An in-depth look at AC

[Frogreaver]

The first chart is similar to how most people think about AC. That's because they are often focused on the case of AC vs a specific enemy. However, if you are the player AC is really expected to protect you over the whole adventuring day against enemies with a variety of attack modifiers.

The second chart assumes you get hit equally by each attack modifier listed. If you compare this chart to the first you'll note that your average chance to be hit and %damage reduction increase match perfectly with the first chart.

The third chart is an extension of the 2nd and shows what happens as you get into AC values where not all those chance to be hit values can improve anymore. You'll note that at the highest AC values shown that the %damage reduction increase actually starts to drop. Showing that adding more AC can in actual gameplay have diminishing returns after a certain point.

In a future refinement I could also add columns to weight the attack modifiers differently by frequency and damage. I could also potentially add in a method to account for the impact of crits.

*Note these charts ignore crits

[Unoriginal]

I'm not sure what you want to demonstrate, sorry.

[Frogreaver]

I'm not sure what you want to demonstrate, sorry.

you can't necessarily just look at average attack modifier vs your AC and then vs the new AC to determine how much "value" additional AC adds.

[JNAProductions]

What's the point of ignoring crits?

Yes, they make the math harder-but they also make it more accurate, ESPECIALLY when you're dealing with really high AC values.

Speaking of which, 23 is a really high AC value in 5E. Like... Using just the PHB, there's literally only one build that can achieve an AC that high without having to put resources in.

[Frogreaver]

What's the point of ignoring crits?

Yes, they make the math harder-but they also make it more accurate, ESPECIALLY when you're dealing with really high AC values.

Do you believe adding crits is going to change the point I'm illustrating? If not, then do I really need to spend the time to be more accurate just to be more accurate?

Secondly, how would you account for crits in this?

Speaking of which, 23 is a really high AC value in 5E. Like... Using just the PHB, there's literally only one build that can achieve an AC that high without having to put resources in.

I'm not sure your point?

[MaxWilson]

Secondly, how would you account for crits in this?

Double-count the twenty, and ignore the fact that static mods don't double.

E.g. for AC 23, you'd take 10% damage from +0-3 (double damage on natural 20), 15% from +4 (double on 20, normal on 19), 20% from +5 (double on 20, normal on 18-19), etc.

[Yakk]

First, the percent increase in toughness does approach 0 as AC goes to infinity.

But that happens long after you have rendered vs AC threats relstively trivial with super-exponentially increasing toughness from higher AC.

I mean, 20% tougher, 25% tougher, 33% tougher, 36% tougher, 38% tougher -- each *multiplies* with previous scaling.

Your effective HP goes from 100 to 120 to 160 to 215 to 290 to 400; +5 AC makes you 4x tougher.

Now critical hits need to be factored in (making it less steep). And after a bit the scaling stops. But it stops after your HP have already become "yes you have HP; near infinite HP" at least from attacks.

[JNAProductions]

Do you believe adding crits is going to change the point I'm illustrating? If not, then do I really need to spend the time to be more accurate just to be more accurate?

Secondly, how would you account for crits?

I'm not sure your point?

To the latter bit of your post, if your whole point is to show "How to interpret how much AC is good for," then it'd be a good idea to use a realistic AC.

To the former... Yes. Yes it would.

If you're being attacked by a monster that gets a mere 50% increase in damage from a crit (such as a 2d6+7 damage monster) your damage from 19+ to-hit going to 20 to-hit isn't a 100% increase in damage reduction, it's a 2/3rds increase. That's a pretty big difference.

I'll agree that it doesn't matter as much in realistic AC ranges (21 is an easy to reach cap on AC-not unbreakable, by any means, but often it'd be the highest in a party) so using that same monster, if they have a +6 to-hit, a accounting for crits only modifies damage by less than 10%, on the aggregate. But that circles back to the issue that you're not using realistic AC values.

[Frogreaver]

Double-count the twenty, and ignore the fact that static mods don't double.

E.g. for AC 23, you'd take 10% damage from +0-3 (double damage on natural 20), 15% from +4 (double on 20, normal on 19), 20% from +5 (double on 20, normal on 18-19), etc.

I get how to do that. I would have probably done +75% damage instead of double. But if the point is actual accuracy as the other poster desired, that's not really getting us there is it?

[MaxWilson]

I get how to do that. I would have probably done +75% damage instead of double. But if the point is actual accuracy as the other poster desired, that's not really getting us there is it?

It improves accuracy (substantially improves accuracy for some ACs) and it's computationally easy, so why wouldn't you make the improvement if you care at all about accuracy?

I agree that it's still not very accurate after you do that, but the main inaccuracy is not from static modifiers on crits--it's the fact that to-hit bonuses are not uniformly distributed the way the OP assumes they are. (They're also not distributed the same way at all tables, and the distribution changes as you go up in level.) But fixing these flaws is not computationally easy within the framework you've chosen, so I can understand why you wouldn't feel the need to try.

[Frogreaver]

First, the percent increase in toughness does approach 0 as AC goes to infinity.

Yea, that's the trivial case where it already takes a nat 20 for anything to hit you.

But that happens long after you have rendered vs AC threats relstively trivial with super-exponentially increasing toughness from higher AC.

I mean, 20% tougher, 25% tougher, 33% tougher, 36% tougher, 38% tougher -- each *multiplies* with previous scaling.

Your effective HP goes from 100 to 120 to 160 to 215 to 290 to 400; +5 AC makes you 4x tougher.

Yes that's precisely what I am showing. That seems to be common knowledge though. What doesn't seem common knowledge is that the actual % increase of effective hp can actually drop as AC increases.

Also consider that the traditional model would show 20%, 25%, 33%, 50%, 100%. Which is 6x tougher. 6x vs 4x is a significant difference IMO.

Now critical hits need to be factored in (making it less steep). And after a bit the scaling stops. But it stops after your HP have already become "yes you have HP; near infinite HP" at least from attacks.

The most you can scale hp to via AC is to a factor of 20x higher. I'm not sure what factor you would need for "enough"

It improves accuracy (substantially improves accuracy for some ACs) and it's computationally easy, so why wouldn't you make the improvement if you care at all about accuracy?

I agree that it's still not very accurate after you do that, but the main inaccuracy is not from static modifiers on crits--it's the fact that to-hit bonuses are not uniformly distributed the way the OP assumes they are. (They're also not distributed the same way at all tables, and the distribution changes as you go up in level.) But fixing these flaws is not computationally easy within the framework you've chosen, so I can understand why you wouldn't feel the need to try.

Do people here no realize what an illustrative example is?

[JNAProductions]

How much 5E have you played, Frogreaver? And what were the games like?

I'm curious as to what informs your experiences here.

[Petrocorus]

Speaking of which, 23 is a really high AC value in 5E. Like... Using just the PHB, there's literally only one build that can achieve an AC that high without having to put resources in.

Which one?

[Frogreaver]

To the latter bit of your post, if your whole point is to show "How to interpret how much AC is good for," then it'd be a good idea to use a realistic AC.

The phenomenon I'm capturing doesn't exist at AC's below 20. I think you know that though and so I question why you would make the criticism?

To the former... Yes. Yes it would.

If you're being attacked by a monster that gets a mere 50% increase in damage from a crit (such as a 2d6+7 damage monster) your damage from 19+ to-hit going to 20 to-hit isn't a 100% increase in damage reduction, it's a 2/3rds increase. That's a pretty big difference.

You are falling into the trap of only factoring in 1 attack modifier. Maybe the biggest point of this thread is that you should avoid that.

How much 5E have you played, Frogreaver? And what were the games like?

I'm curious as to what informs your experiences here.

I absolutely Hate posts like this and not because I haven't played 5e plenty. It comes across as an attempted cheap shot. Nothing in this thread would be invalidated if I hadn't played 5e a single minute, so why even bring it up?

[JNAProductions]

Which one?

Barbarian, level 20, uses a Shield and has a total of 42 or higher between Con and Dex. So a 24 Con, 18 Dex Barbarian with a Shield has a resourceless AC of 23.

The phenomenon I'm capturing doesn't exist at AC's below 20. I think you know that though and so I question why you would make the criticism?

You are falling into the trap of only factoring in 1 attack modifier. Maybe the biggest point of this thread is that you should avoid that.

What exactly IS the phenomena you're capturing?

And I'm not trying to model the entire adventuring day. I'm pointing out that crits matter.

I'd also like to point out that assuming you face the same number of attacks from each hit bonus seems WILDLY unrealistic. If you face three goblins (+4 to-hit, one attack each) lead by a hobgoblin (+3 to-hit, one attack) you'll generally be eating about three times as many +4 attacks as +3, if not more (due to focusing down the bigger threat first, since the hobgoblin deals a lot more damage).

I absolutely Hate posts like this and not because I haven't played 5e plenty. It comes across as an attempted cheap shot. Nothing in this thread would be invalidated if I hadn't played 5e a single minute, so why even bring it up?

Why would you assume it's a cheap shot? I'm legitimately curious-your play experience, as far as I can infer from your posts, doesn't match mine.

Stuff like using 23 AC as a reasonable AC to bother running calculations for, for instance, would indicate games that are very liberal with their stat-boosting magic items, like +1 shields and whatnot. Which doesn't match my experiences with 5E.

[stoutstien]

Which one?

Lv20 barb with maxed con and dex +shield

[Unoriginal]

Do people here no realize what an illustrative example is?

I might be slow or just dead tired, but I personally can't see what you're trying to illustrate or to exemplify here.


I get that you're trying to show that AC should be confronted against varied attack modifiers if you want to make the calculation of AC's effectiveness accurate, but that's about it.

[Frogreaver]

I might be slow or just dead tired, but I personally can't see what you're trying to illustrate or to exemplify here.


I get that you're trying to show that AC should be confronted against varied attack modifiers if you want to make the calculation of AC's effectiveness accurate, but that's about it.

I think you get it 99% of it.

[Hellpyre]

I'm honestly not sure why you think the idea that AC provides no values once you hit the level of natural 20 as the target number is something that goes unacknowelged. It's more generally the case that system conventions lead to monsters with higher raw damage output also having high enough attack bonuses that you don't hit that point for them, while the damage from creatures that have low attack bonuses become much less relevant as you reach a point in your character progression where you are that far above them. As far as I've seen, it's well understood by people invovled in optimization, but tends to be discounted by these sorts of metagame concerns.

[LudicSavant]

Do people here no realize what an illustrative example is?

I think they do.

If you're being attacked by a monster that gets a mere 50% increase in damage from a crit (such as a 2d6+7 damage monster) your damage from 19+ to-hit going to 20 to-hit isn't a 100% increase in damage reduction, it's a 2/3rds increase. That's a pretty big difference.

You are falling into the trap of only factoring in 1 attack modifier. Maybe the biggest point of this thread is that you should avoid that.

That's not a 'trap,' that's JNAProduction using a quite valid illustrative example.

[Unoriginal]

I think you get it 99% of it.

Then I must confess I don't understand how your OP illustrates that.

Barbarian, level 20, uses a Shield and has a total of 42 or higher between Con and Dex. So a 24 Con, 18 Dex Barbarian with a Shield has a resourceless AC of 23.

Do feats and Reactions count as ressources? Because a DEX-focused Ranger/Fighter with studded leather, a shield and with Defense Duelist can go quite a bit higher than 23.

What exactly IS the phenomena you're capturing?

I have to second this question (a second time).

I'd also like to point out that assuming you face the same number of attacks from each hit bonus seems WILDLY unrealistic. If you face three goblins (+4 to-hit, one attack each) lead by a hobgoblin (+3 to-hit, one attack) you'll generally be eating about three times as many +4 attacks as +3, if not more (due to focusing down the bigger threat first, since the hobgoblin deals a lot more damage).

While it's true in principle, focusing on the goblins could also be a good tactical choices as not only they're easier to kill (and removing someone from the enemy side helps your side's action economy prevails) but they're also more likely to hit.

Of course there is the fact goblins are not likely to want to continue the fight if the hobgoblin get killed, compared to the hobgoblin who is likely to want a fight to the death.

[Frogreaver]

I'd also like to point out that assuming you face the same number of attacks from each hit bonus seems WILDLY unrealistic. If you face three goblins (+4 to-hit, one attack each) lead by a hobgoblin (+3 to-hit, one attack) you'll generally be eating about three times as many +4 attacks as +3, if not more (due to focusing down the bigger threat first, since the hobgoblin deals a lot more damage).

Do you understand what an illustrative example is?

Why would you assume it's a cheap shot? I'm legitimately curious-your play experience, as far as I can infer from your posts, doesn't match mine.

Stuff like using 23 AC as a reasonable AC to bother running calculations for, for instance, would indicate games that are very liberal with their stat-boosting magic items, like +1 shields and whatnot. Which doesn't match my experiences with 5E.

Why would someone assume that questioning whether another has played the game they are discussing in order to attempt to undermine their credibility would be anything else?

The point can be both true and not useful for you at the same time. Those aren't mutually exclusive states.

[JNAProductions]

Do feats and Reactions count as ressources? Because a DEX-focused Ranger/Fighter with studded leather, a shield and with Defense Duelist can go quite a bit higher than 23.

I have to second this question (a second time).

While it's true in principle, focusing on the goblins could also be a good tactical choices as not only they're easier to kill (and removing someone from the enemy side helps your side's action economy prevails) but they're also more likely to hit

In reverse order...

Hobgoblins do 1d10+2d6+1 damage, whereas goblins do 1d6+2. The main difference is the hobgoblin has a higher AC (18, as compared to 15) but only 4 more HP.
I would, generally, focus down the hobgoblin first. But, different people will vary, and you could easily replace the specific chosen monsters with others and still get the point across.

Yup.

No-but Defensive Duelist only works against ONE attack, correct me if I'm wrong. Basically, when I say "23 AC" in this context, I'm referring to static AC. AC you can expect to have no matter what, against any number of foes. I do see your point, though! I wasn't clear with what I meant.

Do you understand what an illustrative example is?

Why would someone assume that questioning whether another has played the game they are discussing in order to attempt to undermine their credibility would be anything else?

The point can be both true and not useful for you at the same time. Those aren't mutually exclusive states.

Yes, I do. I just used one earlier, as LudicSavant kindly pointed out.

And because I remember what I was like when I was new to D&D. Not 5th edition, since I had mellowed out by then, it was more 4th edition for me. I was VERY number-focused. Math this, math that, calculate the odds, etc. etc.

It's definitely a good skill to have (and I do like doing probability calculations for various D&D or 40k things, just to figure odds out) but it's frequently not reflective of actual play.

I don't want to demean you or anything like that, but I am legitimately curious what your 5E experiences are like.

[Frogreaver]

I'm honestly not sure why you think the idea that AC provides no values once you hit the level of natural 20 as the target number is something that goes unacknowelged. It's more generally the case that system conventions lead to monsters with higher raw damage output also having high enough attack bonuses that you don't hit that point for them, while the damage from creatures that have low attack bonuses become much less relevant as you reach a point in your character progression where you are that far above them. As far as I've seen, it's well understood by people invovled in optimization, but tends to be discounted by these sorts of metagame concerns.

Then why are you the only one acknowledging it's a true point?

I think they do.

So 90% of this thread has been criticizing the perfectness of the illustrative example, instead of talking about the point it's illustrating. Is that normal?

[ProsecutorGodot]

Do people here no realize what an illustrative example is?

I think it's just a bit confusing to find what's being illustrated here. Of course there are diminishing returns, after a certain point nothing but a critical strike can reach your AC without DM intervention to create an obscene hit bonus.

I'm kind of stuck on the second sentence of your OP though:

That's because they are often focused on the case of AC vs a specific enemy. However, if you are the player AC is really expected to protect you over the whole adventuring day against enemies with a variety of attack modifiers.

The focus of AC against a specific enemy is generally a valid concern in my experience, especially because some of the most available large bonuses to AC rely on active use rather than passive (Shield, Shield of Faith, Dodging*, Defensive Duelist, Kensei Parry) and often makes the consideration to up your AC based on reasoning whether the triggering attack will harm you considerably. Unless I'm reading these charts incorrectly, most reasonably attainable AC totals without any conditionals applied will be a positive swing.

Which I guess could be considered the same as "protecting you throughout the adventuring day" so I'm still back to being a bit confused at things.

Do you understand what an illustrative example is?

Most here are grasping for what is being illustrated with this example. Are you trying to say that AC past 28 is pointless? That there is an obvious diminishing return? That one should consider their entire adventuring day when casting shield if it would boost their AC into the diminishing threshold?

[MaxWilson]

No-but Defensive Duelist only works against ONE attack, correct me if I'm wrong. Basically, when I say "23 AC" in this context, I'm referring to static AC. AC you can expect to have no matter what, against any number of foes. I do see your point, though! I wasn't clear with what I meant.

It works against only one hit, but if (as is common) you have the chance to see the die before deciding whether to DD, it can scale up to 3-4 attacks per round pretty easily, since usually only one attack per round will fall within the range that Defensive Duelist is expected to affect. In an extreme case, such as fighting goblins at low levels when your Proficiency bonus is only +2, Defensive Duelist can be as good as +2 to AC against ~8-10 attacks per round--you only use it when someone hits you by a margin of +0 or +1, which happens only 10% of the time.

[Unoriginal]

Hobgoblins do 1d10+2d6+1 damage, whereas goblins do 1d6+2. The main difference is the hobgoblin has a higher AC (18, as compared to 15) but only 4 more HP.
I would, generally, focus down the hobgoblin first. But, different people will vary, and you could easily replace the specific chosen monsters with others and still get the point across.

Fair.

No-but Defensive Duelist only works against ONE attack, correct me if I'm wrong. Basically, when I say "23 AC" in this context, I'm referring to static AC. AC you can expect to have no matter what, against any number of foes. I do see your point, though! I wasn't clear with what I meant.

True, I had forgotten that it only applied to one attack. A shame really.

Then why are you the only one acknowledging it's a true point?

I don't think anyone here has denied the truth of the point. But I'm not sure that most people here see it as something that requires active acknowledgement as opposed as something that is already understood as being true.

So 90% of this thread has been criticizing the perfectness of the illustrative example, instead of talking about the point it's illustrating. Is that normal?

Maybe it's because people here are confused about how the exemple and the point it's meant to illustrate are related to each other, or because they agree with you on the point itself but find your methodology not fitting for what you're trying to illustrate?

[JNAProductions]

Also, looking at my posts, I apologize if I caused you any offense, Frogreaver. I remain curious, but didn't want to cause any harm.

It works against only one hit, but if (as is common) you have the chance to see the die before deciding whether to DD, it can scale up to 3-4 attacks per round pretty easily, since usually only one attack per round will fall within the range that Defensive Duelist is expected to affect. In an extreme case, such as fighting goblins at low levels when your Proficiency bonus is only +2, Defensive Duelist can be as good as +2 to AC against ~8-10 attacks per round--you only use it when someone hits you by a margin of +0 or +1, which happens only 10% of the time.

Still not what I meant by "Resourceless AC," so maybe I should've said "Static AC"? Would that make more sense, be clearer, all that jazz?

[MaxWilson]

Still not what I meant by "Resourceless AC," so maybe I should've said "Static AC"? Would that make more sense, be clearer, all that jazz?

Oh, sure. I don't disagree with you, and I appreciate your reminder about AC 24 barbs.

I was just making the separate point that Defensive Duelist covers more attacks in practice than many people think, because unlike e.g. Protection style, you can choose to use it only on a hit instead of on an attack. I've found myself taking Defensive Duelist even on Eldritch Knights with Shield and Warcaster, because it winds up saving you from annoying lucky hits in situations that aren't quite deadly enough to be worth burning spell points on.

[Eldest]

So 90% of this thread has been criticizing the perfectness of the illustrative example, instead of talking about the point it's illustrating. Is that normal?

You've provided data and no conclusions. The data is what we can see to critique. If you want your point to be talked about, please take a minute to type it up in a paragraph. Edit it into the OP and put it in the thread too, to make sure everyone sees it.

Edit: I'm very brain dead at the moment, and I get that you're trying to say something about AC being valued somewhat differently based on a range of attack bonuses against you. I don't know what it is.