Return of Reckoning

Illuminati wrote: Sat Apr 19, 2025 10:39 pm We need the E&C math guy to work up if its worth it going negative crit. He seems to have a good handle on the meta and what the efficacy would be to go lower vs other renown selections.

• WL:
  For 44% crit and the default 45% crit damage we get:
  0.45/(1+0.43*0.45) = 0.377

• BW (4Sov - 4 Onslaught):
  For 76% crit and 157% crit damage we get:
  1.57/(1+0.75*1.57) = 0.721

• SW:
  For 64% crit and 70% crit damage we get:
  0.70/(1+0.63*0.70) = 0.486

• Undergeared enemy dps, SnB tanks and enemy healers should be mitigated better by TOU

• When under Absolute Preservation by a Shaman in your group, TOU build will always perform better (take a look at the non-crit damage in the above screenshots for example)

• Guarranteed crit abilities like WL's Force Opportunity or SW's Fell the Weak will be mitigated better by the TOU build (anticrit has no effect there)

• When protected by an absorb shield, the TOU build will always be better (Khaine's Bounty, Soul Shielding, or from ally abilities)

leftayparxoun wrote: Sun Apr 20, 2025 9:49 am

Illuminati wrote: Sat Apr 19, 2025 10:39 pm We need the E&C math guy to work up if its worth it going negative crit. He seems to have a good handle on the meta and what the efficacy would be to go lower vs other renown selections.

Way too complex to answer simply. If we focus on orvr we can, however, check the best case scenario for Toughness over anti-crit in the above build and see if it actually makes sense to go Toughness. If it's not worth it even in the best case scenario, then it's not worth it in general.

We can compare this option to the above original build:


This trades 72 Toughness, 22 Wounds and 16 Initiative from RR for 15% more anticrit.
In order to equalize Wounds, let's go ahead and swap out 1 TOU tali to Wounds.
So, overall, we have: +15 anticrit - 96 TOU - 16 INI with this proposed change.
This results in a -15.1% chance to be crit (when adjusting the original build stats accordingly)

Up next, we have to figure out what the most advantageous ability is for Toughness over anticrit.

Anticrit is largely affected by the enemy player and not the ability, so let's start there.
The average crit modifier of an enemy's attacks on you is
1 + CTBC*CD
where CTBC is your chance to be crit by them (your ctbc + their crit chance) and CD being their average Critical Damage (0.45 by default)

If we insert an x amount of anticrit into the equation, we want to figure out when/which class it will affect the least (= result in the least damage reduction)

Going from 1 + CTBC*CD to 1 + (CTBC - x)*CD , we can write the %damage reduction as:
1 - (1 + (CTBC - x)*CD)/(1 + CTBC*CD)
and we want to minimize this function
It's first derivative with respect to x will be
CD/(1 + CTBC*CD)

What this expression essentially shows us is how "fast" the damage gets reduced if we decrease our chance to be crit.
You will notice that it is a positive value which makes sense because with increasing anticrit our original function (%damage reduction) also gets increased.

To find the enemy class against which anticrit performs the WORST, we have to look at this expression and look where it's the lowest.

We have 3 main candidates for orvr here: WL, BW, skirmish SW
I'm going to examine them at BIS, since there is where you want to optimize your defences for.

• WL:
  For 44% crit and the default 45% crit damage we get:
  0.45/(1+0.43*0.45) = 0.377

• BW (4Sov - 4 Onslaught):
  For 76% crit and 157% crit damage we get:
  1.57/(1+0.75*1.57) = 0.721

• SW:
  For 64% crit and 70% crit damage we get:
  0.70/(1+0.63*0.70) = 0.486

As you can see, vs WL is where anticrit matters the least. So we'll go with that.

Now, let's find out which WL ability cares the MOST about TOU.
Doing that is not as simple as the previous method. We can aproximate it by finding the ratio of the non-Damage Bonus portion of the unbuffed damage of the ability to the Damage Bonus coefficient. The lower the ratio, the more the ability cares about STR/TOU.

It basically will be:
(Base Damage*Mastery_scaling + wDps_coeff.*wDps)/DB_coeff.

After running the numbers, Pounce and Cleave Limb are tied for the lowest ratio (132) so let's go with Pounce due to its usage.


We are finally ready to run the numbers!

Will use my damage calculator for a BIS AOE WL using Pounce against Major's initial build and the one with the proposed modifications (+15 anticrit - 96 TOU - 16 INI). Moreover, I will assume no TOU debuffs take place because that is the ideal situation for TOU %mitigation:
e.g. If increasing TOU from 200 to 300 would decrease the damage from 150 to 100 (1 - 100/150 = 33.3% reduction) then increasing TOU from 100 to 200 would decrease the damage from 200 to 150 (1 - 150/200 = 25% reduction). This illustrates how %dmg reduction per Toughness from Toughness is higher the more Toughness you have.
For that reason we are examining what happens under no TOU debuff on the DOK to check the actual best case scenario for TOU over anticrit.

Let's do it:


As you can see, in the BEST POSSIBLE scenario for Toughness, we see that indeed you take less damage from Pounce on Major's build; 330 instead of 342 (3.5% less damage).

What happens for the other, more common abilities however?

When checking Slashing Blade we see that the average damage is 355 on the anticrit build vs 357 on the TOU build (0.5% less)


and for Whirling Axe the average damage taken for the anticrit build is also lower, at 464 instead of 483 (3.9% less)


And while I earlier said that this is the best case scenario for TOU instead of anticrit, there are some caveats:

• Undergeared enemy dps, SnB tanks and enemy healers should be mitigated better by TOU

• When under Absolute Preservation by a Shaman in your group, TOU build will always perform better (take a look at the non-crit damage in the above screenshots for example)

• Guarranteed crit abilities like WL's Force Opportunity or SW's Fell the Weak will be mitigated better by the TOU build (anticrit has no effect there)

• When protected by an absorb shield, the TOU build will always be better (Khaine's Bounty, Soul Shielding, or from ally abilities)

Personally I'd still advocate for the anti-crit variant because of it performing better vs the things you need to worry about (see Whirling Axe above) and especially since TOU debuffs (KOTBS aura, dps Triumphant proc on you) are so prevalent. I didn't calculate how things look against SWs or BWs, but the initial crit modifier analysis shows that on their end things should look even worse for the TOU build.

Absorb shields are the one thing that could make TOU builds worth it, but ever since the healer patch dropped and the internal cooldown of Khaine's Bounty went up to 3 seconds, I don't think it's relevant enough to justify the TOU variant in orvr context (when focused, that absorb shield will only be a small fraction of the incoming damage).
For smallscale or scenarios I for sure can get behind that idea.