Block Cost Reduction - Hard Cap and Additive or Multiplicative?

DerAlleinTiger · September 2016

Two things here. I'm looking to create some new gear for my tank and potentially tweak some of his traits and stats; but before I go all in on the materials for it I want to know how to work out his block cost reduction.

First off, are the various sources of block cost reduction multiplicative or additive?

For example, say I have a full set of legendary CP 160 heavy armor with shield. All 7 pieces of armor plus the shield have sturdy on them. From what I recall, Sturdy pieces are additive of each other. So that would be 32% block cost reduction from that alone. Then the rank 2 Fortress passive for 1H+shield for another 36%. 100 CP into Shadow Ward for another 25%. Then max rank Defensive Stance for another 8%.

Now, is that additive so that it would equal out to a theoretical (I imagine there's a cap so in reality it wouldn't kick in the full reduction) 101% block cost reduction? Or are some of those multiplicative? And if they're multiplicative, what's the equation for it if it's known?

Second, I'm quite certain ZOS would put a hard cap on block cost reduction because there may be ways of hitting a theoretical 100% reduction cost. So what is this hard cap?

I don't care about what meta there is. I don't care about what physical and spell mitigation numbers I should have first. Those are all things I'm working out. But to do that I want to have context and know the parameters of all the aspects. And the two I need to know are these.

Is it additive or multiplicative and what is the hard cap?

Thank you for any responses.

Asmael · September 2016

BlockCost = (2160 * Sturdy * CP - Items) * Skills

Sturdy bonuses are additive, so you get 32% from your Sturdy total, BUT this value is multiplicative with other cost reduction mechanics.

EDIT: Corrected, abilities are calculated on their own (go figure, #ZosStuff).

hrothbern · September 2016

DerAlleinTiger wrote: »

Two things here. I'm looking to create some new gear for my tank and potentially tweak some of his traits and stats; but before I go all in on the materials for it I want to know how to work out his block cost reduction.

First off, are the various sources of block cost reduction multiplicative or additive?

For example, say I have a full set of legendary CP 160 heavy armor with shield. All 7 pieces of armor plus the shield have sturdy on them. From what I recall, Sturdy pieces are additive of each other. So that would be 32% block cost reduction from that alone. Then the rank 2 Fortress passive for 1H+shield for another 36%. 100 CP into Shadow Ward for another 25%. Then max rank Defensive Stance for another 8%.

Now, is that additive so that it would equal out to a theoretical (I imagine there's a cap so in reality it wouldn't kick in the full reduction) 101% block cost reduction? Or are some of those multiplicative? And if they're multiplicative, what's the equation for it if it's known?

Second, I'm quite certain ZOS would put a hard cap on block cost reduction because there may be ways of hitting a theoretical 100% reduction cost. So what is this hard cap?

I don't care about what meta there is. I don't care about what physical and spell mitigation numbers I should have first. Those are all things I'm working out. But to do that I want to have context and know the parameters of all the aspects. And the two I need to know are these.

Is it additive or multiplicative and what is the hard cap?

Thank you for any responses.

@DerAlleinTiger ,
No cap, only dimishing returns:

As you said: Sturdy is additive with each other for a total possible of 32%.
Fortress passive (36%) and Defensive Stance slotted (8%) are also additive with each other for a total possible of 44%.
100 CP's in Shadow Ward delivers 25%

These 3 factors are multiplicative with each other:
Total effect of all 3:
remaining block cost: (1-32%)*(1-44%)*(1-25%) = 68%*56%*75% = 28.6%
So your totalcost reduction was 71.4%

If you use Jewelry enchants as well for saving an amount of 203 per piece, the formular for the remaining block cost is:

(2,160*(1-25%)*(1-32%) - 3*203)*(1-44%) = (2,160*75%*68% - 609)*56% = (1,102-609)*56% = 276
(2,160*(1-25%) - 3*203)*(1-44%)*(1-32%) = (1,620 - 609)*56%*68% = 385

=> no hardcap on our cost reduction.

There is however a hardcap to our benefit for the amount of hits on our block that will cost us Stamina.
Blocking is handled in 0.5 second time windows and has a hard cap of max 1 hit for cost.
With more than 1 hit in that 0.5 seconds, it will always count for the stamina cost as 1 hit.
(Damage will be from all hits after mitigations)

EDIT:
@DerAlleinTiger ,
I got the Jewelry enchant cost reduction at the wrong place in the formular and corrected that.

DerAlleinTiger · September 2016

Thank you. I was uncertain if it was additive or multiplicative. I figured there was likely a hard cap, but I suppose that if all of the sources are multiplicative (all sturdy pieces counting as one source added together) then a hard cap wouldn't really be necessary unless they wanted a specific cut off point besides just stopping it from being infinite block.

Alright, this helps me immensely. Thank you!

The one person I was trying to get help from previously merely kept saying "Just worry about resistance numbers getting up to 32K, then worry about block cost reduction." Apparently didn't quite get it that I was trying to tweak my numbers to get them up to 32K while knowing the full parameters of what I can move around and what stats I might lose to maximize everything. Because, you know, it's nice to plan out the gear choice before I commit half a dozen stacks of mats and legendary tempers. Could have just said "There's no hard cap." if they know there isn't one. I don't get some people.

hrothbern · September 2016

Cheers

Using Evasion (or NB Blur) is very effective for tanking/blocking:
You have 20% less hits on your block for 20% Stamina cost reduction and less damage as well.

On that balance between Armor Resist and Resources
For PVE
Putting Sturdy on your Armor is more beneficial than Re-Inforced
Especially when that enables you to use Jewelry enchants with Resource Recovery or Resource cost reduction.
If you have several pieces of Jewelry with both Block cost reduction and Resource Recovery or Cost reduction, you can optimise your build easily for the fight to do.
Swapping out Armor is a much more expensive method.
Also,
If you have enough CP's to mitigate damage, the need to get close to 32K starts to diminish.

paulsimonps · September 2016

Asmael wrote: »
BlockCost = (2160 * Sturdy * CP - Items) * Skills
Sturdy bonuses are additive, so you get 32% from your Sturdy total, BUT this value is multiplicative with other cost reduction mechanics.

EDIT: Corrected, abilities are calculated on their own (go figure, #ZosStuff).

I've recently been doing some serious reverse engineering on the PTS and one of the many things I tested was Block Cost. I did all my testing using no other data than what I found myself, I did this by testing as many possible combinations of things that I could to get as much raw data to go through as possible and the formula you linked is mostly correct but there is one thing that is off and when I myself learned what it was my reaction was "This is stupid" but at any rate here is what I found:

BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-Fortress)/100)-(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*(Defensive Posture/100)

The big thing to note is Defensive Posture. What it does is basically subtract 8% of what is left after all the other cost reductions have been applied with the exception of Fortress and it subtracts that with what you get after the other reductions including Fortress. The way this worked took a long time to figure out, I had my raw data that said what my block cost actually was with all my reduction but I just couldn't figure out how Defensive Posture fit into the formula at first. And when I tried this way it fit like a glove. I of course then double check the formula to make sure it fit with all my Data and it did. It looks messy but it works.

hrothbern · September 2016

paulsimonps wrote: »
Asmael wrote: »
BlockCost = (2160 * Sturdy * CP - Items) * Skills
Sturdy bonuses are additive, so you get 32% from your Sturdy total, BUT this value is multiplicative with other cost reduction mechanics.

EDIT: Corrected, abilities are calculated on their own (go figure, #ZosStuff).
I've recently been doing some serious reverse engineering on the PTS and one of the many things I tested was Block Cost. I did all my testing using no other data than what I found myself, I did this by testing as many possible combinations of things that I could to get as much raw data to go through as possible and the formula you linked is mostly correct but there is one thing that is off and when I myself learned what it was my reaction was "This is stupid" but at any rate here is what I found:

BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-Fortress)/100)-(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*(Defensive Posture/100)

The big thing to note is Defensive Posture. What it does is basically subtract 8% of what is left after all the other cost reductions have been applied with the exception of Fortress and it subtracts that with what you get after the other reductions including Fortress. The way this worked took a long time to figure out, I had my raw data that said what my block cost actually was with all my reduction but I just couldn't figure out how Defensive Posture fit into the formula at first. And when I tried this way it fit like a glove. I of course then double check the formula to make sure it fit with all my Data and it did. It looks messy but it works.

@paulsimonps ,

The 36% from fortress and the 8% from defensive stance are additive with each other: they total for 44%.
Which reduces/simplifies your formular to:
BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-(Fortress+Defensive Posture))/100)
This should give you the same numbers

paulsimonps · September 2016

hrothbern wrote: »
paulsimonps wrote: »
Asmael wrote: »
BlockCost = (2160 * Sturdy * CP - Items) * Skills
Sturdy bonuses are additive, so you get 32% from your Sturdy total, BUT this value is multiplicative with other cost reduction mechanics.

EDIT: Corrected, abilities are calculated on their own (go figure, #ZosStuff).
I've recently been doing some serious reverse engineering on the PTS and one of the many things I tested was Block Cost. I did all my testing using no other data than what I found myself, I did this by testing as many possible combinations of things that I could to get as much raw data to go through as possible and the formula you linked is mostly correct but there is one thing that is off and when I myself learned what it was my reaction was "This is stupid" but at any rate here is what I found:

BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-Fortress)/100)-(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*(Defensive Posture/100)

The big thing to note is Defensive Posture. What it does is basically subtract 8% of what is left after all the other cost reductions have been applied with the exception of Fortress and it subtracts that with what you get after the other reductions including Fortress. The way this worked took a long time to figure out, I had my raw data that said what my block cost actually was with all my reduction but I just couldn't figure out how Defensive Posture fit into the formula at first. And when I tried this way it fit like a glove. I of course then double check the formula to make sure it fit with all my Data and it did. It looks messy but it works.
@paulsimonps ,

The 36% from fortress and the 8% from defensive stance are additive with each other: they total for 44%.
Which reduces/simplifies your formular to:
BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-(Fortress+Defensive Posture))/100)
This should give you the same numbers

@hrothbern

LOL this is what I get for overthinking stuff..... But hey at least I wasn't technically wrong

Will make my life easier in the process. And in that case it will make it easier for me to understand some of the ability cost reduction stuff. Sometimes you just need someone to look at your work for a bit.

paulsimonps · September 2016

hrothbern wrote: »
paulsimonps wrote: »
Asmael wrote: »
BlockCost = (2160 * Sturdy * CP - Items) * Skills
Sturdy bonuses are additive, so you get 32% from your Sturdy total, BUT this value is multiplicative with other cost reduction mechanics.

EDIT: Corrected, abilities are calculated on their own (go figure, #ZosStuff).
I've recently been doing some serious reverse engineering on the PTS and one of the many things I tested was Block Cost. I did all my testing using no other data than what I found myself, I did this by testing as many possible combinations of things that I could to get as much raw data to go through as possible and the formula you linked is mostly correct but there is one thing that is off and when I myself learned what it was my reaction was "This is stupid" but at any rate here is what I found:

BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-Fortress)/100)-(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*(Defensive Posture/100)

The big thing to note is Defensive Posture. What it does is basically subtract 8% of what is left after all the other cost reductions have been applied with the exception of Fortress and it subtracts that with what you get after the other reductions including Fortress. The way this worked took a long time to figure out, I had my raw data that said what my block cost actually was with all my reduction but I just couldn't figure out how Defensive Posture fit into the formula at first. And when I tried this way it fit like a glove. I of course then double check the formula to make sure it fit with all my Data and it did. It looks messy but it works.
@paulsimonps ,

The 36% from fortress and the 8% from defensive stance are additive with each other: they total for 44%.
Which reduces/simplifies your formular to:
BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-(Fortress+Defensive Posture))/100)
This should give you the same numbers

@hrothbern

Also it should be even easier if it was like this:

BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-Fortress-Defensive Posture)/100)

Less parenthesis at the end. Also you forgot one in yours

hrothbern · September 2016

paulsimonps wrote: »
hrothbern wrote: »
paulsimonps wrote: »
Asmael wrote: »
BlockCost = (2160 * Sturdy * CP - Items) * Skills
Sturdy bonuses are additive, so you get 32% from your Sturdy total, BUT this value is multiplicative with other cost reduction mechanics.

EDIT: Corrected, abilities are calculated on their own (go figure, #ZosStuff).
I've recently been doing some serious reverse engineering on the PTS and one of the many things I tested was Block Cost. I did all my testing using no other data than what I found myself, I did this by testing as many possible combinations of things that I could to get as much raw data to go through as possible and the formula you linked is mostly correct but there is one thing that is off and when I myself learned what it was my reaction was "This is stupid" but at any rate here is what I found:

BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-Fortress)/100)-(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*(Defensive Posture/100)

The big thing to note is Defensive Posture. What it does is basically subtract 8% of what is left after all the other cost reductions have been applied with the exception of Fortress and it subtracts that with what you get after the other reductions including Fortress. The way this worked took a long time to figure out, I had my raw data that said what my block cost actually was with all my reduction but I just couldn't figure out how Defensive Posture fit into the formula at first. And when I tried this way it fit like a glove. I of course then double check the formula to make sure it fit with all my Data and it did. It looks messy but it works.
@paulsimonps ,

The 36% from fortress and the 8% from defensive stance are additive with each other: they total for 44%.
Which reduces/simplifies your formular to:
BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-(Fortress+Defensive Posture))/100)
This should give you the same numbers
@hrothbern

Also it should be even easier if it was like this:

BLOCK COST=(Base*((100-CP)/100)*((100-#Sturdy*Strength of Sturdy)/100)-(#Enchants*Strength of Enchants))*((100-Fortress-Defensive Posture)/100)

Less parenthesis at the end. Also you forgot one in yours

haha

Cavedog · January 2018

This was a great discussion, but I was looking for a more clear answer on a specific question.

Is it worth it to put the block cost reduction enchant on your jewelry or not?

The way I read this is it's not, especially considering how much a regen glyph can help in the same situation.

Also, where do you guys get the exact math equations for this stuff? We need a book that has all these equations in them so we can work all these things out.....course, that might take the fun out of it in that once people figured out what build was mathematically the optimum that's what everyone would do.

Lightspeedflashb14_ESO · January 2018

Cavedog wrote: »

This was a great discussion, but I was looking for a more clear answer on a specific question.

Is it worth it to put the block cost reduction enchant on your jewelry or not?

The way I read this is it's not, especially considering how much a regen glyph can help in the same situation.

Also, where do you guys get the exact math equations for this stuff? We need a book that has all these equations in them so we can work all these things out.....course, that might take the fun out of it in that once people figured out what build was mathematically the optimum that's what everyone would do.

it is 800% better to put the block cost reduction on your jewelry, you get the cost reduction every 1/4 of a second and you regen ever 2 second, and you do not regen while blocking.

and we do have a good grasp on what is "mathematically the optimum", you would be suprised that are still "like let me play the way i want" or they do not care what is best.