Good Legend Shields

Discussion in 'General Archive' started by daywaker2, Nov 27, 2013.

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  1. MegaNuker

    MegaNuker Forum Ambassador

    I was referring to any level below that will not kill you.
     
  2. _Baragain_

    _Baragain_ Living Forum Legend

    MegaNuker, I understand the mathematical mechanics of this of this game better than most. Both Durrendal and spiro_spula are correct. Block damage reduction is a flat amount that you block on the times you "roll" a block. It does behave like armor in that regard and does apply universally across all kinds of damage and is applied after armor and resistance is taken into account. What I'm describing in my post above is a measure of the overall efficiency of a block rate and block amount. I will give a simplified practical example to better explain it.

    Imagine you take a sample of 1000 hits (or any other suficiently large sample size to account for the random number generator having occasional runs of good luck and bad luck) and each hit does 2000 damage. For the sake of the example, lets assume that it is a physical hit and is only effected by armor value. For this example, lets say the character has 50% damage reduction from armor. That means that each hit does 1000 damage after armor is applied. Without any block rate, the character would take 1000 damage/hit*1000 hits for a total of 1,000,000 damage. Now lets look at the effect of block rate. For this example, I will use my shield that I mentioned before in the build i have and that so-called "God mode" shield with a theoretical 80% block rate, but only the 516 block amount.

    In the case of the "God mode" shield, it would block 800 of the 1000 hits. Each of those blocked hits will be blocked for about 51.8%. That means that those 800 hits will only do a total damage of 385,600 damage as opposed to 800,000 damage. Add that to the unblocked hits of 200,000 damage and you will take a total of 585,600 damage which comes out to an effectiveness of approximately 41.4% of the damage you should have taken is blocked over time ((1M-585K)/1M).

    Now, we will look at my 80%/80% leveled up to 48 with the warlord set. I only block 68.3% of the hits I take as opposed to the theoretical 80%, but each hit is blocked for 76.7% damage as opposed to the 51%. With that in mind, lets take a look at those same 1000 hits. Of those 1000 hits, I would block 683 of them 683,000-683,000 damage*.767= approximately 159,100 damage. Add this to the 317,000 damage from the 317 hits that I would not block, and you get approximately 476,100 damage taken. This efficiency is ((1M-476.1K)/1M) or 52.4%.

    You can go through all the work I outlined above to prove it to yourself for any shield, or you can do it the easy way I showed in my other post. Just multiply (Block Rate %)*(Block Amount %) and you get that same percentage... and that percentage is a true indicator of just how good or not good a shield is. I know some people will want to ignore the evidence, but for a DK, because of the blocker talent, a good 2/2 shield will always beat a good 3/1 shield.
     
  3. Novadude

    Novadude Commander of the Forum

    Does block affect stun or other effects?
     
  4. _Baragain_

    _Baragain_ Living Forum Legend

    No, it does not effect stuns, but it can reduce the damage you take from poison DOT or fire DOT with the same chance and same reduction.
     
  5. MegaNuker

    MegaNuker Forum Ambassador

    @_Baragain_

    OK your example describes a better shield version a lesser shield. Also 80% block reduction will only add to the block of the shield. Fist the 80% reduction at 45 should play out to about a 20% damage reduction at 45. The shield I like was 178% block rate. So if we take your example and use what I know about blocking. At 45 a 516 block should put you around 44% damage reduction. So armor removes 1000 does not apply until you figure your block. 2000 damage blocked for 1020 damaged blocked 50% of that based on armor equals 560 damage. Next shield you 80/80. Should be 64-65% at 45. 2000 blocked is 700 damage. With armor should put it at 350. The 178% block rate should be about 95-96% attacks blocked. So out of 1000 960 will be blocked 40 not blocked. So 960 X 560 is 537,600 and 40,000 makes 577,600. Now the 80/80 shield is only going to block 50% at most. So 350 X 500 70,000 and 1000 X 500 or 570,000.

    Now to the add the two block damage and block % up does not work.
     
  6. trakilaki

    trakilaki Living Forum Legend

  7. _Baragain_

    _Baragain_ Living Forum Legend

    o_O:confused:

    I made that as clear as I can. I am right, and I've done the math to prove it (Two different ways I might add). I have checked in game and the % reduction for 516 is exactly 51.82% (Which in my practical example I rounded to 51.8%), not "around 44%." The number i gave for 50% armor block was only for the sake of realism, but I could have just as easily said, "Lets imagine it does 1000 lighting damage and you have 0 lighting resistance," and the result would be the same. Now lets more on to why else you are wrong.

    The only explanation that could possibly exist for why you do not seem to understand what I'm telling you that there is an upper limit to all the stats in this game. First off, the law of diminishing returns is defined by an equation that I derived with some help on the old forums in the form of
    100%*[X/( X + C )]=Y


    Where X is the stat, C is a constant based on level and type of stat, and y is the % output. See this wiki page which sums up some of my work and the work other people have contributed since and gives the exact equation for block rate and block amount for a LVL 45 character. This could allow you to exactly calculate the block rate (and if you are willing to do the work, the effectiveness) of the shield.

    Nice try, but it is you who does not understand the game mechanics or the math... Fortunately, I do.

    ALL stats do not exceed 80% reduction or 80% chance. In the unlikely event you could get a shield with enough block rate to be near 100% block rate (Impossible because the limit of the function as X approaches infinity is 100%), it wouldn't even get you that far, it would stop at 80%. That is a cap imposed by the developers... And if you are curious, 80% block rate would occur at just below 4000 block rate.

    I did the work for you and here is the math. For the sake of argument, I will assume that the character in question has the Dark Warlord set and the blocker talent selected. (516+150)*[1+(1.78+0.30+0.40)]=2318 block rate. 100%[2318/(2318+959)]=70.73% Block rate. So, you can see, I was generous when I said "Assume 80% block rate." But, I am even more commited to making you see the error in you ways, so I will assume you've used over 3M glyphs on the shield and half a million glyphs on the warlord shoulders (Like I have, After all, I want this to be a fair comparison), giving the new calculation seen here--->. (585+163)*[1+(1.78+0.30+0.40)]=2603 block rate. 100%[2603/(2603+959)]=73.77% Block rate... Still a far cry from the 80% I assumed on the previous post. Now, for the last bit of proof that that so called "God mode" shield is nice, but not as "God mode" as you may think I will recalculate the effectiveness using the equations I mentioned above for a 585+163 block amount and the 30% you get from the warlord set. (585+163)*1.3=972, and 100% [972/(972+479.75)]=66.95%. Multiply the two percentages and you get 49.39% effectiveness... STILL LOWER THAN MY 80%/80% enchantment shield with 52.4% Effectiveness! Like @trakilaki said...


    You can argue with me all you want, but short of the developers themselves, there are few people who understand the math of this game better than me.
     
  8. Mario_Boss

    Mario_Boss Regular

    @Baragain

    In firs example you are taking ordinary shield with block chance of 80%, but in second one you are writing about yours 80/80 lvl 48 with warlord set...

    Not the same shield.

    Unfortunately I only have +126.6% block chance from full moon so i can't compare but i will try to craft or find one at least 80/80 to compare and do the math.

    Btw everything stand in your calculation but i think that you didn't take right % amount of block amount on 80% bolck chance shield.
    I think block amount/reduction is much higher than 50% (especialy with warlord set and on lvl 48)
     
  9. _Baragain_

    _Baragain_ Living Forum Legend

    TO HECK WITH THIS! This is my last try, and if you guys don't get it this time, I give up and you will just remain unenlightened!

    I am talking about two DIFFERENT shields. The first is the supposed "God mode" shield with 178% increased block rate and no stat improving the block damage reduction (1434 rate and 516 block amount at LVL 45, not considering other modifiers). The second one is my shield which has 80% increased block rate and 80% increased block damage reduction (928 rate and 928 block amount at LVL 45 not considering other modifiers). The purpose of comparing the shields was to demonstrate that that "God mode" shield is not that good. My more recent post went a step further and put the two shields on even ground by assuming both shields have been upgraded and that both hypothetical players are using the same gear.

    In my first example, I have a "ordinary shield" with an 80% chance to block, not an 80% increase to the stat. This was supposed to represent a best case scenario of the "God mode" shield approximating the block rate at the developer imposed cape to the actual chance to block stat. In the example above your post, I no longer assumed anything and actually did the calculations for both shields under identical circuimstances.

    I assure you that my math is correct... what is the more likely situation is that you misunderstand that the effectiveness percentage I give represents. so I will try and restate that too in a clearer, more concise way.

    Given:
    A LVL 45 Player using the LVL 35 EX talent "Blocker" is also using the full Dark Warlord set leveled up to 47. That same player has two shields and is trying to determine which is better. One has +178% increased Block Rate enchantments but no Block Damage Reduction. The other shield has +80% increased Block Rate enchantments and +80% Block Damage Reduction enchantments.

    Now, lets assume that that player has as solid of a grasp of the math and mechanics of this game as I do and runs the numbers and discovers the following.

    Shield 1: "God mode"
    2603 Block Rate, (73.77% Chance to block)
    972 Block Damage Reduction, (66.95% damage reduction on block)

    Shield 2: "80/80"
    2069 Block Rate, (68.32% Chance to block)
    1582 Block Damage Reduction, (76.73% damage reduction on block)

    Now that player looks at those two sets of numbers and says "Wow, those are actually rather close to each other... how ever will I chose which is better."

    Now, assuming that player is as smart as me, he will think "Hey, if I multiply those two percentages together, they will give me an 'effectiveness measurement' telling me the average damage reduction over many hits, taking into account the hits that won't be blocked and will take the full damage and the hits that will be blocked and will be reduced."

    So he runs the numbers again and finds the following.
    Shield 1:
    100%*0.7377*0.6695=49.39%
    Shield 2:
    100%*0.6832*0.7673=52.42%

    Thinking to himself again, he says, "OK, so Shield 1 will block about 49.39% of all the damage I take if I average out all the blocked hits and non blocked hits... But Shield 2 will will block 52.42% of all the damage I take once averaged out... I guess I'll be melting that first one. Too bad... I know some people on the forums who would think this is a perfect shield."

    -----------------------------------------------------------------------------------------------------------------
    EDIT:
    All this arguing on this topic has actually made me curious... when I have some time, I'll crunch the numbers on five different theoretical shields based on the "perfect" stat of +60% of a given stat and see which would truly be the "God mode" shield my bet is on the 120/120, But I'll admit it if I'm wrong.
    Shield 1: +0%/+240%
    Shield 2: +60%/+180%
    Shield 3: +120%/+120%
    Shield 4: +180%/+60%
    Shield 5: +240%/+0%
     
  10. MikeyMetro

    MikeyMetro Forum Overlooker

    Lol, shield 5 will = 0% efficiency with your formula. This is only because you have left out a variable for the base stats of any given shield. To correct this your formula should be 100(X+n)(Y+n)=Z, where X is block rate, Y is block DR, Z is efficiency and n is the base stats. Since rate and DR base are equal on any given shield n can be considered as 1. However, certain unique items can modify n (e.g. Warlord set) which could skew the results where a 2x/2x enchantments shield may not be the best. This is a slim chance though. The enchantments on one side of the equatin would have to be very good and on the other side very bad for this to happen.

    I have been following this conversation and have run your theory through many permutations and it holds up. Short of doing a full on mathematical proof of this equation I would have to say you are correct.

    At any rate, during my next alumni reunion at one of my alma matters I will see if I can get your name on a short list for an honorary PhD in Shieldology :)

    Luck be with ye,
    Mikey,
    Tegan

    p.s. This may help with Dr. Horrible's standing with the Evil League of Evil :cool:
     
    Last edited: Nov 29, 2014
  11. _Baragain_

    _Baragain_ Living Forum Legend

    No, you misunderstand my equation then. The percentages used in the effectiveness calculation is the ACTUAL % chance and the ACTUAL % reduction, not the enchantment values. That is also why the example shields all say +X%.

    Actually, false because there is a different constant used in the rate calculation than in the amount calculation. That means that block rate % increases slower than the % block reduction does. However, this is nearly completely offset by the 40% blocker talent. This is why I am of the opinion that 2x/2x is better for a DK, but 3x/1x in favor of rate would be better for the other classes.
    Well, I already have the PhD in horribleness, what harm could one in Video Game Math do (I know a lot more than shields! :D:p).
     
  12. Mario_Boss

    Mario_Boss Regular


    You are using sentences like LETS ASSUME in case of "Good Mod", but then you are using NOW LETS LOOK MY 80/80 LVL 48.

    You see what am I talking about?
    So pls don't start wiht TO HECK WITH THIS. Show some respect.
    I understand now and thank you for explaning in details.

    Regards,

    MB
     
  13. trakilaki

    trakilaki Living Forum Legend

    In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific theory, which is empirical

    in courtesy
    of wikipedia
     
    _Baragain_ likes this.
  14. _Baragain_

    _Baragain_ Living Forum Legend

    Thank you. Exactly what I was thinking but wasn't going to say "given" that I had already given up on them.:p
     
    Darwarren likes this.
  15. Darwarren

    Darwarren Count Count

    A long time ago, a student in a good USA high school would get this information in class. We live in interesting times.
    Thanks for the refresher course, and the analysis of DSO statistical mechanics.

    It's also helpful to remember that DSO is a dynamic system, rather than a static one. The programming is constantly changing, and subject to operational glitches and system flaws. Sometimes, it is more adventure than expected.
     
    _Baragain_ likes this.
  16. jeffzrx

    jeffzrx Active Author

    o_O so my shield's ok then ;) LOL :)
     
  17. Novadude

    Novadude Commander of the Forum

    I think the top number for rate and reduce has bumped up to about 65% but am not sure.
     
  18. _Baragain_

    _Baragain_ Living Forum Legend

    Excellent... Could be better, but it is a very good shield that most DKs would be lucky to have.
     
    Master0fpuppets likes this.
  19. Master0fpuppets

    Master0fpuppets Forum Baron

    1 year of searching for a sheild was back in Septembar they I got so mad at the game and I quit it for almost 3 months. Now That am back I see nothing is changed in terms my in game luck/chanse of geting that sheid I need, I would be happy if I could get 2-1 (2x block 1 reduction) but no, I get everything except block and damage reduction, among 8 last sheild in the pass 3 days not one sheild had any block rate at all or damage reduction, so any help is welcome, what am I doing wrong :(
     
  20. thebearreturns

    thebearreturns Exceptional Talent

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