AC Math thread

[Unicore]

In the spirit of not flipping through 600+ posts to follow 1/3 of a total thread about one issue, I think people have a lot of confusion and concern about how the math of Armor class is going to work out. There are a lot of smart people that are good with math here so I invite those discussions here so they can be followed more easily.

As it stands, it looks like Armor has to have a relatively low base Armor bonus, because it getting set up that an armored fighter with a good shield, at level, is going to be relatively difficult to hit (like 14+ to hit) even for a decent attacker. This means second and third attacks against armored opponents are not going to be good options. I can live with this as long as there are plenty of great options for characters other than attacking. It also seems like this math means that being heavily armored and taking advantage of enemies critically missing you (through feats and such) is a very viable combat strategy.

[Deadmanwalking]

We actually don't know that being heavily armored is better than lightly armored with high Dex. It could be, but there's currently no evidence one way or the other.

As for AC going up more than to-hit...that's sort of a resounding maybe. It seems true at the moment, but we might be missing vital information.

[Rogar Valertis]

In PF1 you can have martials reach AC50+ if you wanted, putting them in the "hit only on roll of 20" for most opponents.
Considering what we've learned of PF2 seems like AC won't reach so high (no more rings of protection, amulets of natural armor, no enhancement magical bonus to shields...).

That said of course an heavily armored opponent should be more difficult to hit than a lightly armored one but that doesn't mean were won't be downsides to choosing heavy armor over light armor as well.

[Malthraz]

It looks like AC forumalar is:

10 + proficiency + armour + dex + shield

So, proficiency is in the armour you are wearing (light, medium or heavy). Is there unarmoured proficiency? I am not sure.

I think proficiency works like this:

You level + your rank (it's not called rank, I think it is something else).

Untrained: -2
Trained: 0
Expert: +1
Master: +2
Legendary: +3

Armour is the armour value. I think this can be increased with the quality of the armour and any runes of potency. So armour is:

AC value + quality + potency.

It is possible that quality and potency do not stack, but I am not sure.

Quality:
Expert: +1
Master: +2
Legendary: +3

Potency is +1 through to +5.

Dex is you Dex mod, but is capped for various armours. I am not sure if there is a cap if you are unarmoured.

You get a bonus to AC if you have spent an action to raise your shield. I suspect that this is +1 or +2.

We know that a chain shirt is +2 AC.

Let's say we have a level 2 Fighter with Dex 14. They are wearing with a chain shirt, a wielding a shield. Let's assume that a shield gives a +2 bonus.

AC is ??: 10 + Pro + Dex + Armour + Shield
AC is 16: 10 + 2 + 2 + 2 + 0 (not spending action on shield)
AC is 18: 10 + 2 + 2 + 2 + 2 (spending action on shield)

Let's say that the Fighter gets some silver and levels up a bit. He gets some fancy, well-made enchanted armour. Let's call it a expert quality, potency 1 breast plate. Let's assume that quality and runes of potency do stack. Also assume that a breast plate has an AC bonus of 4, and a max Dex of 3.
Let's say our fighter is level 4, and at level 4 he becomes an expert at medium armour and in shields. I am just making this up, but it seems reasonable. So:

AC is ??: 10 + Pro + Dex + Armour + Shield
AC is 23: 10 + 5 + 2 + 6 + 0 (not spending action on shield)
AC is 25: 10 + 5 + 2 + 6 + 2 (spending action on shield)

Let's break this down:
Pro is level (4) + expert (1) = 5
Dex is still (2)
Armour is breastplate (4) + expert (1) + potency (1)
Shield is still (2)

Interesting.

[Unicore]

A big question mark, getting to walkingdeadman’s point, is whether there will be many/any AC boosting feats and how they keep up with attack feats. This is a question mark because if they are about the same, there is no bonus to attack that matches the innate armor bonus. I am ok with that math. Offense is already heavily favored over defense and bonuses to attack can easily translate into critical hits. It definitely makes basic iterative attacks less desirable against well armored foes than other action options.

[Hurká]

Mark is a math wiz nonpareil, and other people at Paizo are pretty good at math too. I'm sure they can get the theory right, and certainly better than we can do here with partial information.

If in the Playtest that theory doesn't match our experience or is unbalanced across all experiences, then hopefully they can tweak it to match.

[master_marshmallow]

Taken the information on weapons and attack rolls scaling in such a way that you are supposed to expect (d20 result) > (AC + 10) fairly often in the cases of martial characters as the rules for crits are meant to encourage linear advancement rather than finding the sweet spot of 'just enough to-hit" based on the chart in the Bestiaries.

What this means to me is that I expect CR to impact AC, but not much more than we saw in PF1, because the math engine of the game is meant for those using weapons to crit way more often and trigger a metric f**kton of dice rolling, plus the unique abilities of your weapon, whether it be magical or not. Inspiring "One-Big-Hit" builds seems to be something they are discouraging in PF2 with the action system, but reinforcing with feat design that feels like it was meant for PF1. Because of the way the game is designed, they seem to want your first attack to crit super often, which means they'll likely expect secondary attacks to have a 50% chance to crit (very roughly) and tertiary attacks to have a 50% chance to hit (also very rough).

I expect martial characters stacking attack bonuses to the sky will be both normal and optimal when compared to classes that have less ranks invested in weapon proficiency and less money invested in weapons.

They also seem to want all the different kinds of weapons to matter and told us that they are designing combat feats around the prospect of choosing a combat style and fleshing that out through your advancement, so we see weapons that are agile and have much greater chances to crit on secondary and tertiary attacks where you would expect those crits to pop up way more often, but don't carry as much average damage overall because of the smaller dice size. Double Slice was mentioned to exist as a feat, though at this time I have read nothing more about it, but likely it is meant to equate to Power Attack in such a way that it brings your expected damage up.

Honestly, the relationship between attack bonuses and critical hits on their own is less the problem for me. Rant about math:

Spoiler:

In the Power Attack math thread we saw a staunch comparison between using the titular feat and simply not using it and the results we got showed that there are level caps where the extra damage from the feat doesn't math up to be worth it compared to just making extra attacks. Presumably this is meant to be counter-balanced with the added value of critical hits happening more often, given the balance of the desired (d20 attack roll) > (AC+10) (the premise of this thread) which multiplies all your damage dice, then combined with the fact that there are deadly weapons that add extra dice on a crit which would imply that Power Attack is reliant on weapon choice to find its merit. That might not be bad once you get the extra dice from power attack added into a crit for something like an extra 5dx on a crit, when using the right weapons. Basically, if that 5dx you gain averages out to be better than minimum damage on a guaranteed hit, then the issues presented in that feat's thread are mostly solved. However, there's still the belle curve problem resulting in very wide margins of error in encounter design. But [Fortune] feats are a thing, so there may be a re-roll mechanic implemented similar to 5e, or a feat or ability to raise your expected minimums like in PF1's rogue talents that improve sneak attack. Ultimately this issue seems more important to me than the AC values, because AC is not meant to scale super well on enemies, as NPCs and monsters are no longer going to be built on the same rules foundation as the rest of the entities in the gamespace (PCs). I would expect PC armor to improve significantly more or not depending on how much the devs want to make crits happen and matter on enemies. Gone are the days of designing encounters the same way you would build characters, and I expect a lot of the monster and enemy designs to have a simple ruleset to juxtapose an encounter of any theme and CR similar to what we got in the different rules in Unchained.

[Malk_Content]

One thing to note about AC scaling as fast or faster than attacks is that so far we know of several ways to improve your odds of hitting things and no ways of making yourself harder to hit. I don't mind a system where applying debuffs (flat-footed for example) and basic tactics (getting flank bonuses) are an assumed portion of your ability to hit an enemy.

[Captain Morgan]

Malk_Content wrote:

One thing to note about AC scaling as fast or faster than attacks is that so far we know of several ways to improve your odds of hitting things and no ways of making yourself harder to hit. I don't mind a system where applying debuffs (flat-footed for example) and basic tactics (getting flank bonuses) are an assumed portion of your ability to hit an enemy.

I think taking cover is going to be an action as well. So that one will go both ways to an extent. Rogues also have Nimble Dodge. Not that I disagree with your broader point.

[Catharsis]

I don't mind PC Fighters being relatively hard to hit for other PC Fighters; after all, that situation shouldn't come up often. I suppose most enemies will have lower ACs that a PC Fighter, given they're not bound to the same system as PCs.

The important thing is that AC and to-hit scale at the same rate to allow for a consistent feel throughout the levels. This seems to be accommodated by the proficiency bonus adding your level in both cases, and the same system of qualities and runes being applied to both.

We can be sure that quality and runes do not stack for armor, given that they don't for weapons either. I also don't expect any to-hit feat options, other than raising your proficiency with your weapon.

I'm very curious to hear how heavy armor measures up to 18 Dex + studded leather, and what the typical AC of a Wizard is going to be...

[Catharsis]

That reminds me: I seem to remember a dev (Mark?) saying that crits might account for up to a third of a Fighter's damage output. Now, I'm not sure whether that's crits as a whole, or just the extra damage from crits. I'm also not sure whether that assumes the third attack will be traded away as a matter of course, and whether Power Attack or agile weapons are assumed. What would that say about the game math if it were true?

[Mark Seifter]

Catharsis wrote:

I don't mind PC Fighters being relatively hard to hit for other PC Fighters; after all, that situation shouldn't come up often. I suppose most enemies will have lower ACs that a PC Fighter, given they're not bound to the same system as PCs.

I mean this is even more true in PF1 than in PF2 . A level 1 PC in PF1 can easily have 18 AC without doing anything particularly interesting, and with some attention can have 20+. Meanwhile, the chart for creating a CR 1/2 monster (in theory a kindred to a level 1 NPC in PF1) says to give it 11 AC. In fact that 18 AC that's so easy to hit is the average for a CR 5 enemy in PF1.

[Malk_Content]

It is also hinted that for a lot of classes higher levels of armour proficiency aren't a given, while we know that fighters get Legendary Weapon proficiency before anyone could buy it otherwise, so even with all else being equal I imagine Fighters are going to be up +2 or +3 over the AC scaling of anyone even if their opponent is focusing armour as much as the rules allow (ignoring the not yet revealed but a luded to master of armour class.)

But yeah most fights won't be against a single on CR opponent and of those not every opponent will have the highest armour proficiency.

[Unicore]

Rogar Valertis wrote:

In PF1 you can have martials reach AC50+ if you wanted, putting them in the "hit only on roll of 20" for most opponents.

Considering what we've learned of PF2 seems like AC won't reach so high (no more rings of protection, amulets of natural armor, no enhancement magical bonus to shields...).

That said of course an heavily armored opponent should be more difficult to hit than a lightly armored one but that doesn't mean were won't be downsides to choosing heavy armor over light armor as well.

What we know is going to be radically different in PF2 is that there will definitely be some feats that are designed to take advantage of having either an incredibly high, or incredibly low AC. That has me excited, because if it is close to balanced, it will break down the pressure that "you must build your character this way." I am also excited to see if it is feasible to make equally good characters, one a highly armored character (i'm guessing a paladin), that isn't very strong, but can lock down a battle field with reactions and making it difficult for enemies not to attack them, then punishing them with nasty stuff when they critically miss, and a different character (I am guessing a dwarven druid/maybe barbarian or both) that loves to take critical hits and dish out punishment when they do.

With critical misses only being a issue for characters that build to have abilities that punish it, I think the incentive to Max AC will not be as pressing as the incentive to Max Attack for most characters, so I think the question of "how high does my AC need to be?" will still be a common question for a good chunk of player characters and monsters.

When will it be august?

[LuniasM]

I'm kind of on-the-fence about whether the Item Bonus from high-quality weapons/armor and Potency runes will stack or not in PF2. We know that your quality limits the maximum Potency rune bonus already, so why give quality and Potency the same bonus if they don't stack? My best guess is that some spells and abilities may temporarily grant Potency to a weapon over its normal quality limit, and it also simplifies cases where weapons can't be crafted (such as natural attacks and improvised weapons).

[Malthraz]

I have been thinking about unarmored classes. I suspect there may be a mage-armour cantrip, so that Wizards and Sorcerers do not get left too far behind.

Monks may still get a wisdom bonus to AC.

Everyone else gets at least light armour proficiency.

I think it has been stated that arcane spell failure has been removed, so there may be some scope for mages grabbing proficiency in light armour.

[master_marshmallow]

Plate.
Wizard plate.

[Bardarok]

Malthraz wrote:

I have been thinking about unarmored classes. I suspect there may be a mage-armour cantrip, so that Wizards and Sorcerers do not get left too far behind.

Monks may still get a wisdom bonus to AC.

Everyone else gets at least light armour proficiency.

I think it has been stated that arcane spell failure has been removed, so there may be some scope for mages grabbing proficiency in light armour.

Mark said in a previous post:

"I mentioned this elsewhere, but even in the playtest alone, there is a class that gets legendary AC-based proficiency (just not heavy armor) and a way for non-paladins to get legendary proficiency in a heavy armor and shields."

Which makes me think that there might be an unamrored defense proficiency that Monks could get legendary proficiency in. This would allow some automatic scaling for even unarmored untrained PCs to prevent them from being crit all the time even if they are still always hit.