AC v. DR

[LibraryOgre]

So, you are offered a choice of +X AC or DR Y/-.

If Y is 1, at what point does X make it worth your time? Is there a linear relationship between X and Y (i.e. if Y is 2, is it now 2X?)

[Lonely Tylenol]

That depends on a few things:

1) Is the AC typed, and if so, what type is it?

2) Is the AC valid as touch AC? What about flat-footed?

I value touch AC significantly more than flat-footed, and untyped (or relatively rare) bonuses are of course always worth more. AC 4 as an armor bonus is not worth DR 1/cold iron, because an armor bonus of 4 is relatively easy to emulate, and easy to bypass.

EDIT: also worth noting that the value of DR scales non-linearly with how much damage it actually mitigates, since it lets you survive more hits with a higher value, which, in turn, lets your DR mitigate even more. By its very nature, DR requires the AC to scale non-linearly for it to keep up (and past a certain point, it may as well not matter).

[GilesTheCleric]

I would trade at a rate of 3 AC to 1 DR. There's many ways for AC to not matter; if you're going to get hit, then you're going to get hit. Better to reduce the pain a bit. 2 AC doesn't make much of a difference (there are many ways to get +2 bonuses), and 4 seems significant (many fewer ways to get +4 bonuses).

[OldTrees1]

Depends on my level. First DR > AC. Then AC > DR. Then AC & DR = 0. At low level damage is small so DR can make you immune to damage. Then damage starts to increase but AC is still keeping pace with Attack. Eventually AC falls far enough behind Attack that it is not worth investing in.

[Techwarrior]

As a rule of thumb, I value AC as one of two things usually, 1) better than DR, as it applies to more situations and my AC is going to reduce ALL damage, not just some; or 2) something to reduce the amount of Power Attack an opponent can effectively use. Thus, I tend to value AC as about equal to a relevant DR of 2. I know it's not the best way to look at it, but it's the one that sticks in my head, for big long irrational (human) complicated reasons.

[Ceaon]

So, you are offered a choice of +X AC or DR Y/-.

If Y is 1, at what point does X make it worth your time? Is there a linear relationship between X and Y (i.e. if Y is 2, is it now 2X?)

IMO, there is no linear relationship. That's because very low or very high ACs tend to not care about AC increases.

I.e. if at level 10 you have 50 AC, you are only going to get hit on a 20 anyway, so more AC won't help you. So increasing Y is worth more than increasing X.
If at level 10 you have 14 AC, you will probably only get missed if your opponent rolls a 1. More AC won't really help you, since you will still get hit most of the time (opponent will still always hit you if your AC is 18). So increasing Y is worth more than increasing X.
However, if at level 10 you have, let's say, 30 AC, then the opponent has some trouble hitting you, but if he hits, he deals damage that cannot be easily mitigated by Damage Reduction. Increasing X will help to mitigate more damage than increasing Y.

On top of that, the value of AC depends on the opponents´ ability to hit, while the value of DR depends on the opponents´ ability to deal damage (per hit). Since damage per hit wildly varies per monster, moreso than ability to hit, I'd say that a high DR can make some fights incredibly easy, while in others, it won't really matter at all.

All in all, interesting question. I have no numerical answer to give, though.

[Red Fel]

That depends on a few things:

1) Is the AC typed, and if so, what type is it?

2) Is the AC valid as touch AC? What about flat-footed?

I think this is the key point. All AC is not created equal. A deflection or dodge bonus to AC, for example, is probably better in my mind than an armor bonus; a bonus to touch AC is better still. That said, there are certain contexts where AC is better, certain contexts where DR is better, and certain contexts where neither makes a difference. In essence:

AC: AC is better when dealing with magical attacks that target AC. Why? Because DR applies to (http://www.d20srd.org/srd/specialAbilities.htm#damageReduction) "damage from most weapons and natural attacks." Specifically, a creature with DR "takes normal damage from energy attacks (even nonmagical ones), spells, spell-like abilities, and supernatural abilities." Thus, against any non-weapon attack that targets AC - such as a Warlock's Eldritch Blast, which is a ranged touch attack - AC is superior to DR. DR: DR is better at higher levels when dealing with melee attacks. Why? Because at higher levels, almost everything you're dealing with will have a high enough to-hit to hit you at least once. Given that you will be hit, DR is valuable for taking the sting off. DR is also very useful against enemies that hit multiple times, particularly ones with many natural weapons, because it reduces the impact of every hit. While AC reduces the probability of being hit, it does nothing to reduce the pain once you are hit. Neither: Many spells and abilities bypass both AC and DR. In particular, tactical spells such as Grease or Glitterdust don't deal damage, and thus don't trigger AC or DR, yet can incapacitate or at least seriously hinder an opponent; similarly, save-or-lose spells trigger saves, not AC or DR, and no-save-just-lose spells don't even give you that liberty. Finally, there are other options - such as miss chance - which are often considered superior, since they grant an absolute possibility of zero damage, even on what might be an otherwise successful hit.
As an aside, consider the armor as damage reduction (http://www.d20srd.org/srd/variant/adventuring/armorAsDamageReduction.htm) variant rules. After all, why choose?

[Fouredged Sword]

I actually put them roughly 1-1, so long as you stay withing HD+13 to HD+23 for defense. Above or bellow that and any extra defense is near worthless.

[Larkas]

I actually put them roughly 1-1, so long as you stay withing HD+13 to HD+23 for defense. Above or bellow that and any extra defense is near worthless.

Would you mind explaining how you arrived at those numbers? I was actually considering just that some other day, and couldn't come up with a rule of thumb.

[Fouredged Sword]

For your defenses to function, the thing you are defending yourself from must be able to miss you.

At some point, there was a look at the attack modifiers for various CR's of opponents for CR 1-20. It was roughly determined that if your AC was lower than your HD+13, it didn't matter as everything generally will hit you on a 2, so feel free to tank your AC to as low as you like. Anything past HD+23 and most things will miss you unless they roll a high value. The rule of thumb is that you shouldn't push your DM into the zone of being completely unable to hit your character, but for a non-melee character, one should maintain at least HD+13 AC or should rely on other defenses, and for a melee character HD+23 is about what you should aim for. At high and low levels, things get less solid, with AC being more valuable at low levels and less at high levels.

It's a rule of thumb, so it doesn't always work. I would imagine the values for DR are roughly the same. If you can maintain HD+13 DR/- you should be able to ignore most attacks, but less than that, and you will take damage most hits. DR HD+23 should be able to stop all but the most powerful hits. Now DR is a little harder to quantify it's usefulness because it can be partially effective, and should be compared to HP more strongly, and high HP and DR is more effective than DR and low HP.

TLDR

HD+13 = roughly 50% chance to avoid a hit from a full bab monster with a 16 str - This is the minimum value that is really useful as a first line of defense. If you have lower, you need to be using some other means to avoid hits, and are better off putting your build resources elsewhere than AC for defense.
HD+23 = roughly 95% chance to avoid a hit from a full bab monster with a 16 str - This is about the maximum you should aim for if you want to use AC as a defense, as higher than this is less and less useful.

[Andreaz]

Curse you for making me apply Calculus 3 to D&D.

[Red Fel]

Curse you for making me apply Calculus 3 to D&D.

Calculus 3? Feh. I barely had to calculate the area under a single curve while reading that last post. That's Calc 1, Calc 2 tops.

[dextercorvia]

For your defenses to function, the thing you are defending yourself from must be able to miss you.

At some point, there was a look at the attack modifiers for various CR's of opponents for CR 1-20. It was roughly determined that if your AC was lower than your HD+13, it didn't matter as everything generally will hit you on a 2,

<snip>

HD+13 = roughly 50% chance to avoid a hit from a full bab monster with a 16 str - This is the minimum value that is really useful as a first line of defense. If you have lower, you need to be using some other means to avoid hits, and are better off putting your build resources elsewhere than AC for defense.


Your numbers don't match. How is AC of HD+12 a 95% chance of getting hit, and HD+13 a 50% chance of getting hit?

[Fouredged Sword]

hd+23 is a 95% chance of a miss, not HD+13. HD+13 is 10 less than HD+23, half of a d20.

[Snowbluff]

There's many ways for AC to not matter; if you're going to get hit, then you're going to get hit.

There are many more ways for DR not to matter. DR won't help against most spells, for example. I'm usually much more afraid of spellcasters, so I usually grab better touch AC and some spell resistance to go with my miss chances and immunities.


Would you mind explaining how you arrived at those numbers? I was actually considering just that some other day, and couldn't come up with a rule of thumb.
I usually use 1.5*HD+10 for target AC, and 1.5*HD+15 for PC AC. It fluctuates with level, but I find it handy.

[dextercorvia]

hd+23 is a 95% chance of a miss, not HD+13. HD+13 is 10 less than HD+23, half of a d20.

Right, but you said if your AC was lower than HD+13 you would get hit on a 2 (95% chance of getting HIT). You also said that AC=HD+13 was about 50/50.

1 point of AC cannot make 45% difference

[Fouredged Sword]

Also, the percentages I gave in the above post are compared to a fighter with a 16str. When you actually compare those AC's to real threats within the C10 range, then you are looking at much higher to hit bonuses than the theoretical fighter would have. HD+23 will save you from a good chunk of damage, but not nearly 19/20th of it, more like half. HD+13 will do almost nothing. The idea is that as a rule of thumb, investing less than HD+13 AC should only be done at near zero cost to the character. Investing too much over HD+23 is rude to the DM and causes a AC vs Attack war between you and the DM that leaves the rest of your party vulnerable.

For example, cloud giant, CR 11, to hit with attack +22. He hits a appropriately leveled character with HD+13 AC on all but a 1 or 2.

Indecently the could giant also deals 4d6+18 damage. DR HD+13/- would negate most of his attacks completely.

[Chronos]

It depends on how much of each you have available. There are a lot of things that do very low damage at a time, and a fair number that do only one point at a time. A small amount of DR will completely eliminate that entire category of threats, so if you don't have any DR yet, getting that first point is a big deal. On the other hand, if you're fighting a raging barbarian, a dragon, or the Tarrasque, there's not going to be much difference between DR 1 and DR 10: They're still going to get most of their damage through.

[Big Fau]

Unfortunately, AC is significantly easier to pump than DR and DR is mostly ignored due to how low it is. If you offered me DR 25/- or AC ~45 I'd be tempted to take the DR, but anything lower than 15 wouldn't be worth it.

[Andreaz]

Calculus 3? Feh. I barely had to calculate the area under a single curve while reading that last post. That's Calc 1, Calc 2 tops.
In practice I can fit in as many variables as I want. You can determine that the number of hits you can take before reaching 0 hit points is
20(HP-1)(DMG-DR)-1(AC-AT-1)-1(Camouflage)-1

HP = Hit Points
DMG = Damage
DR = Damage Reduction
AC = Armor Class
AT = ATtack bonus
Camouflage = Camouflage hit chance


Within the domain {(HP,DMG,DR,AC,AT,Camouflage) | HP > 1, DMG-DR >= 1, 2 <= AC-AT <= 20, 0.01 < Camouflage <= 1} You have a smooth function (So Camouflage doesn't get arbitrarily large and DMG-DR don't explode) that describes how many hits you can take if "The Attack Roll is relevant (not confined to nat1s and nat20s)" and "incoming hits are actually dealing any damage" and "camouflage is not 100%", situations where the change is simplified.

If you only hit with Nat20s, AC-AT-1 becomes "1"
If you only miss with 1s, AC-AT-1 becomes 19
If DMG = DR, you are not taking damage
If Camouflage hit chance is zero, you are not taking damage

Note I am not accounting for critical hits or HP gains, for they add some complexity to this function. I am kinda busy studying right now and can't afford to burn time thinking about this until the weekend.

So, back to the domain. This function is compact, so you have maximuns and minimuns on the borders. Those cases are so close to the 'outside domain' scenario i'll not take them into account. Rather I'll look into how to get there the fastest: The Gradient.

If you calculate the gradient of this function at any given point, you'll be given a direction vector with the ratio of each trait. Weight the cost to get as close to that ratio as you can and you'll have the best bang for your buck as far as taking damage goes. This will involve determining how much it costs to increase each attribute from the current score to the one you want, and then putting all traits in relation to one them.


This alone is not enough to decide between AC and DR, for example, because AC is worth different amounts to different attacks. You'll have to eyeball it: figure the 3 relevant ACs (against touch, surprise and normal) and see how the ratio behaves on each. Compare the efforts to the types of enemy you expect. As said before, the same logic applies to DR.

[Red Fel]

So much math.

You're a horrible person, but I like you. :smallbiggrin:

[Andreaz]

You're a horrible person, but I like you. :smallbiggrin:Once you factor in the cost functions, you can even set a level curve of how much money you have and through lagrangian multipliers discover your best shots.

[Snails]

It depends on what you are usually fighting.

If you are usually hit for 5-10 damage, DR 1 stops ~15%.
If you are usually hit for 10-20 damage, DR 1 stops ~7%.
If you are usually hit for 20-40 damage, DR 1 stops ~3%.

When you are in double digit levels, you are not going to die from 1 HD orcs. They are missing you most of the time anyway, even if you did not not substantially pump up your AC.

Playing a front liner, I expect the stronger monsters to hit 70%-80% of the time (unless I am an AC specialist) with their big attacks. +1 AC stops about 7%. But meleeist at higher levels have multiple attacks. Those secondary attacks might only hit 30% of the time, so +1 AC helps ~16% here.

(There are lots of things that attack Touch AC, of course, but a lot of those will effectively bypass your DR anyway.)

tl;dr -- DR is quite good at lower levels, but as you level up into the double digits DR is much less useful than AC. +1 DR > +1 AC (most of the time), but +2 AC > +1 DR.

[Larkas]

What if you get DR 40/+7? Oh, wait :smallbiggrin:

[Seerow]

Playing a front liner, I expect the stronger monsters to hit 70%-80% of the time (unless I am an AC specialist) with their big attacks. +1 AC stops about 7%. But meleeist at higher levels have multiple attacks. Those secondary attacks might only hit 30% of the time, so +1 AC helps ~16% here.


Um, if monsters are hitting 80% on their primary, they're still going to hit 55% on their secondary. Secondaries are -5, not -10.

AC does help more against secondary attacks than primaries though. That much is true.

[sleepyphoenixx]

Keep in mind that a lot of highly dangerous melee monsters use natural attacks, probably with Multiattack. You need high AC or some other way to avoid being hit to survive those.
Getting your AC that high usually isn't cost-effective though, so it's generally preferable to find another way not to get hit.
Even DR 10 can do a lot to mitigate that damage but it's rarely enough to be viable as the sole layer of defense except at very low levels.

DR 10/whatever is relatively easy to get, so it's a great addition to almost any build. More than that or DR x/- in any quantity gets really expensive though so you'll want to get some miss chance and/or high AC in addition to it if you want to survive, and also to protect yourself from things like touch attacks that ignore DR.

If it's a 1:1 tradeoff i'd take AC over DR, especially touch AC, unless my AC is already high enough to get diminishing returns on more.
Also, anything lower than DR 5 is pretty much a waste of time imo. I'd rather get fast healing instead.

[Ravens_cry]

The way I see it, the hierarchy is miss chance, AC, DR. DR stops you from getting damaged once you're hit, AC stops you from getting hit, while Miss chance stops even the possibility of getting hit, negating even a natural 20.

[Fouredged Sword]

The way I see it, the hierarchy is miss chance, AC, DR. DR stops you from getting damaged once you're hit, AC stops you from getting hit, while Miss chance stops even the possibility of getting hit, negating even a natural 20.

This is very true. One defense alone is not nearly as powerful as a good layered defense on a cost per effect basis.

[sleepyphoenixx]

The way I see it, the hierarchy is miss chance, AC, DR. DR stops you from getting damaged once you're hit, AC stops you from getting hit, while Miss chance stops even the possibility of getting hit, negating even a natural 20.

With the caveat that most miss chances can be completely negated by True Seeing (which quite a few monsters have as a continuous ability) so they're not feasible as the only means of defense. Otherwise i agree.

[Ravens_cry]

With the caveat that most miss chances can be completely negated by True Seeing (which quite a few monsters have as a continuous ability) so they're not feasible as the only means of defense. Otherwise i agree.
True, but not all. Blink for example. Of course, against casting casters, touch AC is what generally matters at all, and DR is pretty irrelevant as well.

[Flickerdart]

AC lets you not get hit. DR is very unlikely to perform a similar function. Not getting hit is better than getting hit.

[Chronos]

AC sometimes lets you not get hit. DR works consistently. Consistency is the PC's friend.

[Ravens_cry]

AC sometimes lets you not get hit. DR works consistently. Consistency is the PC's friend. Not as much as you might think. Miss chance sometimes lets you avoid damage all together, while DR, especially the kind PCs can generally access, doesn't really help enough. Plus, quite a few monsters have rider effects where a hit does extra stuff on top of damage.