Warrior vs. Shadow mundus stone

Reeko

I have a few questions that i cannot seem to find on the internet. Atleast not outdated information.

First off, how much weapon damage does the warrior actually give you? Secondly what is the base multiplier for critical damage and how much does shadow actually increase it by? Lastly which is considered better? Particularly for a stamina based Nightblade? I have heard warrior is best until you reach about 50% critical chance, then shadow is better when you are higher than 50%

Any info/math would be appreciated!

Nestor

This should be up to date

http://elderscrollsonline.wiki.fextralife.com/Mundus+Stones

The way I look at it is this, increases to your Critical Strike Damage is not as important as increasing your base damage. Why? You have to Crit to get the extra damage, but your crits are based on your Base Damage. So, you get more damage all the time by choosing Warrior whether you crit or not and get close to the same boost in Crits when those do happen. If you have a character that is sitting at 70% or 80% Critical Chance already, then it might make sense to boost Crit Damage.

Now, it might be useful to get the Mundus that increases your Critical Strike Chance, that might be worth something depending your build.

Reeko

Thanks for the link! Very helpful

This guy did the math between warrior and shadow but its a bit outdated: http://tamrielfoundry.com/topic/nb-dual-wieldbow-pve-dps-build-1-6-6/

TheBull

Yeah it was thought that the shadow stone was broken. At 1.6% increase to crit dmg it's not even an option.

Reeko

TheBull wrote: »

Yeah it was thought that the shadow stone was broken. At 1.6% increase to crit dmg it's not even an option.

That depends on what the base crit dmg multiplier is. For example: if your base crit dmg is 1.5 and you add 1.6% wouldnt that make your crit 2.4? Im awful at math

Kobaal

"Warrior's, come out and Plaaaaayaaaaay"

Reeko

Ok so after much digging this was the most recent info i could find: http://forums.elderscrollsonline.com/en/discussion/162767/critical-damage-multiplier

Tankqull

why or?

Reeko

Tankqull wrote: »

why or?

Or why?

aco5712

why not just exploit and have both. YAY FOR ZOS!

Reeko

After the new update, which is better?

Asayre

I was just thinking about this a couple of hours ago. I mainly play a Sorcerer so was thinking about Apprentice compared to Shadow and Thief but the same concept applies.

The base damage formula is
Base damage = a*(Stam+b*W)(1-Mit)*Attacker_CP * Defender_CP
where a and b are coefficients with b~10.5, W is your weapon damage and Mit is the mitigation. We can roll the Attacker_CP and Defender_CP into the coefficient a without any worries for the analysis. The mitigation is also not important but I'll keep it here for the moment to show you that it can evetually be neglected

The base damage when using the Warrior stone is
Base damage_Warrior = a*(Stam+b(W0+W1))(1-Mit)
Here I have separated your weapon damage component into weapon damage from Warrior stone and associated buffs, W1, and weapon damage from everything else, W0

The average damage with the Warrior stone is
Damage_Warrior = (1-C)*Base damage_Warrior + C*M*Base damage_Warrior
where C and M are your critical chance and critical damage modifier, respectively. With some arithmetic, we obtained
Damage_Warrior = a*(Stam+b*W0)(1-Mit)(1-C+C*M) + a*b*W1*(1-Mit)*(1-C+C*M)

The base damage when using the Shadow stone is simply
Base Damage_Shadow = A*(Stam+b*W0)*(1-Mit)
From this, we can obtain the average damage
Damage_Shadow = (1-C)*Base damage_Shadow + C*(M+S)*Base damage_Shadow
where I have used S for the Shadow stone. Again some maths leads to
Damage_Shadow = a*(Stam+b*W0)(1-Mit)(1-C+C*M) + a*(Stam+b*W0)(1-Mit)*C*S

In order to figure out when the Warrior mundus is preferred over the Shadow mundus, I shall just subtract Damage_Shadow from Damage_Warrior

Damage_Warrior - Damage_Shadow = a*(1-Mit)* [ b*W1*(1-C+C*M) - (Stam+b*W0)*C*S]
a and (1-Mit) are always positive so you simply need to evaluate the second term. I don't have a stamina build so I'll put in some typical values for a Sorc to show you an example

The Apprentice like the Warrior stone confers 167 Spell damage. W1 includes all Spell damage buffs as well so as a Sorcerer I typically run a 26% buff due to Expert Mage and Surge. Thus W1 = 167*1.26=210. We'll stick with a b value of 10.5. My crit chance, C, is 0.42 and my critical damage modifier, M, is 1.51 (I have 1 point in Elfborn). My Magicka is about 40k and my Spell damage from other stuff is around 2k. So my calculation would be

10.5*210*(1-0.42+0.42*1.51) - (40000+10.5*2000)*0.42*0.12 = -397

in my example I should use the Shadow stone. You don't have to take into account divines since it can be factored out.

On a semi-related note have you considered using the Thief mundus stone?

Rather briefly the maths is as follows
Damage_Shadow = (1-C)*Base Damage + C*(M+S)*Base Damage
Damage_Thief = (1-C-T)*Base Damage + (C+T)*M*Base Damage

Damage_Thief - Damage_Shadow = Base Damage ( T*(M-1) - C*S )

Thief is better than Shadow when, T*(M-1) - C*S > 0
This is equivalent to fulfilling the equation below
(M-1) / C > 60/59

Back to my example,
(1.51-1) / 0.42 > 60/59 is true thus the Thief is better for me.

Note that there may be some problems with your critical damage modifier because it seems ZOS rounds it to 2 decimal places so sometimes it doesn't appear to change...

Hope this answers your question!

Summary:
If [ b*W1*(1-C+C*M) - (Stam+b*W0)*C*S] > 0, use Warrior
where b = 10.5, W1 is Weapon damage from Warrior stone including and buffs, C is crit chance, M is crit modifier, Stam is your Stamina, W0 is weapon damage from everything else and S is the Shadow mundus stone (0.12)
otherwise use Shadow

If (M-1) / C > 60/59 is true
where M is crit modifier and C is crit chance then use Thief otherwise use Shadow.

trimsic_ESO

@Asayre When looking at your formulas, I can see that the crit damage bonus is additive.
For instance, if the base damage bonus for a crit is 0.5 and if I invest some CP to have 10% more damage for a crit, then the damage bonus for a crit is 0.5 + 0.1 = 0.6, meaning that a critical hit will do 60% more damage than a normal hit. Do you confirm?

Is it the same formula for the impenetrable trait, but being subtractive instead of additive? For instance 0.5 - 0.1 = 0.4 if I have 10% resist to crit damage?

ADarklore

Ok... too many numbers floating around... so what is the new critical % that Thief offers? I believe on PTS it was 12% but they'd discussed reducing it before it went Live.

Asayre

ADarklore wrote: »

Ok... too many numbers floating around... so what is the new critical % that Thief offers? I believe on PTS it was 12% but they'd discussed reducing it before it went Live.

The thief increases critical chance by 11.8%

trimsic_ESO wrote: »

@Asayre When looking at your formulas, I can see that the crit damage bonus is additive.
For instance, if the base damage bonus for a crit is 0.5 and if I invest some CP to have 10% more damage for a crit, then the damage bonus for a crit is 0.5 + 0.1 = 0.6, meaning that a critical hit will do 60% more damage than a normal hit. Do you confirm?

Is it the same formula for the impenetrable trait, but being subtractive instead of additive? For instance 0.5 - 0.1 = 0.4 if I have 10% resist to crit damage?

As far as I am aware critical damage multiplier is additive but some are a flat increase while others a percentage of the critical damage modifier. The Piercing Spear (Templar passive) and the Shadow Mundus stones give a flat bonus of 5% and 12%, respectively. But Trap Beast (Fighter’s Guild) and Elfborn are a percentage of your critical damage multiplier. So investing CP to get Elfborn to 10% would result in a critical damage multiplier of 1.55 (1+0.5*1.1). Adding in Trap Beast and Shadow should bring your critical damage multiplier to 1.73 (1+0.5*1.1+0.5*0.06+0.12).
I say should because critical damage modifier is rounded to 2 decimal places and makes it a bit challenging to determine the most accurate formula. There should be some interaction with Elfborn and Trap Beast since with a decent number of points in Elfborn the bonus from Trap Beast is 0.07. But I can’t seem to work out where specifically the rounding occurs. Another consequence of the rounding that investment of points in Elfborn results in ‘jumps’. I created a graph earlier to illustrate this point.

You’re right @trimsic_ESO that Impenetrable is subtractive. A legendary armour ‘Increases resistance to Critical Hits by 250’. This is a reduction of approximately 3.5%. There is some error with that number because I only tested with two pieces of Impenetrable. For completeness, this stacks additively with Resilient. For instance if you had 48 points in Resilient (15%). The critical damage modifier is 1.35 (1.5-0.15). Wearing 2 pieces of legendary impenetrable will bring it down to 1.28 (1.5-0.15-0.07).

SanTii.92

So at wich point The shadow is a better option than the warrior?

Reeko

srlamasnrb18_ESO wrote: »

So at wich point The shadow is a better option than the warrior?

When your crit is higher than 50% i believe

Asayre

@srlamasnrb18_ESO

If [ b*W1*(1-C+C*M) - (Stam+b*W0)*C*S] < 0, use Shadow
where b = 10.5, W1 is Weapon damage from Warrior stone including any buffs, C is crit chance, M is crit modifier, Stam is your Stamina, W0 is weapon damage from everything else and S is the Shadow mundus stone (0.12)

If that didn't make sense do the following steps
1. Buff yourself with food and skills
2. Record your weapon damage. This is W0.
3. Get the Warrior Mundus
4. Record your weapon damage, call this W2. Subtract W0 from W2 to otain W1.
5. While buffed record your Critical Chance and Critical Damage Modifier. The simplest way to get your Critical Damage Modifier is to buff yourself appropraite and hit any mob till you get a crit and a non crit. Divide the crit damage by the non-crit to get your Critical Damage Modifier.
6. Put it all the numbers in the top equation
7. If it is negative use Shadow otherwise use Warrior.

Here are some made up numbers if that process didn't make sense.
Weapon damage while buffed , W0 = 1000
Weapon damage while buffed and with Warrior Mundus, W2 = 1200
Then W1 = W2-W1=200
Crit chance is 55% and Critical Damage Modifier is 1.55. Stamina is 30000
Calculate
10.5*200*(1-0.55+0.55*1.55) - (30000+10.5*1000)*0.55*0.12 = 62.25
It is positive so use Warrior

Uneed2Stop

Kobaal wrote: »

"Warrior's, come out and Plaaaaayaaaaay"

LOL DUDE YES