're not wrong, but I think you're getting lost in the weeds. The vast majority of attack rolls fall in the 25-75% likely range. While I didn't solve the equation in the abstract, all evidence points towards it working pretty well for that range. It's like people saying advantage is worth +5: even if it's not true on the tail ends, it's true enough that it's a helpful concept to keep in mind.



It also bears mentioning that this correspondence completely falls apart in situations where your damage can't be forced to vaguely correspond to [Accuracy] * [Damage], which includes stuff like "what if you have advantage on your attacks?" or "what if you get bonus damage on your first successful attack, and get multiple attacks per turn?"

Ok this is hyperbolic - *completely* falls apart? Hardly. Advantage would only impact in the sense that it makes attacks more likely to hit, which weighs towards resistance being the better defense.

4 attack rolls, needs a 15 or better to hit, dealing 2d6+2 each: DPR 12.2
w/ adv: 21.09

Needing an 8 to hit: 24.80 (12.4 w/ resistance)
w/ adv: 34.32 (17.16 w/ resist)

Resistance is better at that point, but we already knew that - they've effectively gotten +5 to their attack roll!

Let's see about "first hit" damage -
3 attacks, needs a 15 or better to hit, dealing 1d6+3 w/ an extra 4d6 on first hit: DPR 18.46
Same, but needs a 8 or better to hit, against resist: DPR 30.3 (15.15 against resistance)

I mean it's not perfect, but IMO it's in the ballpark.
The value here is that even while things like advantage, extremely high or low attacks rolls, or first hit damage can throw it off a bit, I think the fat part of the bell curve when it comes to attack rolls and damage fall into this model pretty well. In general, resistance is worth 7 or 8 points of AC.

[Oramac]

Does this mean that doubling any creature's hp is equivalent to giving it +7 AC?


Ohh interesting - and I would suspect yes, at least in terms of how many rounds it would be expected to survive. That's not usually something that's relevant for a PC, but it would def apply to monsters and encounter design.

This part is very interesting to me. When I'm designing a fight for my players, I nearly always lower the monster AC and increase monster HP. Basically, missing an attack is not fun, so I make it easier for my players to hit, because that's fun.

On the flip side, I don't think I've ever doubled a monster's HP. Usually I'll add somewhere around maybe 15-20% more HP, give or take. On the other other hand, I also don't reduce monster AC by -7 either; usually just -2 or so. So it probably evens out.

Thanks for the info Skrum! This is really useful.

[Atranen]

Sure, because someone with lower AC will take more damage, but it does the same thing no matter what: cuts the damage in half. Using the very first example from the OP without checking the numbers, the character with low AC and resistance will take 28 damage, while the character with high AC will only take 17.5 damage if he also gets resistance. The first character's resistance prevented more damage, but the 2nd character still took less damage overall.

I still don't follow. The claim is "resistance gets stronger with higher AC". In your case, you show characters with high AC and resistance take more damage than low AC and resistance. But that doesn't say whether *adding* resistance has more of an effect for low vs high AC. If I'm asking: "how much damage can I prevent by casting protection from energy", then all else equal, it is better to use on a low AC target.

[JackPhoenix]

I still don't follow. The claim is "resistance gets stronger with higher AC". In your case, you show characters with high AC and resistance take more damage than low AC and resistance. But that doesn't say whether *adding* resistance has more of an effect for low vs high AC. If I'm asking: "how much damage can I prevent by casting protection from energy", then all else equal, it is better to use on a low AC target.

17.5 isn't more than 28. And it doesn't matter how much damage you PREVENT, only how much damage you TAKE. The damage you take can kill you and may require resources to heal, the damage you prevent is irrelevant. It doesn't matter if it's because you avoid damage through higher AC, resistance, positioning that prevents the enemy from reaching you, crowd control measures or killing the enemy before they can attack.

[Skrum]

17.5 isn't more than 28. And it doesn't matter how much damage you PREVENT, only how much damage you TAKE. The damage you take can kill you and may require resources to heal, the damage you prevent is irrelevant. It doesn't matter if it's because you avoid damage through higher AC, resistance, positioning that prevents the enemy from reaching you, crowd control measures or killing the enemy before they can attack.

That's not what the topic is though? I'm literally making a comparison of the protective value of resistance VS armor class. Saying "someone with high armor class AND resistance is better protected" is like, duh, and also not what I'm talking about.

All else being equal, a character with resistance to an attack should expect to take about the same amount of damage as another character with 7 higher AC. That's the takeaway.

[Dr.Samurai]

+6 to hit, 2d8+5 damage, 2 attacks
DPR vs 22: 7.9
DPR vs 15 w/ resist: 8.85

+7 to hit, 2d8+5 damage, 2 attacks
DPR vs 22: 9.3
DPR vs 15 w/ resist: 9.55

+8 to hit, 2d8+5 damage, 2 attacks
DPR vs 22: 10.7
DPR vs 15 w/ resist: 10.25

So, quite close in value overall.

However, it's worth nothing that this is completely normalized damage. In play, two +6 attacks against AC 22, there's a 56% chance that character takes *no* damage on any given round. There's also a 9.75% chance they get crit'd for 4d8+5, which they'd be eating every bit of. In contrast, the character with resistance is going to take damage most rounds, but it'll only be a little bit (and they'll be much more protected from crits, as they're no more likely to be crit'd but they still take only half).
Sorry, I wasn't disagreeing, just saying that I wouldn't have guessed that if asked. I find it an interesting observation, thanks for sharing :smallcool:

Given that most, if not all, of the numbers on this forum are decimals and percent chances that don't really reflect actual gameplay, I don't think anyone should take exceptional issue with this. Seems like it would slot right in with many other assumptions about DPR.

[Skrum]

Sorry, I wasn't disagreeing, just saying that I wouldn't have guessed that if asked. I find it an interesting observation, thanks for sharing :smallcool:

Given that most, if not all, of the numbers on this forum are decimals and percent chances that don't really reflect actual gameplay, I don't think anyone should take exceptional issue with this. Seems like it would slot right in with many other assumptions about DPR.

Oh, yeah, I didn't think you were! Was just adding more examples (that perhaps better reflect actual gameplay).

This is definitely "long arc of a character" information, for sure. Not very useful for any particular battle, but if someone is at the character building stage and they know the DM likes to make monsters with very high attack rolls, it's probably worth considering stacking your resistances instead of AC (for example).

Or, better example, if the table is using flanking, I think that would raise the relative value of resistances. No flanking, stack AC.

[Silly Name]

So, an observation, not really a disagreement but some musing on the value of having Resistance:

AC is an "universal" value - your AC is the same no matter how the enemy is attacking you, or what they're using.

Isn't resistance more of a relative value? Outside of Bear Totem Barbarians, you're unlikely to ever have a laundry list of resistances, so whether it applies or not is a pretty big part of the "calculations".

Suppose I'm playing a Red Dragonborn - I have resistance to Fire, but how much is that resistance "worth" if I don't run into a lot of Fire-using enemies?

I know a lot of questions about "how good is this feature?" are going to be campaign-specific, but I feel that having high AC is pretty much always good, no matter how the campaign is run.

[Atranen]

17.5 isn't more than 28. And it doesn't matter how much damage you PREVENT, only how much damage you TAKE. The damage you take can kill you and may require resources to heal, the damage you prevent is irrelevant. It doesn't matter if it's because you avoid damage through higher AC, resistance, positioning that prevents the enemy from reaching you, crowd control measures or killing the enemy before they can attack.

I don't get it. If you prevent damage, you are not taking it. That matters.


That's not what the topic is though? I'm literally making a comparison of the protective value of resistance VS armor class. Saying "someone with high armor class AND resistance is better protected" is like, duh, and also not what I'm talking about.

Agree. Also, the original comment said


It's also why people are under the false impression that resistance gets weaker with higher AC rather than the opposite.
Nor does it factor in stuff like protecting concentration or avoiding on hit effects.

It's saying there is something counterintuitive, that resistance is stronger on characters with high AC. But it is obvious that high AC+resistance is better than low AC + resistance. The question is, is *resistance* stronger on a high AC or low AC character. If I can choose to cast protection from elements on two party members, all else equal, which should I choose?

It seems low AC, because it prevents more damage.

[stoutstien]

It's saying there is something counterintuitive, that resistance is stronger on characters with high AC. But it is obvious that high AC+resistance is better than low AC + resistance. The question is, is *resistance* stronger on a high AC or low AC character. If I can choose to cast protection from elements on two party members, all else equal, which should I choose?

It seems low AC, because it prevents more damage.

Seeing how most things that protection from energy apply to wouldn't interact with AC to begin with, you would be looking at other things like HP total or secondary reduction features anyways.

Then you have ask the question on who is likely to be targeted to begin with regarding such options as damage is rarely spread out equally and most parties has at least some ability to funnel hostile actions.

Do you have high AC because you don't want to be attacked or because you are practically the only one that does?

[Atranen]

Seeing how most things that protection from energy apply to wouldn't interact with AC to begin with, you would be looking at other things like HP total or secondary reduction features anyways.

Then you have ask the question on who is likely to be targeted to begin with regarding such options as damage is rarely spread out equally and most parties has at least some ability to funnel hostile actions.

Do you have high AC because you don't want to be attacked or because you are practically the only one that does?

Ok, "in the context of most games, it is better to cast resistance on high AC characters because they will be targeted more" may be valid...it will depend on party composition, the specifics of the encounter, etc. But, if all else is equal, it is better to give to low AC characters. Is that fair?

[stoutstien]

Ok, "in the context of most games, it is better to cast resistance on high AC characters because they will be targeted more" may be valid...it will depend on party composition, the specifics of the encounter, etc. But, if all else is equal, it is better to give to low AC characters. Is that fair?

In that case you will pick whoever is likely to get to a win state the fastest with the least resources spent. Most of the time high AC still comes out ahead here as the stray hit/crit is easier to deal with then the time and resources of HP sinking.

[Atranen]

In that case you will pick whoever is likely to get to a win state the fastest with the least resources spent. Most of the time high AC still comes out ahead here as the stray hit/crit is easier to deal with then the time and resources of HP sinking.

I don't follow. You have two fighters in your party. Both go into melee using great swords. One has +1 plate mail. The other is wearing chain. They have the same HP and saves. They deal the same damage.

Who gets protection from energy?

[stoutstien]

I don't follow. You have two fighters in your party. Both go into melee using great swords. One has +1 plate mail. The other is wearing chain. They have the same HP and saves. They deal the same damage.

Who gets protection from energy?

Assuming there is any chance of it being useful then the one with the higher AC as it will use up less resources and if it goes south then they have a marginal edge to recover better. (5% is 5%)
That's why you can't really separate AC and resistance because they feed back into each other.
Like image you had a fear like heavy armor master but for light armor. Even though the attacks are being reduced by the same amount the heavy armor version will come out ahead even if it "prices" less.

[Skrum]

Assuming there is any chance of it being useful then the one with the higher AC as it will use up less resources .

Ok what does this mean.

The question is "identical fighters, but one has less AC." The combat in question will feature creatures that make attack rolls and deal elemental damage that can be protected against by protection from energy.

And you're saying the HIGHER armor class fighter should get the buff.

Like. Why. That fighter is going to take less hits thanks to their AC.

[Mongobear]

I have played a Bear Totem Barbarian from levels 1 to 15. I started out with the Unarmored thing, and managed to find Bracers of Defense on top of having a very high stat array from rolling. I had somewhere around a 21 or 22 AC without outside buffs like Haste/Shield of Faith.

I would never choose not to use Reckless Attacks, whether I was fighting hordes of Orcs or an Adult Dragon and anything in between. I nearly died almost every fight, unless our Cleric was in attendance and duct taped to me.

Around level 11 or 12, our DM let us combine a handful of "magic" items in a magical forge we recovered from an ancient Dwarven city. I managed to combine a handful of things into +2 Adamantine Half Plate, so I took my level 12 ASI as Medium Armor Master, and began wearing it instead and playing the exact same way. My life-span became much longer, and I rarely ever dipped below half HP.

AC is almost negligible, Resistance and the ability to avoid critical hits is way more important. It is better to have a large HP pool as well as mitigation because given enough dice rolling, things WILL hit you, regardless of how min/max'd your AC is.

[stoutstien]

I have played a Bear Totem Barbarian from levels 1 to 15. I started out with the Unarmored thing, and managed to find Bracers of Defense on top of having a very high stat array from rolling. I had somewhere around a 21 or 22 AC without outside buffs like Haste/Shield of Faith.

I would never choose not to use Reckless Attacks, whether I was fighting hordes of Orcs or an Adult Dragon and anything in between. I nearly died almost every fight, unless our Cleric was in attendance and duct taped to me.

Around level 11 or 12, our DM let us combine a handful of "magic" items in a magical forge we recovered from an ancient Dwarven city. I managed to combine a handful of things into +2 Adamantine Half Plate, so I took my level 12 ASI as Medium Armor Master, and began wearing it instead and playing the exact same way. My life-span became much longer, and I rarely ever dipped below half HP.

AC is almost negligible, Resistance and the ability to avoid critical hits is way more important. It is better to have a large HP pool as well as mitigation because given enough dice rolling, things WILL hit you, regardless of how min/max'd your AC is.

"I played with extreme risk/reward tendencies and was surprised when the risk sometimes won...."

[stoutstien]

Ok what does this mean.

The question is "identical fighters, but one has less AC." The combat in question will feature creatures that make attack rolls and deal elemental damage that can be protected against by protection from energy.

And you're saying the HIGHER armor class fighter should get the buff.

Like. Why. That fighter is going to take less hits thanks to their AC.

For some reason it deleted my post...but yes that's how AC and resistance interact.
The closer you play to guidelines of the DMG (PHP only no feats) the closer the values are but feature stacking favors AC and avoidance ans dice manipulation also favors AC.

You kinda run into this yourself with your own example. If resistance is worth 7 AC then is that buff worth more to someone with 18 AC of 15 AC if they take the same attacks?

[Darth Credence]

Here's how I understand the idea. In your "A and B are equal except for AC" situation, it would be the idea that both do what they can until B falls, and A carries on, and putting resistance on A gives more total damage to the enemy because the total number of fighter-rounds would be greater with A resisting. I saw the appeal of the idea, but then I made a spreadsheet to see how it would actually work.

The spreadsheet covers the following - total number of times it takes to hit A, times to hit B, how much damage the monster does to each every hit and assume it has two of those attacks per turn, HP for all of them, and an assumed equal damage per turn from both fighters. Calculated from that is the average damage to each fighter per turn, damage to the monster per turn, and round by round hit points.
What I have found is that it is easier to get to dead monster if you give resistance to the lower AC character.

Monster HPPC HPPC DMGWho resists?Times to hit ATimes to hit BMonster DamageWinner?
200
100
10
A
5
2
40
Initiative winner

200
100
10
B
5
2
40
PCs

200
100
10
A
4
2
40
Monster

200
100
10
B
4
2
40
Initiative winner

200
100
10
A
3
2
30
Initiative winner

200
100
10
B
3
2
30
PCs

170
100
10
A
4
2
40
Initiative winner

170
100
10
B
4
2
40
PCs (both up)

140
100
10
A
4
2
60
Monster

140
100
10
B
4
2
60
Initiative winner


I stopped after those. I tried pushing the number of times it takes to hit A up, and when it takes 8 attacks to hit player A and 2 to hit player B, that flips, but that seems like a much larger difference in AC than specified - if PCB gets hit every other attack, then an 11 or above hits, and for PCA only being hit 1 in 8 that would mean they need a 17.5 to hit, for a difference of 6.5, and I know there aren't half AC. From chain to +1 plate is only a difference of 3, right? I think it will be hard to actually see a 4 to 1 ratio in number of hits they take, and that looks like a decent rule of thumb for where it will be better to buff the harder to hit guy. I guess if the monster will hit PCB every time unless they crit fail, and PCA on a five or higher, you are at the 4 to 1, but that's still a spread of 4 in AC and a monster with a ridiculous to hit bonus.
Feel free to check my math, I cranked it out pretty quick.

[Skrum]

For some reason it deleted my post...but yes that's how AC and resistance interact.
The closer you play to guidelines of the DMG (PHP only no feats) the closer the values are but feature stacking favors AC and avoidance ans dice manipulation also favors AC.

You kinda run into this yourself with your own example. If resistance is worth 7 AC then is that buff worth more to someone with 18 AC of 15 AC if they take the same attacks?

I don't think we're assessing the same thing... And I'm really not sure what you're saying tbh.

Resistance is worth more to the lower AC character *because they're going to get hit more.* The resistance is going to prevent more damage *because they get hit more.*

Reducing damage taken and not getting hit at all are two forms of mitigation. I'm attempting to compare them. What I've found, is that statistically, resistance will mitigate about the same amount as getting 7 more AC.

Like a lot of statistical analysis, this has very little value when talking about a specific context. It only means anything in very large data sets (like, how tough is this character going to be over the course of a campaign).

[Atranen]

Assuming there is any chance of it being useful then the one with the higher AC as it will use up less resources and if it goes south then they have a marginal edge to recover better. (5% is 5%)
That's why you can't really separate AC and resistance because they feed back into each other.
Like image you had a fear like heavy armor master but for light armor. Even though the attacks are being reduced by the same amount the heavy armor version will come out ahead even if it "prices" less.

I don't follow. It uses up the same amount of resources either way; it is the same spell. What do you mean by 'a marginal edge to recover better'?


For some reason it deleted my post...but yes that's how AC and resistance interact.
The closer you play to guidelines of the DMG (PHP only no feats) the closer the values are but feature stacking favors AC and avoidance ans dice manipulation also favors AC.

You kinda run into this yourself with your own example. If resistance is worth 7 AC then is that buff worth more to someone with 18 AC of 15 AC if they take the same attacks?

'Resistance = 7 AC' is an approximation though, which is correct when the to-hit chance is 70%.

Suppose they have a +8 to hit. They hit 15 AC 70% of the time. +7 AC makes them hit 35% of the time, halving damage. Resistance also halves damage.

But, they only hit 18 AC 55% of the time. Resistance halves damage, which is equivalent to making them hit 27.5% of the time. So it is only equivalent to +5.5 AC instead. It has less of an impact when applied to a high AC character.



Another way to get at this is to think of the extreme case. Suppose I have 1 AC and you have 30 AC. They have a +0 to hit. They hit me 95% of the time and you 5% of the time. Who is it more valuable to put resistance on?

[Mongobear]

"I played with extreme risk/reward tendencies and was surprised when the risk sometimes won...."

I never once said I was surprised.

I played both versions exactly the same, with the only difference being reliance on much higher AC vs Lower AC + Crit immunity, and the low AC/crit immunity won.

I wasn't asking questions of the topic.

I was stating my opinion after anecdotal experience spanning the first 3-4 years of 5e's lifespan.

[stoutstien]

I guess if you want to make yourself easier to hit so you feel like you get more value out of resistance go for it but that's not how it works or barb wouldn't be stuck being mediocre at mitigation even if they go for bear totem.

[Atranen]

I guess if you want to make yourself easier to hit so you feel like you get more value out of resistance go for it but that's not how it works or barb wouldn't be stuck being mediocre at mitigation even if they go for bear totem.

No one is saying you ought to lower your AC because it makes resistance stronger. Obviously you want to max AC and max resistance. But given the choice between two targets, resistance does more for the one with lower AC.

[Elenian]

I guess if you want to make yourself easier to hit so you feel like you get more value out of resistance go for it but that's not how it works or barb wouldn't be stuck being mediocre at mitigation even if they go for bear totem.

Nobody is saying this. Obviously higher AC is always better, whether you have resistances or not. What people are saying, correctly, is that, all else being equal, resistances will prevent more damage on a lower AC than a higher one, and so if you have several options for a resist target, it might well make sense to put it on the lowest AC character.

[Witty Username]

And that characters don't need as much AC to have equivalent defenses when they have resistance.

[Yakk]

I was playing around with a DPR calculator, and noticed an interesting coincidence.

Example sets
8 attacks, each needing a 10 or better to hit, dealing 1d8+3 each: DPR 35
Same situation, but needing a 3 or better to hit (7 worse AC): DPR 56 (half is 28*)

3 attacks, each needing a 13 or better to hit, dealing 3d10+15 each: DPR 40
Same situation, but needing a 5 or better to hit (8 worse AC): DPR 78 (resistance to that damage would make it 39)

5 attacks, each needing a 14 or better to hit, dealing 1d6+6 each: DPR 17.5
Same situation, but needing a 7 or better to hit (7 worse AC): DPR 34 (half is 17)

10 attacks, each needing a 15 or better to hit, dealing 4d8 damage each: DPR 63
Same situation, but needing an 8 or better to hit (7 worse AC): DPR 126 (resistance to that damage would make it 63)

4 attacks, each needing a 17 or better to hit, dealing 2d10+8: DPR 17
Same situation, but needing a 12 or better to hit (5 worse AC): DPR 36 (half is 18*)

=================
I was just plugging numbers, so I used a whatever attack values came to my head. But I think there's something interesting in there - the AC/attack values that are the most "common" converge on resistance being worth about 7 AC.

Needing a 13 to hit is a monster with a +7 bonus attacking a plate/shield character (20 AC)
Needing a 14, well that's can be +6 against 20, or the same +7 against 21 (the character took defensive fighting style)
Needing a 15, that would be +6 against 21 (CR 5 wraiths for example have a +6 attack bonus, and deal 4d8+3 damage)

*The outliers - at very high armor class, armor becomes better. The chance to hit gets so low that reducing by half doesn't buy as much
At lower AC values, resistance is worth more - if the enemy is probably going to hit, better to be resistant
So, you can ignore "# of attacks" and "damage per attack" -- what matters is total potential damage and accuracy (and how much is dice, which crit, and how much is static, which doesn't crit).

Second, if you use a really simple model -- that each +1 ATK/AC changes DPR by 10% -- you'll find that 1.1^7 = 1.9487171, or about 2x.

If your to-hit is somewhere in the 50-50ish range, each +1 modifier to hit swings the damage actually dealt by around 10% in an exponential manner.

(The curve is actually hyperbolic, not exponential - but exponential is easier to model, and fits pretty well).

In a game like D&D 4e, that 10% was baked into the math. Monsters gained +1 ATK/AC/NAD each level, and so did PCs. So +4 ATK and +4 DEF over 4 levels boosted damage by about 50% and mitigation by about 50%.

And if your defence goes up by 50% and your mitigation goes up by 50%, your total power -- total damage you do before you die in a fight -- doubles.

Monsters HP and damage also scaled with (level+3). So a level 14 monster had (17/13) times the HP and (17/13) times the damage and 1.5x the accuracy and 1.5x the mitigation, for a total of almost 4x the power.

XP was (very) roughly the square root of power, because 2 monsters each worth 100 XP where worth 200 XP; they would do 3 times the damage of 1 monster if fought without AOE before dropping (and good focus fire by PCs).

Elites had 2x the HP and 50% more damage output (roughly), and solos had 4x-5x the HP and 2x-2.5x the damage output (these numbers got tweaked as the game progressed), plus bonuses to mitigation.

This doesn't quite model 5e as well, as the range of acceptable accuracy vs defence is higher in 5e. You are supposed to fight CR 1-2 monsters at level 17+ sometimes in 5e, unlike 4e; and similarly, CR 16+ monsters are fair game for a level 10 party (if a deadly fight).

This means that the AC vs HP math is fundamentally different in 5e than 4e as the assumption isn't that you are within 3-4 points of 50% accuracy. That is just true for "peer" monsters, not for mooks.