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Deep Analysis Needed: Building Crit vs. Damage

Hi, I am trying to “math”, but I am not great at it.

Can someone check the comparison below between a Crit and Non-Crit partial build and let me know which does more “DPS” (damage)?

A few things:

  1. I didn’t do a whole entire build. I did just enough to try to create an apples to apples comparison.
  2. I kept affixes in “parity” between the builds. i.e. if a piece of gear had 2 crit affixes, then it had 2 damage affixes. If it had one crit, then only 1 damage.
  3. Base Gear differnces: Build 1 uses as much Crit on base items. Build 2 swaps to anything meaningful for DPS (mostly attack speed).

Ok, here we go.

The two builds are Beastmasters using Swipe.

  • One is maximized for Crit, and damage is added secondarily.
  • Second is maximized for damage only, with no crit whatsoever.
  • The Passive trees are identical except changing the Crit nodes for Penetration nodes.
  • Swipe Tree exchanges crit nodes for damage nodes.

Build 1:

Summary:

  • Base phys damage: 101
  • Attack Speed: 15%
  • Crit chance: 61%
  • Crit multi: 447%
  • Physical Melee Damage: 450%
  • Physical Penetration: 0%
  • Swipe: +200% Crit Chance, +100% Crit Multi

Build 2:

Summary:

  • Base phys damage: 116
  • Attack Speed: 45%
  • Crit chance: 5%
  • Crit multi: 200%
  • Physical Melee Damage: 834%
  • Physical Penetration: 21%
  • Swipe: Damage increased: 60%, Cull @ 14%

Analysis:

Build 1:
Base: 101
Increased damage: 450% * 101 = 454.5
Crit damage: 79% crit chance for 547% crit multi = 547 * .79 = 432.13% bonus
Crit damage (including Swipe): 432.13% * 454.5 = 1963.89 per hit
Attack Speed: 15% (115%) * 2486.12 = 2258.47 “effective damage”

Build 2:
Base 116
Increased damage: 834% * 116 = 967.44
Swipe More Damage: 68% (168%) * 967.44 = 1625.30
Penetration: 21% (121%) * 1625.30 = 1966.61 per hit
5% crit chance for +100% = 200/5 = 5% (105%) x 1966.61 = 2064.94 per hit average
Cull: 1/0.86 = 1.16 * 2163.27 = 2395.33
Attack Speed: 45% (145%) * 1638.34 = 3473.23 “effective damage”

So, there ya go.
Is there a “cutoff” point where building crit vs. damage is better one way vs the other?

r/theydidthemath… :wink:

I’ll leave the math to someone else… a spitting furry quadruped perhaps…

one thing I noticed here is that, imho, the Attack speed is going to throw your apples to apples comparison a little out of whack… if you could somehow match attack speed, then it might be an easier calculation…

You’re assuming that said quadruped isn’t bone idol (and not a bone idol).

I’ll leave it to @Tunk (& probably @dammitt) who’s way better at maths than me 'cause I ain’t done a multifactorial/multivariate analysis in a good ~25 years.

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One of the beautiful things about a well-designed ARPG is that there are so many skill combinations that two builds can have completely divergent philosophies and still perform similarly, depending on how well gear supports it.

IN GENERAL, whether or not to go Crit or full damage depends on the following parameters:

  1. Does your main damage skill have a flat base Crit option that helps get to 100% easier? It’s much easier to get to 100% Crit chance from a base 15% (with a skill that has a +10% Crit chance in the nodes) than to get from the standard 5%. That’s a difference between having 567% increased Crit chance and 1,900% increased Crit chance.

  2. Do your other skills provide good sources of % increased Crit Chance so you’re not burdened with having to place those affixes on your gear (War Cry and Frenzy Totem provide good sources of increased Crit chance as buffs)?

  3. Do you have good sources of %Crit Multiplier? If you can get 100% Crit Chance, then Crit multipliers are effectively a multiplicative damage increase.

  4. If you can’t get 100% Crit, how many sources of “More” damage do you have on your main skill? In your Build 2, the 40% and 20% nodes are both multiplicative, so your Swipe damage is 68% increase over not taking those nodes, instead of 60% if the 2 nodes were additive.

  5. Do you plan on implementing DoT on your build? If you’re stacking DoTs that align with your damage type (Physical & Bleed damage both go off your %Physical damage), then you can stack damage that way as well, and %Attack Speed becomes much more important since the faster you apply DoTs, the more stacks of DoT you can apply.

Those points are enough that you get a good sense of how to build around a skill. I can tell you now, Swipe is best used with Crit Werebear Druid, as I’ve theorycrafted something like 700% Crit multiplier alongside 100% Crit chance, so that Crits are doing 7X more damage than non-Crits. You’re not going to easily find a way to get 7X more damage by getting more %Physical damage or getting more damage nodes.

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I was told there would be no math.

Briefly in my head and rounded several times I come to the first build on about 2025 DPS and the second in about 2279 DPS.
→ Shall one properly recalculate. :stuck_out_tongue:

Is this right?

(all math moved to OP of thread)

Where is your crit chance in variant 1?
I assumed 5% base crit chance on the first one.
(So 61% + (5*200%) = 71% Crit Chance)

As I said, let someone calculate that who likes that. What does the build planner (I haven’t tested it yet) say? :slightly_smiling_face:

EDIT:
And the culling is also differently strong depending on the monster life.

I am not sure how Swipes “+200% crit chance” affects that base of 61%.

Your Base Crit + another 200 % on that.

I assume you’re taking into account the conversion factor of ~1.49 to go from attack speed to actual hits per second?

But it’s a % of max hp the actual hp number is irrelevant (all things being equal), so cull acts as a 1 / (1 - cull%) more modifier.

I just assumed 0% attack speed means base damage, and X% bonus attack speed = bonus to that, and I represented that as “DPS” even if it isn’t how much damage per clock second. If that makes sense. Maybe DPS isn’t right, maybe “effective overall damage” would be better?

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If you have 10,000 DPS and the opponent has 10,001 life, culling is no longer fully active.
Otherwise, with much higher life bars, you are of course right.

EDIT:
Just thought I’d note that, seemed important enough to me, won’t argue about it any further. :slightly_smiling_face:

So, 9% x 200% = another 18%?
61+18=79% crit chance?

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Yes.

Oh, one more thing… sooner or later, we all seem to come to the conclusion that your variant 2 seems to be stronger.

ok, great, I updated it. I moved that to the OP, too.

Unfortunately, your Crit damage calculations are not right. A Critical hit is 100% more damage than a standard hit, or a 2X multiplier, so for Build 2, the average damage is 1.05, not 1.10

For build 1, you have 79% to hit for 4.47X multiplier, which will result in an average damage of 3.82, since 21% of the time, you’re dealing regular damage hits.

Culling is an interesting case, as it’s always percentage based, and the higher corruption you run, the more health an enemy has. A 14% cull for a boss with 500,000 HP is 70,000 damage, which is much more in one hit than your standard Swipe. You want to have enough damage to kill white enemy trash in 1 hit, but then using the cull mechanic to wipe out the bulky monsters as quickly as possible. Anything that takes more than 7 hits to kill, you’d want to have the cull option, and you can use the attack speed function to determine how many seconds it takes to perform those 6 hits before the killing blow.

I can’t comment on what penetration does, and whether it’s a straight multiplicative increase, or if it intertwines with Resistance Shred, which is also on certain items and skills.

I added in +100% Crit Multi from the Swipe tree, for 5.47x.

Fixed the other.

You can think of cull as the enemy having less HP and there fore a more DMG multiplier. The eq for more DMG this way is {1/(1-%hp cull)}-1.

Ex: 10% cull is 1/(1-.1)= 1/.9= 1.111. this it is an 11% more DMG.

50% cull is 1/.5=2 thus a 100% more DMG multiplier.

Pen and res shred are a more DMG multiplier. You can assume that an enemy has 0 res and use the sum of pen and res shred as a more DMG multiplier. As the enemy get resistance you will loose DMG but when you compare the effect of pen/res shred vs w/o it will become a better choice.

For example, if you have 25% pen you will do 25% more DMG (assuming no modifiers). Then you fight an enemy with 75% res. W/o pen you will deal 75% less DMG. So if your raw hit is 100 you would deal 25.

Taken together, 25% pen on 75% res means the enemy effectively only has 50% res and now you deal 50 DMG. Thus you deal 100% more DMG compared to without pen.

Tl;Dr. You can take the sum of pen/res shred as a more multiplier that will only get more valuable as the enemy gets more res