Double Slice should not be nerfed- plus math

[master_marshmallow]

Coming from a few different threads we've been having a lot of discourse over the impact and utility of feats, and on how combat works overall in PF2. Generally, we've been looking at the various combat styles to see which ones offer the most versatility and usage at the table so when you're building characters you understand what the differences are and can plan you tactics/builds accordingly.

Most of these are choices in the fighter class, or duplicated from the fighter for comparison:

Double Slice [A\]
"Make one Strike (see page 308) with each of your two melee weapons, each at your current multiple attack penalty. The second Strike takes a –2 circumstance penalty if it’s made with a weapon that doesn’t have the agile trait (see page 182). If both attacks hit, combine the attacks’ damage, and then add any other applicable enhancements from both weapons. For purposes of resistances and weaknesses, this is considered a single Strike. This counts as two attacks when calculating your multiple attack penalty (see page 305)."

This trades out and straight up upgrades a secondary attack into a primary, it improves your odds of both hitting and landing crits with that attack making it very potent, it also adds the damage in together before applying weakness/resistance.
This one is the big daddy of combat feats in this playtest book. "Why is this?" you might ask, and the answer comes in two-forms:

1) it has clear benefits to use over not using any feats at all
&
2) It has multiple uses in different scenarios, mostly because it lacks the [open] trait and can be used with either primary, or secondary attacks.

Let's look at some math:

[A] Strike -0 [A\] Double Slice -5/-5 (for one-handed plus agile) or -4/-4 (for double agile)

As a 'full round attack', nothing comes close to this kind of potential for martially oriented characters. That is essentially a +6 to your tertiary attack if you were using any other style, creating a scenario where you'll have the best attack bonus/crit chance in the game.

Algebra: h-c= % chance to hit (maximum= .9), c= % chance to crit (minimum =.05), ndx= multiples of dice, STR= STR modifier
(h-c)(ndx+STR) +(c)(2)(ndx+STR)
This formula intends to map your potential damage expectations, but it does not account for the size of the distribution spread of weapon damage, but rather relies on the average in its place, meaning the math will be off here a little until we integrate both systems

[lvl 1 fighter] STR 18, +6 to hit, average enemy AC 13 (rough math because the book isn't organized for it) d6+4 damage, twice from agile weapons

(.5)(7.5) + (.15)(15) = 6 damage on a single hit; 12 on a double

Compare this to not using DS, but just attacking twice:
(.5)(7.5) + (.15)(15) = 6 damage on a primary plus
(.45)(7.5) + (.05)(15) = 4.125 damage on a secondary equals
10.125 damage potential.

As you can imagine, increasing your chance to hit vastly improves your damage potential, and it improves your crit chance as well, proportionally inflating that value even more.

Now, let's look at a 'full attack'

Double Slice:
(.5)(7.5) + (.15)(15) = 6 damage on primary, plus
(.45)(7.5) + (.05)(15) = 4.125 on first secondary, plus
(.45)(7.5) + (.05)(15) = 4.125 on second secondary equals
14.25 damage potential

No feat investment:
(.5)(7.5) + (.15)(15) = 6 damage on primary, plus
(.45)(7.5) + (.05)(15) = 4.125 on first secondary, plus
(.25)(7.5) + (.05)(15) = 2.625 on tertiary equals
12.75 damage potential

Double Slice first:
(.5)(7.5) + (.15)(15) = 6 damage on first primary, plus
(.5)(7.5) + (.15)(15) = 6 damage on second primary, plus
(.25)(7.5) + (.05)(15) = 2.625 on tertiary equals
14.625 damage potential

Thus, Double Slice will always improve your damage potential, generally as you progress and your secondary attacks gain a higher chance to crit you will see the value of using double slice second increase over time. This is doubly true for Rangers using Hunt Target and fighters using Agile Grace to further reduce secondary penalties on agile weapons. You get the free choice to use the feat as either primary or secondary attacks, and your tactics can change depending on movement and crit chance, which grants freedom and utility.

Power Attack [open] [A\]
Make a melee Strike. It gains the following enhancement. Enhancement You deal an extra weapon damage die. If you’re at least a 10th-level fighter, you deal two extra weapon damage dice. This counts as two attacks when calculating your multiple attack penalty.

This forces you to make a single primary attack, at the cost of not making a secondary attack. In exchange, your damage gets improved upon by a single die until 10th level, when you get two dice. It has the [open trait] meaning it can never be done as a secondary attack, and it forces any other attack you make to be a tertiary one.

[lvl 1 fighter] STR 18, +6 to hit, average enemy AC 13 (same math) d12+4 damage

No feat:
(.5)(10.5) + (.15)(21) = 8.4 damage on a primary plus
(.45)(10.5) + (.05)(21) = 5.775 on a secondary equals
14.175 damage potential

Power Attack:
(.5)(17) + (.15)(34) = 13.6 damage potential

full round:
(.5)(10.5) + (.15)(21) = 8.4 damage on a primary plus
(.45)(10.5) + (.05)(21) = 5.775 on a secondary plus
(.25)(10.5) + (.05)(21) = 3.675 on tertiary equals
17.85 damage potential

full round with Power Attack:
(.5)(17) + (.15)(34) = 13.6 on primary plus
(.25)(10.5) + (.05)(21) = 3.675 on tertiary equals
17.275 damage potential

Thus, Power Attack will almost always make you worse, by the numbers.

Are there more feats that improve damage beyond this for any class? These two are the one's mainly used for comparison to see what feats designs work in PF2 vs what feats do not. Double Slice not only produces better numbers in every scenario it is used in, but it includes multiple scenarios that it can be used for, where other abilities that tax your actions give you nothing back for this.

Compare the odds of improving crits at later levels with double slice, when damage increases and you'll find the feat never loses its value. As the game progresses and your ability to attain more critical hits also improves, feats like Power Attack, Dual-Handed Strike, Blade of Justice, and the like in order to retain value over the course of a character and actually be worth the action tax (which invariably removes the chances to hit with one or more attacks because duh) then there needs to be an increase to the attack roll on such abilities. Ideally you will improve the odds of landing a crit with primary attacks by an amount equal to the difference in how much Double Slice improves the odds to crit with secondaries. This usually works out to around 10-15%, meaning you'll want a +2 or +3 to be included on feats like Power Attack to really balance them out and make them worth more than taking secondary attacks. Let's spitball the math on Power Attack including a +2:

(.4)(17) + (.25)(34) = 15.3 damage potential

This ultimately gives it an edge over someone just not using Power Attack, since it cannot be combined with secondary attacks, you'll never see scenarios where it really changes a full round overall, other than simply adding much more value to Power Attack being used.

What does this mean for Double Slice? The feat in the title? It means that it functions as intended and improves upon the character taking it, and we should be looking at it not as something OP compared to the rest of the options, but rather as the bar by which the rest of the options need to be raised in order to make the rest of the math work better.

Please feel free to check my math, this one took a while to do the calcs and devise a formula. If anyone wants to help deal with using distribution curves in place of static averages I would be very much inclined to read up on it.

[master_marshmallow]

Comparing the ratios on the math I just did, spitballing a potential bonus on action taxes to attack roles, using double slice usually grants around 15% damage over not using it, giving Power Attack a +2 bonus gives it around 10% more damage, where a +3 gives it around 14%.

The question comes into finding out the exact place to put this extra bonus and whether or not it should scale and how a scaling bonus affects the game at later levels.

[master_marshmallow]

So I wanna look at level 10 builds and compare what Agile Grace does for Double Slice compared to Certain Strike for Power Attack.

Agile Grace reduces the penalties for using agile weapons to -3 and -6. Certain Strike is one action, but it's failure effect treats it as a hit with minimum value (all 1's on the dice).

[Level 10 fighter] STR 20, Master Proficiency +2, +2 weapons; melee +19
Average AC for level 10 enemies= 26.6 -> 27

hit: 8-20, crit 18-20 (15%)

Double Slice, two agile weapons (3d6+5)
(.5)(15.5) + (.15)(31) = 12.4 on primary plus
(.5)(15.5) + (.15)(31) = 12.4 on primary equals
24.8 damage potential

Power Attack, BFW (5d12+5)
(.5)(37.5) + (.15)(75) = 30 damage potential

full attacks

Agile Grace
(.5)(15.5) + (.15)(31) = 12.4 on primary plus
(.5)(15.5) + (.15)(31) = 12.4 on primary plus
(.3)(15.5) + (.05)(31) = 6.2 on tertiary equals
31 damage potential
or
(.5)(15.5) + (.15)(31) = 12.4 on primary plus
(.45)(15.5) + (.05)(31) = 9.6 on secondary plus
(.45)(15.5) + (.05)(31) = 9.6 on secondary equals
31.6 damage potential

Power Attack & Certain Strike (8 damage)
(.5)(37.5) + (.15)(75) = 30 on primary plus
(.8)(8) + (.1)(24.5) + (.05)(49) = 11.3 on tertiary equals
41.3

Certain Strike (3d12+5)
(.5)(24.5) + (.15)(49) = 30 on primary plus
(.55)(8) + (.35)(24.5) + (.05)(49) = 15.425 on secondary plus
(.8)(8) + (.1)(24.5) + (.05)(49) = 11.3 on tertiary equals
56.725 damage potential

Certain Strike is a force to be reckoned with.

[Arachnofiend]

Am I reading that right that a 2-handed Fighter with no feat investment will do more damage than a TWF Fighter with Double Slice? Maybe Power Attack should just be removed then, rather than buffing it so the gap between the two playstyles is even wider.

[Vidmaster7]

Or reduce it but remove the extra action cost.

[Pramxnim]

Great to see another math analysis on the Fighter feats. A couple of comments:

Your Double Slice damage is lower than it should be because the optimal setup for a TWF is to use a non-agile weapon and an agile weapon, not 2 agile weapons. This means 1 weapon will be a d8, and you’re missing a bit less than 1 damage per weapon die.

There are several errors in your level 1 calculations:

- the accuracy should be 70%, not 65% (you’re hitting on a 7, not 8). You have the secondary and tertiary calculations right, but are underestimating primary damage by about 10% of 1d6+4, or by 0.75

- The aforementioned optimal TWF configuration will end up changing the math, resulting in a damage increase of 0.7 (only applies to the first attack with your non-agile weapon). This damage is 0.65 * 3 = 1.95 for your level 10 calculations.

- The Lvl 1 Power Attack calcs are severely overestimating the damage of secondary and tertiary hits. Also starting accuracy should be 70% here as well. You’d either have 70% on the first hit, then 45% on the second, and 20% on the 3rd, or 70% then 20% if you started with Power Attack.

The result is your Power Attack calc looks a lot better at level 1 than it should.

- Finally, when you go to apply a theoretical attack bonus to Power Attack, you didn’t raise overall accuracy. A +2 bonus would result in 80% accuracy and 30% to crit. The damage should looks like .5 * 17 + .3 * 34 = 18.7

Now, for your level 10 calculations:

- As mentioned above, Double Slice should be doing slightly more damage (1.95 to be exact)

- In your Certain Strike calculations, you used 30 for the primary attack damage, which is the same as primary Power Attack damage. Should be less because you’re just doing a normal Strike here. Correct ED for Strike + CS + CS is 45.925

Your calcs have shown me that Certain Strike is very powerful, adding a whopping 6.4 expected damage on a 3rd Attack and making 2H a better option than TWF, even with Power Attack’s mediocrity. Nay, you’ve shown me that when Certain Strike is obtained, one should immediately retrain out of Power Attack, because that feat is just a waste of actions for a 2H Fighter.

Edit: Even if PA seems like it does more expected damage than Double Slice, DS gives you more chances to crit, and Weapon Property runes that add damage dice help bridge the gap snce they get applied twice on DS activities.

At 65% accuracy, a single Power Attack has a 15% chance to crit, but a DS will crit at least once 41.225% of the time. That’s a lotta crits, and will bring about big swings more often, even if expected damage of DS + Strike is lower than PA + Certainly Strike

[master_marshmallow]

Pramxnim wrote:

Great to see another math analysis on the Fighter feats. A couple of comments:

Your Double Slice damage is lower than it should be because the optimal setup for a TWF is to use a non-agile weapon and an agile weapon, not 2 agile weapons. This means 1 weapon will be a d8, and you’re missing a bit less than 1 damage per weapon die.

There are several errors in your level 1 calculations:

- the accuracy should be 70%, not 65% (you’re hitting on a 7, not 8). You have the secondary and tertiary calculations right, but are underestimating primary damage by about 10% of 1d6+4, or by 0.75

- The aforementioned optimal TWF configuration will end up changing the math, resulting in a damage increase of 0.7 (only applies to the first attack with your non-agile weapon). This damage is 0.65 * 3 = 1.95 for your level 10 calculations.

- The Lvl 1 Power Attack calcs are severely overestimating the damage of secondary and tertiary hits. Also starting accuracy should be 70% here as well. You’d either have 70% on the first hit, then 45% on the second, and 20% on the 3rd, or 70% then 20% if you started with Power Attack.

The result is your Power Attack calc looks a lot better at level 1 than it should.

- Finally, when you go to apply a theoretical attack bonus to Power Attack, you didn’t raise overall accuracy. A +2 bonus would result in 80% accuracy and 30% to crit. The damage should looks like .5 * 17 + .3 * 34 = 18.7

Now, for your level 10 calculations:

- As mentioned above, Double Slice should be doing slightly more damage (1.95 to be exact)

- In your Certain Strike calculations, you used 30 for the primary attack damage, which is the same as primary Power Attack damage. Should be less because you’re just doing a normal Strike here. Correct ED for Strike + CS + CS is 45.925

Your calcs have shown me that Certain Strike is very powerful, adding a whopping 6.4 expected damage on a 3rd Attack and making 2H a better option than TWF, even with Power Attack’s mediocrity. Nay, you’ve shown me that...

Accuracy and crit shouldn't weigh together, the weight of crits needs to be separated from the weights of non crits, with their respective proportions added in, so for a 70% hit chance and 15% crit chance, I'd be looking at (.55) for non crits, improving some of the numbers for sure. (h-c) and (c) should add up together to get (.70). nerd stuff

I stuck with two agile weapons because I wanted to see how much better using two secondaries at -3 compared to a one-hand and an agile off at -5/-5. The goal was for it to improve my crit chance.

I can run calcs on different weapon configurations (planned on showing the difference in weapon dice anyway).

I think I'm also gonna run through and calc the AC averages and modes based on the Bestiary, as I've discovered the game really is designed in a very boring way with all the 27s that popped up in the lvl 10 creatures, it makes the game very homogeneous in that crit chance 100% of the time is determined by a primary attack, and if you don;t have +2 proficiency you can cut crits right out of your expected play style.

Martial characters need a boost for it to be worth it. My suggestion is to maintain the action taxing for such abilities, which reduces overall damage, but increase attack and damage bonus with such abilities to make up for it.

More math forthcoming.

[Kerobelis]

You Are also looking at the best levels for power attack (1 & 10) A’s those are the levels where the extra dice are added first. If you look at power attack when magic items increase, power attack can be worse than two normal attacks (level 4, 8, 12, 16, 20). I believe you pointed this out in a different thread and it should be highlighted.

[Kerobelis]

Certain strike, damage on a miss! Wasn’t that a huge complaint about D&D 4th edition? I recall lots of arguments about this concept for martial abilities.

[master_marshmallow]

Certain Strike has it's limitations, it is an action, and a [Press] ability, so it only works on secondary attacks or worse.

But yes, it's pretty good. At 12th level you can have Agile Grace and Certain Strike and make some silly powerful attacks.

And yes, I did map the ranges and averages of both feats in another thread, for this one I finally figured out the formula for calcing DPR.

[Kerobelis]

The last certain strike calc is wrong for the first attack. I think you copied the power attack total. The calc is right but it adds to 19.6 instead of 30.. The overall total would then be 46.3. Still better than power attack plus certain strike.

One last suggestion, it would be nice to see the base case damage in each scenario with no feats. Just 3 attacks.

Keep up the good work!

[master_marshmallow]

What if weapons only ever scaled to 3 dice, naturally by their quality, and weapons scaled to +5 as before, but only through other magical qualities that have the bonus baked in?

Mundane quality determines damage, magical quality determines accuracy?

[Pramxnim]

master_marshmallow wrote:

What if weapons only ever scaled to 3 dice, naturally by their quality, and weapons scaled to +5 as before, but only through other magical qualities that have the bonus baked in?

Mundane quality determines damage, magical quality determines accuracy?

I dunno how that would work without adjusting monster hp at higher level. It would also mess with the delicate balance between martial and spellcaster damage that I’m sure Paizo has spent a lot of time on.

I understand that accuracy must be separated into hit rate and crit rate, I just used it because I was lazy and didn’t want to type 55% hit and 15% crit multiple times.

You may be misunderstanding how Agile works. As long as your 2nd and 3rd+ attacks are made with an agile weapon, it will have a better MAP. So if I swing a Longsword and then a Shortsword twice, my MAP will be +0/-4/-8, no different from swinging a Shortsword 3 times. Therefore the optimal choice for a TWF character is to have 1 agile and 1 non-agile Weapon for pure damage consideration.

Forceful: The Forceful Weapon trait works incredibly well with Certain Strike, upping its Expected damage considerably (by 1-6 on a secondary Strike and by 2-12 on a tertiary strike). Even with a lower damage die (the Falchion is Forceful and does d10 damage), I suspect it’ll be better than using Certain Strike with a d12 Weapon.

Speaking of Certain Strike, your calculations assume a TWF uses just normal Strikes for their tertiary attacks. Since Fighters have 2 floating feats, one of which can be used to learn Certain Strike, there’s no reason they would not use it as well.

Deadly and Fatal: Some smaller damage dice weapons have Deadly (Glaive, Spear, Rapier, Scythe, Starknife, Katar, Filcher’s Fork) and Fatal (Light Pick, Pick, Great Pick) which affects damage on a crit. Since TWF crits more often (because of Agile), it might be good to try calculations with these weapons in consideration.

My gut instinct is that Deadly will not improve expected damage too much, but Fatal (limited to Picks and a Monk special attack option) does improve expected damage, even with a lower damage die to start with.

[master_marshmallow]

So I was testing two agile weapons before, to take advantage of the agile property, now I'll compare damage using a one-handed weapon and an agile, and see how Certain Strike interacts.

corrected math:

Spoiler:

[lvl 1 fighter] STR 18; melee +6
average AC: 13 (d6+4 damage)

Double Slice:
(.5)(7.5) + (.2)(15) = 6.75 damage on a primary plus
(.5)(7.5) + (.2)(15) = 6.75 damage on a primary equals
13.5 damage potential

Agile weapon in off hand:
(.5)(7.5) + (.2)(15) = 6.75 damage on a primary plus
(.45)(7.5) + (.05)(15) = 4.125 damage on a secondary equals
10.875 damage potential.

Strike plus Double Slice:
(.5)(7.5) + (.2)(15) = 6.75 damage on primary, plus
(.45)(7.5) + (.05)(15) = 4.125 on first secondary, plus
(.45)(7.5) + (.05)(15) = 4.125 on second secondary equals
15 damage potential

Three agile attacks:
(.5)(7.5) + (.2)(15) = 6 damage on primary, plus
(.45)(7.5) + (.05)(15) = 4.125 on first secondary, plus
(.25)(7.5) + (.05)(15) = 2.625 on tertiary equals
12.75 damage potential

Double Slice plus Strike:
(.5)(7.5) + (.2)(15) = 6.75 damage on first primary, plus
(.5)(7.5) + (.2)(15) = 6.75 damage on second primary, plus
(.25)(7.5) + (.05)(15) = 2.625 on tertiary equals
16.125 damage potential

[lvl 1 fighter] STR 18, +6 to hit
average enemy AC 13, (d12+4 damage)

two-handed weapon:
(.5)(10.5) + (.2)(21) = 9.45 damage on a primary plus
(.4)(10.5) + (.05)(21) = 5.25 on a secondary equals
14.7 damage potential

Power Attack:
(.5)(17) + (.2)(34) = 15.3 damage potential

three strikes:
(.5)(10.5) + (.2)(21) = 9.45 damage on a primary plus
(.4)(10.5) + (.05)(21) = 5.25 on a secondary plus
(.15)(10.5) + (.05)(21) = 2.625 on tertiary equals
17.325 damage potential

Power Attack plus tertiary:
(.5)(17) + (.2)(34) = 15.3 on primary plus
(.15)(10.5) + (.05)(21) = 2.625 on tertiary equals
17.825 damage potential

[Level 10 fighter] STR 20, Master Proficiency +2, +2 weapons; melee +19
Average AC: 27
hit: 8-20 (65%), crit 18-20 (15%)

Double Slice, two agile weapons (3d6+5)
(.5)(15.5) + (.15)(31) = 12.4 on primary plus
(.5)(15.5) + (.15)(31) = 12.4 on primary equals
24.8 damage potential

Power Attack, BFW (5d12+5)
(.5)(37.5) + (.15)(75) = 30 damage potential

full attacks

Double Slice then Strike, with Agile Grace:
(.5)(15.5) + (.15)(31) = 12.4 on primary plus
(.5)(15.5) + (.15)(31) = 12.4 on primary plus
(.3)(15.5) + (.05)(31) = 6.2 on tertiary equals
31 damage potential

Strike, then Double Slice with Agile Grace:
(.5)(15.5) + (.15)(31) = 12.4 on primary plus
(.4)(15.5) + (.05)(31) = 7.75 on secondary plus
(.4)(15.5) + (.05)(31) = 7.75 on secondary equals
27.9 damage potential

Power Attack & Certain Strike (8 damage):
(.5)(37.5) + (.15)(75) = 30 on primary plus
(.8)(8) + (.1)(24.5) + (.05)(49) = 11.3 on tertiary equals
41.3

Certain Strike (3d12+5)
(.5)(24.5) + (.15)(49) = 19.6 on primary plus
(.55)(8) + (.35)(24.5) + (.05)(49) = 15.425 on secondary plus
(.8)(8) + (.1)(24.5) + (.05)(49) = 11.3 on tertiary equals
46.325 damage potential

[lvl 1 fighter] STR 18; melee +6
average AC: 13 (d8+4)(d6+4)

Double Slice:
(.5)(8.5) + (.2)(7) = 7.65 damage on a primary plus
(.5)(7.5) + (.2)(15) = 6.75 damage on an agile primary equals
14.4 damage potential

Agile weapon in off hand:
(.5)(8.5) + (.2)(7) = 7.65 damage on a primary plus
(.45)(7.5) + (.05)(15) = 4.125 damage on a secondary equals
11.775 damage potential.

Strike plus Double Slice:
(.5)(8.5) + (.2)(7) = 7.65 damage on a primary plus
(.4)(8.5) + (.05)(17) = 4.25 on first secondary, plus
(.45)(7.5) + (.05)(15) = 4.125 on second secondary equals
16.025 damage potential

Strike plus two agile attacks:
(.5)(8.5) + (.2)(7) = 7.65 damage on a primary plus
(.45)(7.5) + (.05)(15) = 4.125 on first secondary, plus
(.25)(7.5) + (.05)(15) = 2.625 on tertiary equals
14.4 damage potential

Double Slice plus Strike:
(.5)(8.5) + (.2)(7) = 7.65 damage on first primary plus
(.5)(7.5) + (.2)(15) = 6.75 damage on second primary, plus
(.25)(7.5) + (.05)(15) = 2.625 on tertiary equals
17.025 damage potential

[Level 10 fighter] STR 20, Master Proficiency +2, +2 weapons; melee +19
Average AC: 27
hit: 8-20 (65%), crit 18-20 (15%)

Double Slice, (3d8+5) (3d6+5):
(.5)(18.5) + (.15)(37) = 14.8 on primary plus
(.5)(15.5) + (.15)(31) = 12.4 on primary equals
27.2 damage potential

Agile in off hand:
(.5)(18.5) + (.15)(37) = 14.8 on primary plus
(.4)(15.5) + (.05)(31) = 7.75 on secondary equals
22.55 damage potential

Double Slice plus Strike, with Agile Grace:
(.5)(18.5) + (.15)(37) = 14.8 on first primary plus
(.5)(15.5) + (.15)(31) = 12.4 on second primary plus
(.3)(15.5) + (.05)(31) = 6.2 on a tertiary equals
33.4 damage potential

Strike plus Double Slice, with Agile Grace:
(.5)(18.5) + (.15)(37) = 14.8 on primary plus
(.45)(15.5) + (.05)(31) = 8.525 on secondary plus
(.45)(15.5) + (.05)(31) = 8.525 on secondary equals
31.85 damage potential

Strike plus Double Slice, with Agile Grace (using main hand):
(.5)(18.5) + (.15)(37) = 14.8 on primary plus
(.35)(18.5) + (.05)(37) = 8.325 on secondary plus
(.45)(15.5) + (.05)(31) = 8.525 on secondary equals
31.65 damage potential

Double Slice plus Certain Strike, with agile weapon(8):
(.5)(18.5) + (.15)(37) = 14.8 on first primary plus
(.5)(15.5) + (.15)(31) = 12.4 on second primary plus
(.7)(8) + (.2)(15.5) + (.05)(31) = 10.25 on a tertiary equals
37.45 damage potential

Double Slice plus Certain Strike, with one-handed weapon(8):
(.5)(18.5) + (.15)(37) = 14.8 on first primary plus
(.5)(15.5) + (.15)(31) = 12.4 on second primary plus
(.8)(8) + (.1)(18.5) + (.05)(37) = 10.1 on a tertiary equals
37.3 damage potential

As ever, please check my math. This shows that hunt target/ Agile grace really aren't that great to a character when compared to taking Double Slice and Certain Strike.

The conclusion is that martial classes need more chances to crit.

[master_marshmallow]

Certain Strike and Agile Grace are both gated at 10th level and are thus incompatible until level 12. I'm gonna look into when Doubling Rings become a factor compared to investing in weapons.

[Pramxnim]

Your math checks out. I'll just add that Agile Grace can combine with Certain Strike, so that on a tertiary attack with Certain Strike + Agile Grace (at lvl 12):

(.60)(8) + (.30)(15.5) + (.05)(31) = 11 on a tertiary
So 14.8+12.4+11 = 38.2 damage potential

With the Fighter's high base attack bonus, each bonus to attack / penalty to enemy AC matters more, because they increase your crit rate.

Another note: writing out (.50)(18.5) + (.15)(37) makes it easy to follow your steps, but I'm lazy, so for my calcs, I'll just be condensing it to (.80)(18.5), aka doubling the crit rate and adding it to the hit rate before multiplying with the average damage of an attack. This won't work on Deadly and Fatal weapons, but for those cases, I'll write the formula out in full.

Let's examine what happens when the enemy is flat-footed, since that situation will come up frequently during play. It translates to a 10% boost in accuracy, or in our Fighter's case, a 10% increase in crit rate:

Lvl 1 Fighter, Melee +6, AC: 11 (flat-footed):

Double Slice:
(.50+.60)(8.5) = 9.35 on a primary plus
(.50+.60)(7.5) = 8.25 on an agile primary equals
17.6 damage potential.

Agile weapon in off hand:
(1.10)(8.5) = 9.35 damage on a primary plus
(.70)(7.5) = 5.25 damage on a secondary equals
14.6 damage potential.

Strike plus Double Slice:
(1.10)(8.5) = 9.35 damage on a primary plus
(.60)(8.5) = 5.1 on first secondary, plus
(.70)(7.5) = 5.25 on second secondary equals
19.7 damage potential

Strike plus two agile attacks:
(1.10)(8.5) = 9.35 damage on a primary plus
(.7)(7.5) = 5.25 on first secondary, plus
(.45)(7.5) = 3.375 on tertiary equals
17.975 damage potential

Double Slice plus Strike:
(1.10)(8.5) = 9.35 damage on first primary plus
(1.10)(7.5) = 8.25 damage on second primary, plus
(.45)(7.5) = 3.375 on tertiary equals
20.975 damage potential

As you can see, the damage increase is pretty significant with just a 10% boost in accuracy (+2 to hit or -2 to enemy AC). Let's see the damage potential of Power Attack under the same conditions:

lvl 1 fighter STR 18, +6 to hit, average enemy AC 11 (flat-footed) d12+4 damage:

No feat:
(1.10)(10.5) = 11.55 damage on a primary plus
(.60)(10.5) = 6.3 on a secondary equals
17.85 damage potential

Power Attack:
(1.10)(17) = 18.7 damage potential

Full Round:
(1.10)(10.5) = 11.55 damage on a primary plus
(.60)(10.5) = 6.3 on a secondary plus
(.35)(10.5) = 3.675 on tertiary equals
21.525 damage potential

Full Round with Power Attack:
(1.10)(17) = 18.7 on primary plus
(.35)(10.5) = 3.675 on tertiary equals
22.375 damage potential

We see the same thing here. I'd have to plug in the numbers to an Excel sheet and see what the damage comparison looks like at various different levels, and maybe re-evaluate my initial instinct to just say "buff Power Attack to high heavens". I think it needs a buff, but would have to math out exactly how much of a buff so it doesn't overshadow other options in various situations.

EDIT: On the topic of crits, Martials crit more often with any source of bonus to hit, assuming they normally hit on a 10 or less (55% accuracy or more), because each +1 to hit from that point on adds directly to crit rate. Simply flanking is +10% to crit. I don't think they need more help to crit, unless you want to see 40-50% crit rate builds, and that might just be a bit silly.

[master_marshmallow]

I've found that crit rates only matter on primary attacks across the board.

The only time my math is showing a chance for secondary attacks to improve their crit rate is by a small chance if using agile weapons and agile grace against outlier enemies with much lower than average AC. Even then, at most you'll see 10%.

Keen weapons are a factor, as they crit on a 19 or 20.

[Pramxnim]

I've made a rudimentary calculator on Google Sheets. Just copy the sheet to your drive to tinker with it.

Fighter accuracy seems to hover around 60-70%, settling at 60% at higher levels (needing a 9 to hit). For TWF, the best option each turn at this accuracy is to Strike, then Certain Strike twice. If your Accuracy improves (whether by flanking or whatnot), Double Slice becomes the best option again. These conclusions are with both Certain Strike and Agile Grace. Certain Strike becomes the best option to use the moment it comes into play.

After looking at the data, we can see that as the rules are currently, fighting with a 2H weapon yields more damage than TWF, but not because of Power Attack.

Double Slice slightly outperforms Power Attack and level 20, and scales better with accuracy.

Certain Strike is better than both PA and DS, which makes sense given that it's a higher level feat. It does get worse with increased accuracy though, letting DS overtake it when flanking.

Looking at various ways to buff PA, I notice that:

Simply letting PA give +2 Circumstance bonus to attack makes it deal ~10 more damage than DS.

Having PA deal 1 more damage die makes it slightly better than DS

Any additional damage die on top of the 3rd one makes PA the clear superior choice

Regardless of buffs to Power Attack, Certain Strike still overperforms it by a significant margin, such that the optimal damage path in a turn is to Strike and then use Certain Strike twice.

Conclusion: PA is slightly behind DS at higher levels, and definitely worse than just swinging twice, whether with 2 normal Strikes, or a Strike followed by a Certain Strike. However, it only needs a small buff to become relevant. Either make it give a bonus to Attack or have it give +3 damage dice instead of +2 damage dice.

[Pramxnim]

Someone on Discord pointed out that Power Attack is an enhancement and it only counts as 2 attacks for MAP if you hit. Looks like I'll have to fix the formula for calculating PA + Strike or PA + Certain Strike damage, since it just became a bit more complicated.

Someone should make an analysis of Furious Focus too, to see if that feat is good enough. Right now it basically only applies on the 2nd Strike of the turn because it has the Press trait, making it super narrow.

[master_marshmallow]

Pramxnim wrote:

Someone on Discord pointed out that Power Attack is an enhancement and it only counts as 2 attacks for MAP if you hit. Looks like I'll have to fix the formula for calculating PA + Strike or PA + Certain Strike damage, since it just became a bit more complicated.

Someone should make an analysis of Furious Focus too, to see if that feat is good enough. Right now it basically only applies on the 2nd Strike of the turn because it has the Press trait, making it super narrow.

Furious Focus rings as a trap option to me, as it literally only enhances your ability to fail with a non agile weapon. It forces a three round attack, and isn't that great a buff.

[Pramxnim]

Surprisingly, once I crunched the numbers, Furious Focus is better than Power Attack when you actually get to full attack (it's no different than 2 Strikes otherwise).

I've also included a Forceful toggle option. At high levels, a forceful d10 weapon is better than a d12 weapon when doing a 3+ attacks with Certain Strikes, but less effective otherwise.

The highest DPR against a target dummy is a level 20 Fighter using a Falchion and doing Strike + Certain Strikes + Certain Strikes + Certain Strikes round after round.

[master_marshmallow]

So we found the ceiling?

[Pramxnim]

I think I did. A level 20 Fighter swinging at a Star-Spawn of Cthulhu with 60% accuracy.

He has Certain Strikes (10), Desperate Finisher (12), Savage Critical (18), Weapon Supremacy (20).

He's wielding a +5 Falchion which has the Forceful trait.

Our Fighter uses the action granted from his Quick condition to Strike at the Star-Spawn. Then he uses his 3 actions to use Certain Strikes and finishes up with a 4th Certain Strikes via Desperate Finisher, giving up his Reaction for the Round.

The Fighter makes a total of 5 attacks, with an expected damage of:

(.50)*(40)+(.10)*(80) = 28 damage on the Strike
(.60)*(19)+(.25)*(46)+(.10)*(92) = 32.1 damage on the 1st CS
(.85)*(25)+(.10)*(104) = 31.65 on each subsequent CS

Total expected damage: 28+32.1+(3)(31.65) = 155.05 damage

If we're flanking, total expected damage is 173.85 damage.

That's the most damage I can think of doing in 1 round.

[master_marshmallow]

Nice, this is valuable. 10th level this comes online?

[Pramxnim]

Yeah, you just need Certain Strikes. At lower levels, you can sub Furious Focus for a lesser, but similar effect.

As a bonus, I tried the Glaive and got pretty close numbers (148.15 at 60% acc and 171.25 at 70% acc), so either weapon is fine. Certain Strikes means that a lot of your damage is coming from misses anyway.

[Twilight_Arcanum]

Go back to page 89 of the playtest and read the side bar on Press attacks.

Press attacks
1) Can only be used on attacks with a MAP of -4 or greater (usable after two attack with agile grace or one normal agile attack)
2) Do not generate their failure effect on a CritFail

So this means that your certain strike data is going to be off.

Taking the fighter from the 10th level example

hits the average 27ac enemey on an 8 and would critfail on a theoretical -2

That means his secondary is going to critmiss on a 3 or lower ie a 10% less chance of doing the minimum 8 damage than you had calculated

The third attack will then critmiss on a 8 or lower for a 40% less chance of doing the minimum 8 damage.

These hold pretty steady for the optimized fighter with a non agile weapon and the ones for an agile weapon are similar 5% closer to the value of them always working.

For an agile weapon with agile grace you'll have to completely redo it i'm afraid as you will only be able to press when the MAP is -6

[Twilight_Arcanum]

To help with the math, provided your secondary attacks can crit miss on something higher than a 1 but lower than 11 then it will always add .45(minimum damage)to the base DPA(damage-per-action) which is a pretty big boost still.
So at 10th level it should add 3.6, with forceful 4.95 on the first iterative and then 6.3 on any additional. At level 20 it should add 5.85,8.55 if forceful 1st iterative, and 11.25

Certain strike gets worse if you have a high chance to hit on your iterative or a high chance to crit miss

[Pramxnim]

You're right, I am overestimating Certain Strikes on 3rd attacks. The -10 to Hit for 2H-Weapons increases the crit fail chance, and the fail chance alone is only about 45% for the +25 attack vs. 44 AC case.

Thanks for bringing this to my attention. It's good to have someone else spot your mistakes and bring them to your attention.

I'll look at the data taking into account Agile Grace as well. I hadn't noticed you needed MAP to be -4 or greater to take advantage of the Failure effect. Looks like Certain Strike is not the be-all-end-all of Fighter builds.

Gotta give kudos to Paizo on the Fighter balance. Its options may seem weirdly disproportionate, but once you dig deeper, you'll see that the end result is well balanced (with Power Attack being a bit undertuned).

[master_marshmallow]

Well, it obviously won't be worth it because different styles are keyed to different functions. I think Dual Handed Strike exists for dueling builds, but it's still worse than two attacks.

The core choices at 1st level seem okay. I'm interested in the effects of keen on the game.

Then I'll wanna look into ranged potential.

[Pramxnim]

So, after wrestling with the whole Certain Strikes thing and how to code it, I ran into a problem where my hit rate, crit rate, crit fail chances were all going out of whack at extremes (where you only hit or miss, but don't crit). I spent some time fixing those, but there's still some issues when your attack bonus is equal to the enemy AC (aka you always hit them). However, those cases don't really apply in normal gameplay, so I'm going to ignore them.

Now, after applying the new Certain Strikes math to max DPR calculation, we have our Fighter attacking with a +5 Falchion at 60% accuracy:

(.50)*(40)+(.10)*(80) = 28 damage on the Strike
(.45)*(19)+(.25)*(46)+(.10)*(92) = 29.25 damage on the 1st CS
(.45)*(25)+(.10)*(104) = 21.65 on each subsequent CS

For a total of 122.2 dmg in 1 round. Quite a far cry from the previous 155.05 figure. A Glaive with the new calculations does 119.8 dmg in 1 round.

Now, if you want to eke out even more damage, let's assume our +5 Magic Falchion is made out of Orichalcum has 4 of the Corrosive/Flaming/Frost/Shock property runes. They ignore resistance and add up to 4d6 on a hit. It doesn't look like this extra damage is multiplied on a crit, and the crit effects from Flaming and Shock add Persistent Damage, which don't stack, so we won't have to factor it into our calculations much.

To calculate expected damage from our elemental properties, we just have to add together the accuracy of each of our 5 attacks and multiply it with the average damage of 4d6:

Added dmg = (.60+.35+.10+.10+.10)*(14)=17.5

If we don't kill the enemy outright, the persistent damage will trigger at least once and deal an average of (2d10+2d6) = 18 dmg. Our chances of critting at least once in our barrage of attacks, given we crit 10% of the time on each attack, is:

1-(0.9)^5 = .40951
Expected Persistent Damage (1 tick) = .40951*18 = 7.37
Total expected dmg from property runes = 17.5+7.37 = 24.87

If we push it to the limits, maximum DPR of a 2H Fighter is 122.2+17.5+7.37 = 147.07.

[Mark Seifter]

Great math crunching, Pramxnim. We did work really hard to run the numbers between all sorts of different weapons and different combat styles, and you see that in some of the glaive vs falchion vs other weapon analysis (unlike in PF1 where eventually a few weapons scaled far and away above the others). I agree we could probably up the higher-level scaling on Power Attack a little as well.

[master_marshmallow]

I personally think martial characters who trade actions should be doing so with a higher crit chance, rather than more damage. Without inflating damage more, you can fine tune the crit ratio. If Power Attack scaled up in your ability to crit, there would be as much incentive to activate it in place of strikes or a [press] ability in a secondary attack slot. It would be a good design incentive for martial characters to do this with their class features.

It would have the benefit of not needing to redo the whole system.