Disciplined strikes by the numbers, how good is it? How does it compare to other classes?

[cactot]

I was a little confused regarding how good Disciplined Strikes actually is, so I thought that I would actually take a few minutes to try and figure it out. 

 

Based upon my understanding of the game mechanics as they are today, I did a quick calculation to see exactly how good disciplined strikes is in various situations.  I have used these three scenarios to see how the benefit varies based upon stat adjustments: No advantage (attack/deflection even), +10 attack advantage, -10 attack disadvantage.

 

Base attack formula is as follows, roll 1d100 and adjust based upon advantage/disadvantage and compare to the following:
1-30 miss
31-50 graze (-50% damage)
51-100 hit
101+ crit (+25% damage, +50% penetration)

 

IMPORTANT NOTE:  Because the penetration system is nearly impossible to normalize and account for I will be ignoring it.  In reality crits perform a little better than shown above because it will cause over-penetration in some cases, and remove under-penetration problems in other cases.  

 

I will assume the base damage is a static 100, to simplify the math. 

For a baseline we have average damage with matched attack/defense. 

 

I will be using shorthand that looks like this:
(100*0.5)+(50*0.2) = 60% weapon damage

 

For explanation of what I am writing we have full damage (100) with a 50% likelihood (0.5) + half damage graze (50) with a 20% likelihood (0.2) for a total of 0.6, or 60% weapon damage on average.  I left off crit, as you cannot roll over 100 on a 1d100, so crits shouldn't be possible in this situation.

Here is the same example, but with a 10 point attack advantage.  This would look like:

 

1-20 miss
21-40 graze (-50% damage)
41-90 hit
91+ crit (+25% damage, +50% penetration)

(100*0.5)+(50*0.2)+(125*0.1) = 72.5% weapon damage

 

You can see in this one we now have a 10% (0.1) of doing crit damage (+25%, for a total of 125)

Moving the other way we have a 10 point attack disadvantage.
(100*0.4)+(50*0.2) = 50% weapon damage

 

Based upon this, you see that if base chance to hit is 50%, any advantage is converted directly into crit chance, and any disadvantage is removed directly from crit chance.  If crit chance is 0%, further disadvantage is subtracted from the chance of making a "hit".  

Disciplined strikes, because of intuitive, has a slightly adjusted base (because it gives +5 accuracy from perception increases).  Here is what the base looks like:
1-25 miss
26-35 graze
36-45 graze converted to hit
46-70 hit
71-95 hit converted to crit
96+ crit

 

For simplicity, because of the 50% graze to hit and hit to crit, and as far as I know a graze cannot convert to a hit and then convert to a crit, what I have done is take half the BASE ranges (which are determined by accuracy relative to defense) and cut them in half, allocating the upper "half" to upgrade damage type.   For example, with even attack/deflection there will be a 25% chance of getting a hit that is upgraded to a crit.  If deflection goes up by 10 (for a 40% base chance to get a hit) there would be a 20% chance of getting a hit that is upgraded to a crit. 

 

From this point forward I will mostly not be showing my work, and will just show the shorthand.

Average damage (matched attack and defense):
(50*0.1)+(100*0.35)+(125*0.3) = 5 + 35 + 37.5 = 77.5% weapon damage
Damage increase: 29%

Average damage (10 point attack advantage)
(50*0.1)+(100*0.35)+(125*0.4) = 5 + 35 + 50 = 90% weapon damage
Damage increase: 24%

Average damage (10 point attack disadvantage)
1-35 miss
36-45 graze
46-55 graze converted to hit
56-77.5 hit
77.5-100 hit converted to crit
(50*0.1)+(100*0.325)+(125*0.225)  = 65.625% weapon damage
Damage increase: 31%

 

 

It is also worth re-calculating it for Devoted, as they get twice the standard crit damage bonus.  

Devoted average damage:
(50*0.1)+(100*0.35)+(150*0.3) = 5 + 35 + 45 = 85% weapon damage
Damage increase: 41.7%

Devoted average damage (10 point attack advantage)
(50*0.1)+(100*0.35)+(150*0.4) = 5 + 35 + 60 = 100% weapon damage
Damage increase: 37.9%

Devoted average damage (10 point attack disadvantage)
(50*0.1)+(100*0.325)+(150*0.225) = 5 + 32.5 + 28.125 = 71.25% weapon damage
Damage increase: 42.5%

 

Conclusion:

The intuitive buff is more impactful the lower your accuracy is compared to the target's deflection, and is about a 12% higher damage increase on Devoted than on a base fighter. 

 

Compared to similar buffs:

Eternal devotion (Paladin) + 20% lash damage

Lightning strikes (Monk) 35% attack speed + 30% lash damage.

Swift Flurry (Monk) 35% attack speed + (average weapon damage * (1 + (crit chance * ( ∑ 0.3^n ))  

 

Since ∑ 0.3^n = 0.4286 at 100% crit chance it would do 42.86% extra damage. 

 

Lightning strikes is the highest average damage in most cases, with a total of 75.5% damage increase (1.3*1.35).  In order to match that with Swift Flurry you would have to hit 70% crit chance.   That would mean you would need a 45 point accuracy advantage in conjunction with the intuitive buff.  It would be effectively impossible to get without the intuitive buff (you would need +70 accuracy advantage). 

 

 

Thoughts?  Let me know if I messed up any assumptions or any of my math. 

[Boeroer]

I just know that when you combine Disciplined Strikes with Swift Flurry and Blast (and manage to reach 4+ enemies with the AoE) often a chain reaction starts that kills all enemies at once.

 

Same happens with Swift Flurry + Kalakoth's Minor Blights as a one handed weapon with One Handed Style and Merciless Gaze.

 

In most other cases Swift Flurry "feels" less powerful than Lightning Strikes which very much fits with your calculations.

 

You could use a single rapier and its modal and also use Thunderous Blows in order to stack Tenacious with Disciplined Strikes (and be near or even over 70% crit rate) - but why bother when you can also dual wield with Lightning Strikes and likely do more damage because of speed and be more versatile / can react more quickly because of shorter recovery?

Edited May 2, 2018 by Boeroer

[AndreaColombo]

Subbing thread.

[cactot]

I just know that when you combine Disciplined Strikes with Swift Flurry and Blast (and manage to reach 4+ enemies with the AoE) often a chain reaction starts that kills all enemies at once.

 

Same happens with Swift Flurry + Kalakoth's Minor Blights as a one handed weapon with One Handed Style and Merciless Gaze.

 

I hadn't considered the idea that each target impacted by the AOE had a different crit roll that was eligible for activating flurry, nor would I have thought to use rods in melee combat.  Good stuff!   I wonder if that would apply to driving flight as well? 

 

Also, one thing you might know the answer to one thing I am not clear on:

 

The fighter's mob stance refers to "threatened" targets and targets "around" the fighter.  Neither of these are ever defined.  Do you happen to know if the area encompassed by these two variables is influenced by weapon reach?  If so, using a reach weapon like a staff or a pike could be very effective with mob stance turned on.  It would significantly increase your ability to stack recovery time buffs, and would cascade to hit far more targets when you do score a killing blow.

[kmbogd]

I know that in the game's cyclopedia a miss is reflected in separate pages as being either <=30 or <=25. I haven't had the chance of seeing which is the correct version, but I am inclined to say 25 not 30. Also the malus of 50% or the bonus of 25% are not multiplicative but additive. This means for instance that a graze is not actually half of the damage resulted from a hit resolution. A very simplified model of the dmg formula is something like: base_weapon_dmg *(modifier1 + modifier2+....+modifierN + 1)*MightModifier. This is an oversimplification and is not really the precise formula (you can read MaxQuest's post for that). Contrary to what one would believe, the modifier for a graze is not really -0.5 but 1-1/0.5=-1. The formula above is good if the sum all modifiers is above 0, otherwise even the whole formula is a bit different.

Edited May 3, 2018 by kmbogd

[Madscientist]

Copied from thr other thread:

 ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

MaxQuest has found the damage formula. I post it here so you do not have to search those threads for the formulas.

 

-------------------------------------------------

 

FinalDamage = (RolledDamage * DamageMultiplier + AdditiveDamageBonus) * PostAdditiveDamageMultiplier

DamageMultiplier is influenced by:
- weapon quality bonus (e.g. fine/exceptional/superb)
- weapon type bonus (e.g. sharp)
- bonus damage talents (e.g. two-handed style, sneak attack, soul whip)
- crit bonus
- over-penetration bonus

PostAdditiveDamageMultiplier is influenced by:
- might damage coefficient
- modal malus (like -50% from daggers modal)
- graze malus
- under-penetration malus

As for AdditiveDamageBonus, am not completely sure but it can include flat damage bonuses; think of Novice's Suffering from PoE1.

Question: Now, how are these multipliers actually calculated? Additive or multiplicative?
Answer: additive with a big twist:
- all damage coefficients are broken into steps
- now, if it's value is above 1, the step will be (value - 1)
- and if the value is below 1, the step will be (1 - 1 / value)
- after that all these steps are added up, into one big coefficient
- if the value of this coefficient is above 0, the group multiplier will be (coefficient + 1)
- and if the value of this coefficient is below 0, the group multiplier will be [1 / (1 - coefficient]

 

-------------------------------------------------

This is for the second version of the beta.

 

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

 

I did understand the formula of PoE1.

But regarding damage and speed, its impossible for me to tell what is the final effect of a modifier when there are several other modifiers as well.

[kmbogd]

In the latest beta, apart from might I don't think there is any other "PostAdditiveDamageMultiplier", everything else (graze malus, under penetration malus, modal malus) has been put into "DamageMultiplier" area. You can see an example of this change in post #10 from the below link where I exemplified how the graze damage was obtained:

 

https://forums.obsidian.net/topic/97058-backstab-175-instead-of-150/

Edited May 3, 2018 by kmbogd

[cactot]

Hmm, so if I am reading that correctly, a 50% damage bonus would be a multiplier of 1.5, but a 50% damage malus would be a multiplier of 0.666... (a reduction of 33%, which means the unmodified damage is 50% higher than the malus-adjusted damage)

 

That makes sense, as it makes it a little harder to mitigate damage down to 0.  

 

Ultimately, if you ignore other factors that are too difficult to account for (like penetration/under penetration) the simplified formula I used before is still roughly a good guideline.  

 

The primary differences would be that the non disciplined strikes damage percents would all go up by 3.2, and the disciplined strikes damage percents would go up by half that.  So it would reduce the benefit of disciplined strikes slightly.

 

Just for fun, lets see what it looks like when you have a 30% might bonus with the new adjustments (still ignoring under and over penetration), and see how that changes things.

 

Base, with no attack advantage or disadvantage:  

1-30 miss
31-50 graze (-50% damage additive 30% might bonus in same step, for a final damage multiplier o 0.83 (a 17% total damage reduction))
51-100 hit (30% might bonus)

(83*0.2)+(130*0.5) = 81.6% average weapon damage

 

 

Same but for devoted (which would be a 5 point attack advantage because of per buff):

Crit damage would be (100*(1+0.5))*1.3) = 195 damage.  

(83*0.1)+(130*0.35)+(195*0.3) = 112.3% weapon damage
Damage increase: 37.6%

 

 

It looks like the effects of might slightly decrease the relative benefit of disciplined strikes, that is a bit surprising to me.

  

 

Here is another one with lash.  Base, with no attack advantage or disadvantage:  

1-30 miss
31-50 graze (+30% damage applied first, then 0.66 multiplier from damage malus = 85.8 total damage)
51-100 hit (30% lash bonus)

(85.8*0.2)+(130*0.5) = 85.8% average weapon damage

 

And with Lash and might bonus:

1-30 miss
31-50 graze (base * lash = 130 damage, then multiplier of 0.83 for 107.9)
51-100 hit (base * lash = 130, then multiplied by 30% might bonus)

(107.9*0.2)+(169*0.5) = 106.1% average weapon damage

 

This is quite close to the benefit seen by a devoted with disciplined strikes, and higher than you would see from a non-devoted fighter with disciplined strikes (which would do 102.6% average damage, because they crit for 32.5 less damage).  Considering lightning strikes still has a 35% speed bonus, so DPS wise it would come out well ahead of even the devoted with disciplined strikes.  Penetration related damage will swing the damage back in favor of fighters (particularly devoted) by some amount, but it is extremely difficult to quantify by exactly how much.

 

Then put all of them together, devoted with the lash and might:

Crit damage would be (100*(1+0.5+0.3))*1.3) = 234 damage.  

(107.9*0.1)+(169.5*0.35)+(234*0.3) = 121.3% average weapon damage
 

[cactot]

Okay, so I am trying to quantify the impact of penetration.  Here is the (probably incorrect) guesstimations I am making based upon other games:

 

Armor ratings follow a semi-normal distribution, with values near the median being the most frequent, and low armor values being relatively more common than a high armor value equivalently far from the median (due to both caster mobs of all levels and "trash" mobs having low armor values, while extreme high armor values are limited to elite mobs). 

 

Here is the distribution odds that I came up with (source: pulled straight from my tush)

 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.1 0.09 0.07 0.05 0.03 0.01 0.01 0.01

 

 

Based upon that we should be able to find the average damage bonus/malus to apply to the formula. 

 

8 pen            

12 pen (Crit)

          0.25  

30% bonus

    0.075   0.42  

30% bonus

    0.126 0.38  

no bonus

        0.52  

no bonus

      0.1  

25% malus

    0.025   0.03  

25% malus

    0.0075 0.09  

50% malus

    0.045   0.01  

50% malus

    0.005 0.18  

75% malus

    0.135   0.02  

75% malus

    0.015         sum 0.205           sum 0.0275         mult 0.8298755187           mult 0.9732360097                          

10 pen

           

15 pen (crit)

          0.33  

30% bonus

    0.1   0.52  

30% bonus

    0.156 0.49  

no bonus

        0.47  

no bonus

      0.07  

25% malus

    0.0175   0.01  

25% malus

    0.0025 0.05  

50% malus

    0.025   0  

50% malus

    0 0.06  

75% malus

    0.045   0  

75% malus

    0         sum 0.0875           sum 0.0025         mult 0.9195402299           mult 0.9975062344

 

 

So a non devoted with an 8 pen weapon would have an average damage on a hit of:

(100*1.075)(0.8298) = 89.2% damage

 

With a 30% might bonus:

(100*1.075)(1.095) = 107.6% damage

 

On a crit:

(100*(1 + 0.126 + 0.25))(0.973) = 133.88

 

With a 30% might bonus and a crit:

(100*(1 + 0.126 + 0.25))(1.2225) =168.22

 

Devoted, regular hit:

(100*1.1)(0.9195) = 101.15% damage

 

Above, with might bonus:

(100*1.1)(1.2125) = 133.38% damage

 

Devoted, crit:

(100*(1.156 + 0.5))(0.9975) = 165.19% damage

 

Devoted with might, crit:

(100*(1.156 + 0.5))(1.2975) = 214.87% damage

 

 

Not too shabby!

 

Well crap, it ruined all my formatting

Edited May 3, 2018 by cactot

[kmbogd]

Ok, so I just confirmed in-game that grazes start at 25. Which is actually a bug since 25 should be the last value for a miss (1-25) equating to a 25% default chance. A graze should happen between 26 and 50 equating to another 25%. With grazes happening between 25-50, we have a 26% default chance for this attack resolution, while misses have a 24% default chance (1-24).

 

In any case the cyclopedia descriptions are bugged as they kept the old system with 30 in place for some pages (attack resolution,graze) and updated it to 25 for other pages (miss).

[Tommy1984]

Then put all of them together, devoted with the lash and might:

Crit damage would be (100*(1+0.5+0.3))*1.3) = 234 damage.  

(107.9*0.1)+(169.5*0.35)+(234*0.3) = 121.3% average weapon damage

 

Are you sure about this? Last time I checked the damage scores in the beta the bonus from might was a full multiplier.

 

So your formula should look like this:

(100 [damage] * 1.3 [might] * (1 + 0.25 [crit] + 0.25 [devoted])) * 1.3 [overpenetration]) = 253,5 damage

 

Not sure if multiple crit damage multipliers are additive (as shown in the formula) or also multiplicative with each over. I need to test this more.

 

(edit: sorry ... I confused overpenetration bonus and might bonus in your formula)

 

 

I'm also interested in the question: Are battle axes (+20% crit damage) or sabres (+10% damage) better for classes that often do crits?

Edited May 3, 2018 by Tommy1984

[kmbogd]

 

I'm also interested in the question: Are battle axes (+20% crit damage) or sabres (+10% damage) better for classes that often do crits?

 

 

In another thread I posted an excel file which works as DPS calculator. It has quite a few abilities added, weapon modals, attributes, weapon styles etc. It's a work in progress but it is functional. You could also give me the particular scenario you had in mind and I could provide you with an answer.

[cactot]

 

 

I'm also interested in the question: Are battle axes (+20% crit damage) or sabres (+10% damage) better for classes that often do crits?

 

 

In another thread I posted an excel file which works as DPS calculator. It has quite a few abilities added, weapon modals, attributes, weapon styles etc. It's a work in progress but it is functional. You could also give me the particular scenario you had in mind and I could provide you with an answer.

 

 

You mind linking to the thread?

[kmbogd]

Post #56 from this link: https://forums.obsidian.net/topic/96636-two-handed-style-seems-weak/page-3?do=findComment&comment=1996688