What is the perfect legendary shield; 2.0

Well on thinking about it ,I +1 that

here is why, br =block rate% bc= block chance % and d is damage

net damage you take
= (1-br)*bc*d+ d(1-bc)

= (1-br)*bc*d+d-bc*d
=d - bc*d + bc*d - br*bc*d
=d - br*bc*d
=d(1-br*bc)

here, 1-br*bc represents the net percentage of damage you take over several hits

Lets take an example now, say br*bc = 0.6


according to baragain's formula effective HP will be HP*1.6 where as according to Armando it would be HP/0.4=HP*2.5

 

baragain's formula is incorrect. Just think of this easy example: Imagine you have 100%block strength. This means 100% of incoming damage gets reduced, you receive 0 damage. EHP = immortal. According to baragains formula your EHP would then be HP×2.

/e: I haven't read through all your formulas/startposts yet, but I'm pretty sure this is the reason why justice performs so well in your calcs, a result that seems very unlikely to me

 

Some interesting questions regarding the math. I'll dig into it and get back to you all with an answer.

And Armando wins the gold medal. It should use the same basic form as armor/resistance effective HP. When I first proposed "Effectiveness" of shields over a year ago, it was supposed to only be for comparing shields with pure rate/strength values. What a 64% effectiveness for a 80%/80% was supposed to mean is that it reduces the damage you take by 64% on average "converts" it into the same type of stat as armor/resistance.

I will reprogram/re-run the examples and update the first post and comment when completed. Additionally, I will adjust my thread on effective HP. I suggest the German one do likewise.

I am very interested to see the results of the changes and if ULTRA is right, or if my numbers happened to be right through luck.

 

I actually also dug deeper...
Here are my results, just to give everyone a complete image.
User @ZweBa suggested, in the German thread, to compose the effectve HP as a sum of the effective HP with and without block, weighted with the block rate:


As you can see, this leads to a formula very similar to @_Baragain_ 's

- apart from that (1-Blockstrength) divisor.

However, I still think it makes more sense to calculate the average percentage of damage getting through first (as @ekant1992 did above), and then divide the BaseHP by this number:


(I simplified all formulas by using armor instead of (Armor+ Resistance)/2, just for the sake of readability...)
I have to admit I still didn't figure out the exact divergence between both approaches, but I suppose it's something about the addition of fractions...

In the end, I trust you, @_Baragain_, to figure out what is ultimately correct.
Already now, thanks for the discussion, consideration and your announced renewed investigation efforts!
I am also very curious on what will turn out to be the ideal shield!

 

Some nice equation manipulation there. Brings a tear to my eye.

Sadly, there is a problem with this formula in the very first line. It applies block rate at the same time as Armor/Resist where as damage reduction from those is independent of block rate. After examination, I've modified my equation and it matches the one seen here:

I've broken it down a little further. It isn't as simplified, but it is easier to explain the three major parts of the equation.

Spoiler: Simplified

Part 1: BaseHP
This should be self explanatory if you are smart enough to be critiquing my math to begin with.

Part 2: Accounting for armor/resistance
As I discussed in the 1H DK thread on armor/resistance, the choice to weight these evenly is geared towards the fact that, depending on the situation, either could be more or less important. But the math... lets simplify it to a single number, 75%. If you reduce the damage you take by 75% of the damage, you only receive 25% of the damage, and that is what the (1-75%) represents. That means, if you have 10,000 instead of receiving 10,000 damage and dieing (in the case of 0%), you only 2,500 (or 25%) of the damage. This is 1/4 of your Base HP which means that you effectively multiply your HP by 4 (or "4/1" or "1/0.25") to give you an effective HP of 40,000. That means, with 75% reduction, you could take 40,000 of non-reduced damage before expiring.

Part 3: Factoring in Block
If the previous part makes sense to you, then all I need to do is convince you that "%BlockStrength x %BlockRate" yields a stat that acts the same as regular reduction, but is applied in parallel with the reduction from armor.
Instead of reinventing the wheel, I'll quote myself from a long time ago...

While the way block strength and block rate have changed, the use of the percentages has not changed. I hope that this proves that this behaves just like damage reduction from armor/resist. If not, then ask and I'll try to explain it better.
...
Therefor, if it behaves just like armor/resistance reduction, then it follows that it's factor in effective HP should take the same form as the one for armor/resistance.

What does this mean?
That means, if you could some how get 80% armor, 80% resistance, 80% Block Rate, and 80% block amount, then your effective HP would be your base HP multiplied by 13.889:


This also means that the max that a shield with only block rate and block damage reduction can improve your HP by is 2.778 times. Now, I will go back to my opening post and fix my equations and include the same normalization that I had before (only with the right functions) and see if there is a shield out there that can beat 2.778.

 

Well, I don't think the problem with that formula is that it applies block rate to armor/resistance, as there are 2 parts, first for unblocked hits, second for blocked hits, and the armor/resistance is taken into account equally in both cases. If you look at the second line, that becomes very clear.

I rather assume the problem is adding two separate hitpoint calculations in contrast to adding up weighted effective damage and then dividing the HP through that number.

As for me, you're preaching to the converted - explaining my own formula to me ;-).

Yup, that was also what I concluded, here:

Good luck with your Excel sheet - don't forget your ingame dailies over this! ;-)

 

I could see it either way, but I'd have to dig in to the formula you referenced to find where the flaw lies. I am now confident in mine because the "Block Effectiveness's" equivalence to the armor/resistance reduction is based on averaging over thousands of hits and can be viewed as independent of the armor calculation, and the armor calculation applies to 100% of hits.

...........................
I'm in the same boat as you are here:

I still can't tell you why it is wrong, because on the surface it seems to make sense, but I did some dimensional analysis and I can say beyond a shadow of a doubt that the one from ZweBa is wrong because the dimensional analysis for the blocked damage component doesn't match the dimensional analysis of the armor component.

I thought about this for close to an hour and I can't tell you why it is wrong (yet), but the dimensional analysis doesn't lie.

EDIT:
I've got it!
While we pull out the 1/(1-Armor) from both, the dimensional analysis made me look at the flaw. In the first term, the unblocked term, it would have the dimension of "Blocked/%Redux" even though it would be more accurately labeled "NotBlocked/%Redux" as opposed to the other term reading "Blocked^2/%Redux^2"
We are adding two unrelated terms. The issue is introduced that the Block strengths is in terms of "%Redux/Blocked" and the "Blocked" is never canceled out and the other result is that it introduces the Block Rate into the formula without anything to cancel it out. On the other hand, my old "Effectivness" immediately cancels it out and put it purely in terms of %Redux.

It is a little convoluted, but I hope it makes sense to you.

 

First of all, sorry for keeping you busy so long, away from your Excel analysis and the game...
On the other hand I suppose you had some "scientific explorer" fun with it, similar to me, and after all we want to make sure we're using the right approach now.... so I don't think this time spent on checking it is wasted!

I have to admit you lost me at first with the dimensional analysis - curiously, in spite of my IT studies and some good physics education in high school, I can't remember ever having heard of it before. :-(
And my last encounter with linear algebra was some 18 years ago...
However some quick reading suggests it is a good way to check formulas like this one; and I think I also understand by now what you did, and your reasoning. Thanks!

I still don't really see/understand the methodic/logical error in setting up ZweBa's formula in the first place, but it is not so important.
Trying to put it in simple words, I'd still say the mistake is adding up two different, weighted effective HP calculations, as opposed to dividing BaseHP by weighted effective damage.

Anyway, I am also, still and even more, convinced that the 1/%Redux approach is right.

I'll leave you to your Excel analysis and return to the German forum, where ZweBa in between has posted data and conclusions from some extensive practical testing he has done.
More stuff to read, understand, analyse and reply to ... xD


Edit: Only now I saw that you already finished your number crunching and changed your initial post accordingly. WOW!
Thanks a lot, once again, for your efforts and insights!

Seems I was right in my believe that my current wolf slayer shield is already pretty good; it reaches an HP factor of 2.58 .
(even if that CHR is really bad of course...)



I have two more remarks on your Excel formula:

1. In the blue part, you use H$3*$F6 as total block efficiency. For H5, that should probably be $F5 there, not $F6.
But I do assume you entered your formula correctly in Excel and just copied the formula for H6 and not H5 here, by accident.

2. (copied from my first post in this thread ;-))
As far as I can see, the green part only takes armor and resistance into account.
So any blocking by Dragan pauldrons and helmet alone is not taken into consideration? Is that intended?

What I mean is that with Dragan helmet and pauldrons you already have a certain block efficiency, even without a shield.
To correctly measure the effect of the shield alone, this "Dragan block" should be accounted for in the "effective HP without shield", no?

I don't think anyone would have thought in that way, anyway. It was rather important to notify people who are using your results about the formula change, though.
But kudos for the way you dealt with that mistake! I really appreciate your transparency here, besides the incredibly fast corrections!
Not everyone would have dealt with such an "attack" on all their previous work so constructively, I'm sure about that.

 

That is correct. It seems that in my tiredness I had the wrong cell selected when I copied. I'll correct it here in a second.

Yes and no. It is not intended insofar as you ought to have that Warlord Block Rate/Block Strength, even without a shield, but yes in that it compares the full setup (Warlord items and shield) versus a build with the same armor, HP, resistance, but with nothing blocking related. In that case, the effectiveness multiplier included the block related stats from the Warlord set with the shield which is not necessarily 100% accurate, but if you were not using the Warlord gear in a 1H for the purpose of the blocking stats, then there would be significantly better choices when it comes to over all armor/HP. If you ignore the block related stats, the warlord helmet/pauldrons only have 693+446=1139 armor and 309 HP, which you could get from just one item. I feel that you could view the block related enchantments pointless to a 1H DK without a shield and you might as well just roll them up into the effectiveness of the shield itself. As said, it's not 100% accurate, but you wouldn't use the Warlord set in a 1H build if it wasn't for those block stats.

I'm OCD about my math and I take a great amount of pride in my work, but not so much pride that it keeps me from admitting when I make a mistake. Instead, that pride and OCD nature made me fix it as fast as possible so I wouldn't have a reason to be embarrassed of a simple mistake.

I know that I am sort of approaching your post backwards, but it is just the way my brain thought of responses. It is a lot of fun to exercise my mind in these ways, so you are right when you say that this was in no way a waste of my time. The game holds only a moderate amount of challenge for me anymore (ever since I soloed Mortis Fatal with reds shortly after getting my new 2H) and looking under the hood of DSO is actually more interesting to me at times than actual game play... What I wouldn't do to be able spend a day with the source code of this game

My degree is in mechanical engineering and we used dimensional analysis to validate equations... it is a very bad way to attempt to generate formulas unless it is just simple conversions, but it is very useful for checking if you've combined your formulas right. You can run the units of each variable through to make sure your expected output units match the units you input. It doesn't take long, but tells you when you've made a simple mistake.

 

God job.
I think it is a god way to calculate how much Dammage you can stay as a DK for the Q fatale Bosses.
Some time ago i calculated to. Unfortschnatly i lost my Formular. But i put the Formal in a Exelprogram frome Google.
Iff i type youre Numbers in my list i got other resolts. :/ So i gess one off us is not right.

Buy the way i am not exited about affektive Health. Some Bosses do moustly Physical dammage some moustly Elementary Dammage.
Better to separate thouse to and see how much ist Elemantry Health at Q2 fatal fore example.

"As promised:


"

I coled the Effective HP(Elementary only) : ResistancePerformanceIndax ... RPI
and the other Physical : HealthPerformanceIndex .. HPI

https://docs.google.com/spreadsheets/d/1Y_cK2son82J9UwtzAG60mXiA6Y7En1UGSBJ3KS20dTA/edit#gid=42


EDIT:
... youre Formular must be right we have the same resolut but youre Pixel is incorect... I was wondering becouse the Formular looked so crrectly. I think i hade the same way to calculate when i created the Google Calculator.
EHP: 54.369
HPI:71162
RPI: 44.025


=
=SUM(HP)/(((1-((Amore+Resi)/2)/100)*(1-(BlockS/100)*(BlockR/100))))


Armando
EDIT


Greetings
Potzi
frome Grimmag

 

@Potzi in English only, please.

Cheers.

 

Oh, and I forgot to mention, the Shield Calculator spreadsheet is now available for download in the opening post.

It is true that some bosses do more physical and others do more elemental, but unless you are building two different builds that focus on Armor in one and Resistance in the other, your build needs to be able to handle both.

 

Thanks for that, I will certainly be using it.
Also, I will provide a link in your name in the German Forum... later.
Currently I'm pretty busy with the (old, autumn) Dragan event on the test server .

 

I'm a bit confused by all the calculations and all the math in here, so I have one question.

I dropped this yesterday at Q3 and I want to know if it's better than the Vargulf Round Shield I've been using (it had 132% of block rate)



As you can see I am using full dragan set, and I get a ~72% block rate with this config.

Thanks for your help

EDIT:

Here are my overall stats with that config



EDIT 2: Already did the calculations, thanks Armando

 

Instinctively, I would say it's quite a bit better due to that block strength value.
But it also depends on your total HP, armor etc.
For comparing 2 specific configurations, you could either use Baragain's effective HP formula here or Potzi's HPI calculator here.
Or provide us with full screenshots of shield and char stats, and I can calculate the values for you ;-).

 

The legendary shield is better right now.

One thing to keep in mind is that as you glyph up the pauldrons and legendary shield, your block rate and hp will improve. My guess is that it will take 1, maybe 2 shield upgrades and 3 or 4 more pauldron upgrades to get to 80% block. At that point you'll have 80% rate and 68% strength, trumping the vargulf shield.

It should be pretty apparent that glyphs won't improve your block stats if you use the vargulf shield, as you'll already have 80% block rate.

 

Dropped in Blackborg today...

 

This is my perfect shiled heheehehehe