Tenacity test result = BROKEN

bvira · February 2017

I tested tenacity extensively for the first time and so many things are broken:

1. Dmg Resistance (DR) is reduced by Tenacity DR (TenDR)

Total DR = TenDR+(1-TenDR)*DR

This means your tenacity is reducing the effectiveness of DR buffs such as Astral Shield etc.

2. Crit Resistance (CR) effectiveness is reduced by Total DR

Effective CR = (1-Total DR)*CR

~~This means having a higher DR actually causes you to take more dmg from crit (logic LOL!)~~
Not true, I forgot that Effective CR and Total DR are additive. Nonetheless, effectiveness of CR shouldn't be reduced by having a higher DR!

3. Arp effectiveness is reduced by both Arp Resistance (AR) & TenDR (for non-crit attacks)

Effective Arp = Your Arp*(1-Opponent's AR)*(1-Opponent's TenDR)

4. Negative DR causes you to take more dmg

If enemy's Effective Arp > your Total DR then you'll take additional dmg (i.e. >100% of their tooltip dmg)

5. Crit with non-zero Arp - No idea how it works

I've looked at the simplest scenario where TenDR = CR = AR = 20%; DR = 0% and get attacked 2 times with different Arp

Pre-mitigated Dmg	Mitigated Dmg;	Attacker's Arp	Observed DR
5830.2	4080.5	11.7%	30.01%
5830.2	4915.8	45.9%	15.68%

If you assume that the formula takes the form analogous to that for non-crit attacks
i.e. Observed DR = (DR with some modifiers)-Attacker's Arp*(Arp resist with some modifiers), then:
DR with some modifiers = 34.9%
Arp resist with some modifiers = 41.87%

But I have no idea how to get those numbers, maybe someone can help by looking at the results below:
[LINK] Spreadsheet for test results.

Summary:
Damage for non-crit: Dmg*(1-[DR*(1-TenDR)+TenDR-Arp*(1-TenDR)*(1-AR)])
Damage for crit with zero Arp: Dmg*(1-[DR*(1-TenDR)+TenDR+CR*(1-Total DR)])
Damage for crit with non-zero Arp: ???

Correct me if I've made any mistake(s).

thefabricant · February 2017

Mind posting some examples with the thread? I don't pvp, but just curious. What I mean is some act logs where you provide dr, tenacity dr, base damage etc and show that the actual results match the expected results.

Unknown · February 2017

This content has been removed.

ltgamesttv · February 2017

bvira said:
I tested tenacity extensively for the first time and so many things are broken:

1. Dmg Resistance (DR) is reduced by Tenacity DR (TenDR)

Total DR = TenDR+(1-TenDR)*DR

This means your tenacity is reducing the effectiveness of DR buffs such as Astral Shield etc.

2. Crit Resistance (CR) effectiveness is reduced by Total DR

Effective CR = (1-Total DR)*CR

This means having a higher DR actually causes you to take more dmg from crit (logic LOL!)

3. Arp effectiveness is reduced by both Arp Resistance (AR) & TenDR

Effective Arp = Your Arp*(1-Opponent's AR)*(1-Opponent's TenDR)

4. Negative DR causes you to take more dmg

If enemy's Effective Arp > your Total DR then you'll take additional dmg (i.e. >100% of their tooltip dmg)

Correct me if I've made any mistake(s).

Please tell me if I'm wrong, this type of math is NOT my forte, but allow me to attempt an example, and you can tell me where I've made my mistakes.

Lets use an example here of a player with 45% tenacity DR, 70% tenacity armpen, 45% tenacity crit resist, and 20% regular DR vs a Player with 130% resistance ignored.

So firstly let's find the players "Total DR": 45%+(1-45%)*20%= 56% Total DR (Significantly less than 20% +45%)

Next let's find their Effective CR: (1-56%)*45%= 19.8% effective crit resist (The tankier they are, the less crit resist does for them, so those high DR targets are going to be hit harder by Vorpal than lower DR targets?).

Now le'ts see about the other players arm pen effectiveness: 130%*(1-70%)*(1-45%)= 21.45% effective arm pen

In this example I assume you'd subtract the 21.45% EAP from the 56% TDR to get 34.55% remaining DR after arm pen? I must be doing something wrong because with the armpen curve it'd be really difficult to even get above 20% DR. Also, does negation factor in to the original equation when it's active to find the player TDR?

bvira · February 2017

tolkienbuff said:

So, please correct me if I misunderstand but let's say my GWF has 130% resist ignore and a typical PVPer has 70% AR and 45% tenacity DR it would look like:

130%x(1-70%)x(1-45%)= 21.45% effective arp? Meaning if the player I attack has say 20% DR then I will do 101.45% of tooltip damage to them?

Yes you're right!

bvira · February 2017

thefabricant said:
Mind posting some examples with the thread? I don't pvp, but just curious. What I mean is some act logs where you provide dr, tenacity dr, base damage etc and show that the actual results match the expected results.

I have the data on a table that's kinda a mess, I'll sort things out and post it later.

ltgamesttv · February 2017

bvira said:

tolkienbuff said:

So, please correct me if I misunderstand but let's say my GWF has 130% resist ignore and a typical PVPer has 70% AR and 45% tenacity DR it would look like:

130%x(1-70%)x(1-45%)= 21.45% effective arp? Meaning if the player I attack has say 20% DR then I will do 101.45% of tooltip damage to them?
Yes you're right!

I went back and did some additional maths to see how that might pan out if I included your other statements. Do I understand them as well? or have I made a mistake. It seems like total DR is going to be a pretty high cap considering the amount of armor pen you'd need to overcome 56% total DR.

I feel I may be missing something? However it would explain why pugs end up with a negative DR and are getting one shotted without tenacity in PVP?

chemodan007 · February 2017

I'm not 100% sure, but the last time the formula was:
FinalDamage = InitialDamage*(1-DR+(1-Tenacity_RI_resist)*RI_attacker)*(1-Tenacity_DR) for non crit
and
FinalDamage = InitialDamage*(1-DR+(1-Tenacity_RI_resist)*RI_attacker)*(1-Tenacity_DR)*(1-Tenacity_Crit_resist) for crit.

It was checked for a long time ago. If someone has more recent information, please share.

demonmonger · February 2017

Sweet baby jesus!

bvira · February 2017

chemodan007 said:
I'm not 100% sure, but the last time the formula was:
FinalDamage = InitialDamage*(1-DR+(1-Tenacity_RI_resist)*RI_attacker)*(1-Tenacity_DR) for non crit
and
FinalDamage = InitialDamage*(1-DR+(1-Tenacity_RI_resist)*RI_attacker)*(1-Tenacity_DR)*(1-Tenacity_Crit_resist) for crit.

It was checked for a long time ago. If someone has more recent information, please share.

Dmg for non-crit is bascially the same as what I've posted.

However, for Crit with non-zero Arp the formula doesn't work. Have a look at the data here, I can't really make sense of even the simplest scenario where TenDR = CR = AR = 20%; DR = 0%.

Look at the bottom of the spreadsheet for the conflicting data.

bvira · February 2017

tolkienbuff said:

I went back and did some additional maths to see how that might pan out if I included your other statements. Do I understand them as well? or have I made a mistake. It seems like total DR is going to be a pretty high cap considering the amount of armor pen you'd need to overcome 56% total DR.

I feel I may be missing something? However it would explain why pugs end up with a negative DR and are getting one shotted without tenacity in PVP?

Sorry I have no idea what is the formula for Crit with non-zero Arp because it gives very weird result.

Have a look at the result from the spreadsheet and maybe you can figure it out.

jonkoca · February 2017

Too dumb to understand all the maths at this time of the morning... in conclusion, should I be trying to crit in pvp, or not..? Given a crit severity of about 150..?

ltgamesttv · February 2017

Short answer: If they have high DR and you have low RI crit is better. If you have high RI and they have a low DR crit is worse than power.

It's all situational and stat dependent. One obvious exception: Crit is best for piercing damage all the time.

jonkoca · February 2017

Cheers, I'll keep my vorpal and high crit then. Phew, that would have been a seriously expensive reshuffle.

mamalion1234 · February 2017

tolkienbuff said:
Short answer: If they have high DR and you have low RI crit is better. If you have high RI and they have a low DR crit is worse than power.

It's all situational and stat dependent. One obvious exception: Crit is best for piercing damage all the time.

AND if you have based on weapon damage dots which stat? ( jagged blades for example)

ltgamesttv · February 2017

mamalion1234 said:

tolkienbuff said:
Short answer: If they have high DR and you have low RI crit is better. If you have high RI and they have a low DR crit is worse than power.

It's all situational and stat dependent. One obvious exception: Crit is best for piercing damage all the time.
AND if you have based on weapon damage dots which stat? ( jagged blades for example)

Jagged blades is procced off of crits. So, if you want it to proc frequently you'll need to invest in some crit.

mamalion1234 · February 2017

tolkienbuff said:

mamalion1234 said:

tolkienbuff said:
Short answer: If they have high DR and you have low RI crit is better. If you have high RI and they have a low DR crit is worse than power.

It's all situational and stat dependent. One obvious exception: Crit is best for piercing damage all the time.
AND if you have based on weapon damage dots which stat? ( jagged blades for example)
Jagged blades is procced off of crits. So, if you want it to proc frequently you'll need to invest in some crit.

OK which second stat could benefit jagged blade?

plavia · February 2017

i used this forumle:

FinalDamage = InitialDamage*(1-DR+(1-Tenacity_RI_resist)*RI_attacker)*(1-Tenacity_DR)

i made a case study on me and it explain the other boons in the guild.
DC with mix PVP set with 3.2k tenacity.

if i take def guild boon i take damage
ID*(1-0.48+(1-0.7)Arp(1-0.4)=ID*(0.52+0.3*Arp)0.6

==>for 100K hit with 100% Arp its = 49K

if i chose 11% incoming healing my def reduce by 6.4k (guild level 17)
i get
ID*(1-0.32+0.3*Arp)0.6 = 59K

for me both boons worth it

if i buff myself it get starnge
with divine + 1 empower exaltation i can increase by 37% DR
ID*(1-0.85+0.3Arp)0.6= 27K

with dipslace fate boon + 60% DR
ID*(1-1.45+0.3Arp)0.6= -9K

in this case it will be 0?

bvira · February 2017

plavia said:

if i buff myself it get starnge
with divine + 1 empower exaltation i can increase by 37% DR
ID*(1-0.85+0.3Arp)0.6= 27K

with dipslace fate boon + 60% DR
ID*(1-1.45+0.3Arp)0.6= -9K

in this case it will be 0?

DR has a hard cap of 80% so you can have DR that is off the charts and still receive 20% dmg.

plavia · February 2017

if DR is cap on 80% than and tenacity is cap due to armor availability

best i can protect myself (max teancity i can have)
ID*(1-0.8+(1-0.75)Arp(1-0.45)=ID*(0.2+0.25*Arp)0.55 = ID*(0.11+ 0.14Arp)

i will always take 11% of the damage, even if the opponent have 0 Armor Peneteration

each %ArP increase damage by 0.14% (this number not depend on DR, its only dpened on tenacity)

for 100% Arp i take 24% damage (no matter what buff or def I have)

i also have deflect and absorb mechanics. but still its alot of damage
ppl do thousands damage in PVE, i should be one hit kill from allmost every class

bvira · February 2017

plavia said:
if DR is cap on 80% than and tenacity is cap due to armor availability

best i can protect myself (max teancity i can have)
ID*(1-0.8+(1-0.75)Arp(1-0.45)=ID*(0.2+0.25*Arp)0.55 = ID*(0.11+ 0.14Arp)

i will always take 11% of the damage, even if the opponent have 0 Armor Peneteration

each %ArP increase damage by 0.14% (this number not depend on DR, its only dpened on tenacity)

for 100% Arp i take 24% damage (no matter what buff or def I have)

i also have deflect and absorb mechanics. but still its alot of damage
ppl do thousands damage in PVE, i should be one hit kill from allmost every class

You actually have to use your actual DR to calculate even if DR > 80%, so if you have 120% DR and attacker's RI is 0 then your expected DR would be 122% but since hard cap is 80%, it becomes 80%.

If RI is 100% instead, then your expected DR = 91.75% and again since hard cap is 80%, it becomes 80%.

So yes having DR > 80% is good against Arp.

And ppl are doing insane dmg in PvE mainly because they have pets + bonding + PvE gears.

plavia · February 2017

OK
assuming i have max teancity

if my DR - 25%Arp > 80%
Final damage =ID*(0.2)0.55 = 11% ID (lowest possible damage)

else
Final damage =55% -55%DR + 14%Arp

with 100% Arp you break even with 27%DR and do serious damage (55% of your damage)
with 150% can allmost break 40% DR

ltgamesttv · February 2017

bvira said:

plavia said:
if DR is cap on 80% than and tenacity is cap due to armor availability

best i can protect myself (max teancity i can have)
ID*(1-0.8+(1-0.75)Arp(1-0.45)=ID*(0.2+0.25*Arp)0.55 = ID*(0.11+ 0.14Arp)

i will always take 11% of the damage, even if the opponent have 0 Armor Peneteration

each %ArP increase damage by 0.14% (this number not depend on DR, its only dpened on tenacity)

for 100% Arp i take 24% damage (no matter what buff or def I have)

i also have deflect and absorb mechanics. but still its alot of damage
ppl do thousands damage in PVE, i should be one hit kill from allmost every class

You actually have to use your actual DR to calculate even if DR > 80%, so if you have 120% DR and attacker's RI is 0 then your expected DR would be 122% but since hard cap is 80%, it becomes 80%.

If RI is 100% instead, then your expected DR = 91.75% and again since hard cap is 80%, it becomes 80%.

So yes having DR > 80% is good against Arp.

And ppl are doing insane dmg in PvE mainly because they have pets + bonding + PvE gears.

As far as the DR you will also have to factor in things like negation. A GWF may only have 28% DR but then in most any fight they'll have full stacks of negation as well. According to what you said, if I understood correctly, having Armpen > than enemy effective DR turns into bonus damage (i.e. they get a negative DR). In which case, armor pen is likely most effective against low DR targets wearing elven battle for example. Your effective RI will be > than their effective DR and you will get bonus damage against them if they don't deflect it.

The weird thing for me to try and wrap my head around is that it seems Power + Crit and low RI may be better against high DR targets that you can't overcome with RI? For example, should you aim for a build that gives you enough arm pen that it does more damage to low DR targets and not enough that it affects high DR targets then build in crit for thos high DR targets?

What I mean is Crit seems double nerfed by tenacity. It gets nerfed by Crit resist, then by Arm pen resist, then by effective DR? If that's the case, sacrificing RI for Power may be better? (Meaning crit is mostly saved by the 20% minimum effectiveness).

bvira · February 2017

tolkienbuff said:

As far as the DR you will also have to factor in things like negation. A GWF may only have 28% DR but then in most any fight they'll have full stacks of negation as well. According to what you said, if I understood correctly, having Armpen > than enemy effective DR turns into bonus damage (i.e. they get a negative DR). In which case, armor pen is likely most effective against low DR targets wearing elven battle for example. Your effective RI will be > than their effective DR and you will get bonus damage against them if they don't deflect it.

The weird thing for me to try and wrap my head around is that it seems Power + Crit and low RI may be better against high DR targets that you can't overcome with RI? For example, should you aim for a build that gives you enough arm pen that it does more damage to low DR targets and not enough that it affects high DR targets then build in crit for thos high DR targets?

What I mean is Crit seems double nerfed by tenacity. It gets nerfed by Crit resist, then by Arm pen resist, then by effective DR? If that's the case, sacrificing RI for Power may be better? (Meaning crit is mostly saved by the 20% minimum effectiveness).

I would say Crit is absolute trash because of how it interacts with Arp Resist.

Power vs Arp is a bit tricky and which one is better is situational. Generally Power is more reliable and consistent.

Arp won't increase your dmg if you can't mitigate enemy's DR down below 80%, and sometimes gives weaker dmg bonus than power even if enemy's DR is low. But Arp is often better than Power even if you can't fully mitigate enemy's DR (e.g. if you mitigate it down from 80% -> 60%, your dmg is doubled).

Suppose your base power is 40% with 0% RI and you wanna see if +8000 Power or +8000 Arp is better. I'll ignore crit since it complicates things.

Example 1) +8000 Power; Against High DR/AR
Power dmg bonus = 40% + 20% = 60%
Your RI = 0%
Enemy's total DR = 100%
Enemy's Arp Resist = 70%
Dmg effectiveness: 1.6*0.2 = 0.32

Example 2) +8000 Power; Against Low DR/AR
Power dmg bonus = 40% + 20% = 60%
Your RI = 0%
Enemy's total DR = 40%
Enemy's Arp Resist = 20%
Dmg effectiveness: 1.6*0.6 = 0.96

Example 3) +8000 Arp; Against High DR/AR
Power dmg bonus = 40%
Your RI = 0% + 80% = 80%
Enemy's total DR = 100%
Enemy's Arp Resist = 70%
Dmg effectiveness: 1.4*0.2 = 0.28

Example 4) +8000 Arp; Against Low DR/AR
Power dmg bonus = 40%
Your RI = 0% + 80% = 80%
Enemy's total DR = 40%
Enemy's Arp Resist = 20%
Dmg effectiveness: 1.4*0.984 = 1.38

In general Power is more effective against high DR/AR; Arp better against low DR/AR.
There are just so many factors to consider (base power, base RI, enemy's DR/AR) which make direct comparison very difficult. If you consider crit as well it'd be even harder to compare because having high crit makes Arp less desirable.

forumnamesuxs · March 2017

@solbergx
In reference to you PvP crit post, read through this one.

Tenacity test result = BROKEN

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