Assessing the Value of Concentration/Resolve for Melee Fighters

[Livegood118]

Hi all,
 
I was wondering if someone with some math skills could help me work out the value of concentration in combat, particularly as it pertains to investments in resolve vs other attributes. Everyone still around here is a grog so let's all assume we're playing on POTD
 
Concentration in Pillars can be gained from a number of different sources, the three main ones being the Resolve attribute (+3 per point), the Holy Meditation spell (+30, long duration) and Crowns for the Faithful (+75).
 
The Interrupt mechanic works as follows:
 
– Target must land at least a graze 
– Roll d100 + Attacker's Interrupt Rating (+0 on Hit / -25 on Graze / +25 on Crit) vs Concentration + 75
 
To start with, a few observations:
 
– Concentration seems to decrease in worth relative to increases in a character's absolute defence (Deflection, Fort, Reflex, Will). If you're not getting hit at all, there can't be a concentration check.
– Concentration seems to decrease in worth the less a character is hit/targetted overall. Meaning, if you've got a good front line that can draw aggro, it seems wiser to invest in more offensive stats for backline casters/ranged characters than investing in resolve for the few times the character does get hit.
– If a backline character with low concentration does get targeted, any investment in resolve for concentration/deflection may not  be worth it anyway because you'll probably be getting crit at least 50% of the time anyway unless you switch to a hatchet/good shield.
– Investments in resolve can increase overall durability, and hence damage in a fight, since under certain circumstances a character would survive attacks that they otherwise would not have survived had the character made an investment in resolve.
– Of course the corollary of the above is also true in certain circumstances, meaning that if you'd killed a dude faster as a result of investments in more offensive attributes, you wouldn't have had to have invested in resolve in the first place.
 

So, let's look at a dual fist Monk build:

 

18 Might

12 Con

16 Dex

10 Per

12 Int

10 Res

 

Monks are naturally going to get hit a lot when dual wielding. They've got decent base deflection, good endurance and great health but with dual wielding you're never going to get high enough deflection to not take a load of hits on POTD. Monks always want high Might because of the way that lashes work. Like almost any melee class in PoE, Veterans recovery is a decent talent to take and it scales with both Might and Intellect, so because of that you can trade some Con for these stats, gaining bonuses to Torment's Reach AoE at the same time (though the loss of Fortitude sucks a bit ...)

 

For this kind of build, what I'm wondering is if you took the points that you've invested in Dexterity and put them in to Resolve instead (+18% Action Speed vs +18 Concentration), could you hypothetically do more damage by virtue of the fact that you aren't getting interrupted?

 

Here's another example of a Barbarian Build for 2h/DW with 74 attribute points spent:

 

16 Might

10 Con

10 Dex

10 Per

18 Int

10 Res

 

Now, normally you'd probably want to spend your last four attribute points in Dexterity for an extra 12% action speed, but are there circumstances where investing those in to resolve could actually lead to more damage?

 

We know from MaxQuest's attack speed research (https://forums.obsidian.net/topic/72272-combat-mechanics-attack-speed-recovery/) that Dexterity gives diminishing returns with more points invested so 10 to 16/17 is kind of the sweet spot.

 

From anecdotal experience, I would say that Monks and Barbarians get interrupted at least 20 times a fight in the early game. Let's assume that these are "average" interrupts for 0.5 seconds. If you never got interrupted at all you could gain at least 10 seconds of time attacking. Of course, in realty, with 5/6 points investment in resolve that would have otherwise gone in to Dexterity, I guess you might only save 2-3 seconds. Hypothetically though, couldn't this pay off offensively more than investing in Dex?

 

I don't know is the answer, so I'm looking forward to hearing what people think.

 

edit: fixed equation

Edited March 8, 2017 by Livegood118

[MaxQuest]

That's a good question.

 

Looking at Dex vs Concentration, there is certainly a sweet spot on that axis somewhere, where 1 point in resolve becomes more important than 1 point in dex. And it's position depends on:

- how often are you hit

- are you ok with being hit

- do you have any means to rise your concentration directly (buffs, potions)

- do you have any cc means to make concentration a non issue

 

P.S. When trying to solo Alpine Dragon, I had to take Potion of Spirit Shield, and actually increased Res from 3 to 5 on behalf of Dex. I was even thinking of increasing it higher, until I've decided, screw it! I am using scrolls. Confused/Paralyzed enemies don't interrupt)

[Livegood118]

I actually forgot about the potion ^^

 

Let's take an example and say you've got a melee character that's going to get hit 35 times in a fight and you've got a character that has 16 dex/10 res vs 10 dex/16 res. Let's assume the "average" interrupt rating on the hits is 0.5 secs and that the enemy attacking has 15 Per:

 

d100 + interrupt vs 75 + Conc

x + 15 vs 75 

x = 60 = 40% chance of interrupt on hit for 10 res char

 

x + 15 vs 75 + 18

x + 15 vs 93

x = 78% = 22% chance of getting interrupted per hit for 16 res char

 

Assume 35 hits

35*0.4 = 14 Interrupts = 14*0.5 = 7

35*0.22 = 8 Interrupts = 8*0.5 = 4 

 

So, 6 points of dex in to resolve means you get an extra 3 seconds of time in the fight, and you also can't discount the extra +6 deflection that'd help you avoid a few hits as well.

 

My feeling is that it's probably not worth the trade ...?

Edited March 9, 2017 by Livegood118

[indika_tates]

I think this is exactly the barbarian dilemma. You have a character that can deal a lot of damage to multiple mobs at the same time, but you have skills that are contradictory in order to achieve it (frenzy). If you activate it you are converting hits into critical hits (-10 deflection) that are a guaranteed interrupt so in the end you can get the opposite of what you are looking for (attack speed) for being constantly interrupted. But what can you do to avoid it? You can raise RES instead of DEX but if you are not getting interrupted RES points are not worth it.

 

On the other hand there are potions/spells/items that can mitigate this problem like spirit shield, holy meditation and celebrant gloves so you have another ways to avoid interruptions better than spending points into an attribute that it's only worth it if you are interrupted or you have a specialized deflection character (Fighter). It's very hard to get an outcome of RES/DEX balance because every mob has different stats and there is a random factor on every encounter. You may get interrupted 50 times against ogre druids and 10 against xaurips. What is worth on one encounter is not worth it in another one.

 

As a general rule based on my own experience in this game I tend not to dump RES below 10 to make use of concentration buffs when you really need it. Specially as a barbarian. Having a front-line character with dumped RES and relying DPS on him/her is a sentence of death.

[JerekKruger]

We know from MaxQuest's attack speed research (https://forums.obsidian.net/topic/72272-combat-mechanics-attack-speed-recovery/) that Dexterity gives diminishing returns with more points invested

 

In absolute terms, every point of Dexterity gives exactly the same bonus i.e. for each point above 10 you act 3.003% faster* than you do with 10 Dexterity, and for each point below 10 you act 3.003% slower than you do with 10 Dexterity.

 

In relative terms the bonus decreases with each additional point of Dexterity. By this I mean that the increase in speed from going from Dexterity n to Dexterity n+1 decreases as n increases. That said, the difference isn't all that much: going from Dexterity 3 to Dexterity 4 results in a 3.80% increases in speed; going from Dexterity 10 to Dexterity 11 results in a 3.00% increase; and going from Dexterity 19 to Dexterity 20 results in a 2.36% increase.

 

However it's not clear to my mind that the relative increase is what matters. What we know is that for each point of Dexterity above 10 the number of actions you can perform in 1s increases by a flat 3.003%, and to my mind that flat increase is what actually matters. Yes the increase when going from Dexterity 19 to Dexterity 20 is only 2.36%, but that is 2.36% of an already faster speed.

 

*Here x% faster means that in the time it took to perform one action with Dexterity 10, you can now perform 1 + x/100 actions. Note that because Dexterity effectively acts as a overall multiplier, this is genuinely an x% increase in speed (unlike + Attack Speed bonuses which only apply to part of an action resolution).

[Livegood118]

Hmm ... my understanding was that the reason Dex has less relative effectiveness is because the 5 frame delay after each attack->recovery animation becomes a greater and greater portion of the overall action, such that it was never a true 3% reduction in the first place.

 

So, if we take a hypothetical example and say 10 actions are performed in a 10 second period and each second is 30 frames.

 

That's 300 frames overall, 50 of which are irreducable 5 frame delays and 250 of which are actions/recovery. Dex only reduces this 250 portion.

 

Let's then compare 19 Dex vs 20 Dex vs 21 Dex. 250/1.27 = 196.85, 250/1.3 = 192.3, 250/1.33 = 187.96

 

21 Dex = 62.04 Total Frames Saved

20 Dex = 57.7 Total Frames Saved

19 Dex = 53.15 Total Frames Saved

 

19 Dex -> 20 Dex = 4.55 extra frames saved

20 Dex -> 21 Dex = 4.34 extra frames saved

 

It's a pretty minuscule difference and probably more noticeable in the lower dex ranges.

 

However it's not clear to my mind that the relative increase is what matters. What we know is that for each point of Dexterity above 10 the number of actions you can perform in 1s increases by a flat 3.003%, and to my mind that flat increase is what actually matters. Yes the increase when going from Dexterity 19 to Dexterity 20 is only 2.36%, but that is 2.36% of an already faster speed.

 

My understanding was that, based on the above, you look at the total number of frames reduces per each point invested in dex.

 

I haven't sat in a maths class in nearly eleven years though so I'm not sure ^^

 

 

I think this is exactly the barbarian dilemma. You have a character that can deal a lot of damage to multiple mobs at the same time, but you have skills that are contradictory in order to achieve it (frenzy). If you activate it you are converting hits into critical hits (-10 deflection) that are a guaranteed interrupt so in the end you can get the opposite of what you are looking for (attack speed) for being constantly interrupted. But what can you do to avoid it? You can raise RES instead of DEX but if you are not getting interrupted RES points are not worth it.

 

On the other hand there are potions/spells/items that can mitigate this problem like spirit shield, holy meditation and celebrant gloves so you have another ways to avoid interruptions better than spending points into an attribute that it's only worth it if you are interrupted or you have a specialized deflection character (Fighter). It's very hard to get an outcome of RES/DEX balance because every mob has different stats and there is a random factor on every encounter. You may get interrupted 50 times against ogre druids and 10 against xaurips. What is worth on one encounter is not worth it in another one.

 

As a general rule based on my own experience in this game I tend not to dump RES below 10 to make use of concentration buffs when you really need it. Specially as a barbarian. Having a front-line character with dumped RES and relying DPS on him/her is a sentence of death.

 

 

Yeah - looking at the numbers, if Res gave +5 concentration it seems like there'd be a very arguable case for it, but with so much readily available crowd control spells and cheap means of increasing concentration I think Dex is probably better off overall. Of course dumping res if you've got a melee char is a big no-no.

[JerekKruger]

Hmm ... my understanding was that the reason Dex has less relative effectiveness is because the 5 frame delay after each attack->recovery animation becomes a greater and greater portion of the overall action, such that it was never a true 3% reduction in the first place.

 

Oh, that's a good point. I had forgotten about the 5 frame delay. As you calculate though, it's a fairly minor difference.

 

My understanding was that, based on the above, you look at the total number of frames reduces per each point invested in dex.

 

The problem with looking at the reduction in frames per point of Dexterity is frames are (essentially) a measure of time, not speed/rate. Because speed and time are inversely related, the increase in action speed (number of actions per second) is not linear in the reduction of frames per action. Therefore comparing reductions in frames can be misleading.

 

Taking your example we get the following (I've accounted for the 5 fram delay this time):

 

Dex 21 = 5 + 25/1.33 = 23.80 frames per action = 1.261 actions per second

Dex 20 = 5 + 25/1.30 = 24.23 frames per action = 1.238 actions per second

Dex 19 = 5 + 25/1.27 = 24.69 frames per action = 1.215 actions per second

 

In this particular case the increase in actions per second going from Dexterity 19 to 20 is the same (to four significant figures) as going from 20 to 21 i.e. 0.023, 

 

Let's look at the change going from Dexterity 10 to 11:

 

Dex 11 = 5 + 25/1.03 = 29.27 frames per action = 1.025 actions per second

Dex 10 = 5 + 25/1.00 = 30.00 frames per action = 1.000 actions per second

 

Here the difference (to four significant figures) is 0.025, so you can see more clearly that you do gain more the earlier points of Dexterity than you do from later ones, though the difference is pretty tiny. Just for completeness, let's look at going from Dexterity 1 to 12:

 

Dex 1 = 5 + 25/0.73 = 39.25 frames per action = 0.764 actions per second

Dex 2 = 5 + 25/0.76 = 37.89 frames per action = 0.792 actions per second

 

So the absolute most you'll gain from a single point of Dexterity is 0.028, only 0.005 (0.5%) more than you gain when going from 20 to 21.

 

EDIT: to answer your original question, I'd say from a purely intuitive point of view that it's not worth exchanging Dexterity for Resolve when building melee characters. I think the problem is too complicated to really answer purely mathematically, since there are so many different situations you might be in i.e. enemy accuracy, enemy attack speed, number of enemies attacking your character, interruption value of enemies and, perhaps most importantly, difficulty of fight (if a fight's relatively easy, who cares about being optimal).

Edited March 9, 2017 by JerekKruger

[Boeroer]

Your last part is important. It's a difference if you fight a single troll or a bunch of wichts. Against the troll you need no RES at all. He hits hard but is very slow so it doesn't matter much if he interrupots you once or twice. Wichts on the other hand hit like wet noodles but very fast. With dumped RES you will be screwed. 

Edited March 10, 2017 by Boeroer

[Livegood118]

Hmm - trying to draw some conclusions from this thread:

 

– Maybe it's fair to say that high resolve vs Dex for the purposes of increasing concentration is more useful in the early game where:

(a) you lack the means to hard CC enemies, such that concentration no longer becomes an issue; and

(b) you lack the means to increase your absolute defences such that concentration isn't an issue; and

© you lack easily accessible ways of increasing your concentration through abilities/items; and

(d) enemies will probably have slightly lower PER

 

I mean, there's a reason that the earliest parts of the game on POTD are usually the hardest, and its because you're getting ganked by large crowds of enemies without the means to control them/up your own defences.

 

– It probably doesn't make sense to ever dump resolve on characters that will be engaged in melee a lot (e.g. <10) unless you've got a particular means of dealing with it/like buffing it every single fight.

 

– Under the right circumstances, it seems concentration can be a very useful stat indeed for the amount of time it saves, particular on chars that are always going to get hit a lot in melee.