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Thread: Understanding diminishing returns - A closer look ( HOW DOES IT WORK)

  1. #1
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    Understanding diminishing returns - A closer look ( HOW DOES IT WORK)

    Hey everyone,


    I have an interest in the value of parry/parry rating for warrior tanks, however before i can address them ( which will take place in another thread *hint hint*) I have some questions about DR. This is an effort to better understand what diminishing returns are, how the effect of dr functions, and its practical application to theorycrafting.... specifically on parry.


    below is the basic formula Ive been using.. is this correct?

    Code:
    1   1   k
    - = - + -
    x'  c   x 


    x' is avoidance after diminishing returns
    x is avoidance before diminishing returns
    c is the dodge/parry cap (65.631440% for warriors, paladins and DKs, 116.890707 for druids)
    k is a constant equal to 0.9560 for warriors, paladins and DKs, 0.9720 for druids


    Assuming this is the correct approach, I was planning on working out the DR on graph paper, and recalculating at intervals of 100, starting at an initial value of 1000.

    so ..

    1000
    1100
    1200

    and so on, all the way thru 4800.


    In this approach, Im assuming that the value of parry rating BEFORE dr is consistent. That is, that the slope will remain consistent and the value of parry increases exponentially as the amount of parry rating increases.


    My goal here is to understand the before-and-after-dr value of parry, and compile as much information regarding the slope of each as the amount of parry rating increases.

    Is this the right approach for what im trying to do?

    HOW DOTH THOU CHECK THE ARITHMETIC?!?!?!?!?!?!?!?
    Last edited by truculent; 04-21-2011 at 03:18 PM.
    Reev: So, do I macro /dance into Shield Slam now? Raysere: Yes, I hear it increases your DPS Gold balance gear quality attractiveness to the opposite gender considerably

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    The value of Parry Rating for a warrior is more variable than its impact on Parry alone because Parry has other interactions with the warrior class though Hold the Line.

    You use a lot of "Parry" and not enough "Parry Rating" in your questions. You don't get Parry, you get Parry Rating which is converted into Parry.

    Your comment about exponential growth is actually invalid. It would be linear. If the value of Parry Rating is not subject to deminishing returns, then the value in terms of Parry that you gain from one point of Parry Rating to the next is constant. It's only when you consider other factors such as Hold the Line would you introduce additional variability into it's value. It's because Parry is subject to deminishing returns that the function is logrithmic (the opposite of exponential growth). Simply removing the deminishing returns though turns the function linear, not exponential.
    "In anything, if you want to go from just a beginner to a pro, you need a montage." /w TankSpot WTB Montage for Raiders.

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    To answer your questions more directly...

    Quote Originally Posted by truculent View Post
    below is the basic formula Ive been using.. is this correct?
    Yes, that is the formula for deminishing returns on the combat table events of dodge and parry. The source you copied it from is correct.

    Quote Originally Posted by truculent View Post
    My goal here is to understand the before-and-after-dr value of the stat, and compile as much information regarding the slope of each as the amount of parry increases.

    Is this the right approach for what im trying to do?
    Why would you care about the value before deminishing returns? It isn't like you would make a decision to get or ignore a stat based on what it would be worth if a core game mechanic didn't exist.

    Quote Originally Posted by truculent View Post
    HOW DOTH THOU CHECK THE ARITHMETIC?!?!?!?!?!?!?!?
    1+1=2 in any base notation other than binary.
    Rules of arithmetic are pretty universal.
    "In anything, if you want to go from just a beginner to a pro, you need a montage." /w TankSpot WTB Montage for Raiders.

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    If it helps, I write the equation in a slightly mixed around format (via algebra):

    Code:
             cx
    Y(x) = ------
           x + ck
    NOTE: Y(x) is parry after DR and x is parry before DR (and only parry that is affected by DR. Base parry, for example won't be factored into the equation, but parry rating and parry from strength will).

    What this form lets you see is how the waveform will end up. It will be asymptotic and converge at Y(x) = c if you let X go to infinity.

    You're interested in knowing how much parry you get out of each "step" of parry you get, you can actually see that via the derivative (slope of the line) if you know calculus, which would be:

    Code:
    dY(x)     (c^2)k
    ----- = ----------
      dx    (x + ck)^2
    This tells you how "efficient" your current level of parry DR is. If dY(x)/dx = 0.56, then your next bit of parry (infinitesimally small bit) will only net 56% of it's value.

    Back in WotLK, I plotted these values against the old linear non DR parry for an example:


    The Y axis is in units of the ratio, since you can compare the DR curve to the non DR curve easily.

    Mind you the actual values of that chart are no longer valid (based off the old parry DR constants before CATA), but the trends are the same. What you'll see at X as it goes towards infinity is the DR curve will converge on the value of C, meaning the highest amount of parry you could ever have is 65.63% + whatever your base parry is. The "k" constant affects how quickly it converges to that 65.63% point.
    Last edited by jere; 04-21-2011 at 03:29 PM.

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    [QUOTE=Quinafoi;504141]The value of Parry Rating for a warrior is more variable than its impact on Parry alone because Parry has other interactions with the warrior class though Hold the Line.
    Quote Originally Posted by Quinafoi View Post
    You use a lot of "Parry" and not enough "Parry Rating" in your questions. You don't get Parry, you get Parry Rating which is converted into Parry.
    agreed. I will adjust the op.

    Quote Originally Posted by Quinafoi View Post
    Your comment about exponential growth is actually invalid. It would be linear. If the value of Parry Rating is not subject to deminishing returns, then the value in terms of Parry that you gain from one point of Parry Rating to the next is constant. It's only when you consider other factors such as Hold the Line would you introduce additional variability into it's value. It's because Parry is subject to deminishing returns that the function is logrithmic (the opposite of exponential growth). Simply removing the deminishing returns though turns the function linear, not exponential.

    Yea, again, ill correct my OP so that my questions are more clear to the reader, But correct me if im wrong.. considering HTL, dosnt the value of parry ( not parry rating, but parry itself) grow exponentially? That is, the singular event on the combat table x the uptime of HTL ?
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    Just to re-inforce, remember that the DR equation does NOT count base parry (or dodge if doing dodge)
    Last edited by jere; 04-21-2011 at 03:35 PM.

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    Quote Originally Posted by Quinafoi View Post
    To answer your questions more directly...


    Yes, that is the formula for deminishing returns on the combat table events of dodge and parry. The source you copied it from is correct.


    Why would you care about the value before deminishing returns? It isn't like you would make a decision to get or ignore a stat based on what it would be worth if a core game mechanic didn't exist.


    1+1=2 in any base notation other than binary.
    Rules of arithmetic are pretty universal.
    Im interested in its pre-dr value so that i have a base line to compare the diminished value. In other words, Im most interested in the loss of value parry rating suffers per 100 point interval.

    yes, i understand 1+1=2 .. but please understand that as Im sure this is all elementary to you, this degree of crafting is fairly new to me.. so im trying to measure twice cut once .
    Reev: So, do I macro /dance into Shield Slam now? Raysere: Yes, I hear it increases your DPS Gold balance gear quality attractiveness to the opposite gender considerably

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    Quote Originally Posted by jere View Post
    If it helps, I write the equation in a slightly mixed around format (via algebra):

    Code:
    cx
    Y(x) = ------
    x + ck
    NOTE: Y(x) is parry after DR and x is parry before DR (and only parry that is affected by DR. Base parry, for example won't be factored into the equation, but parry rating and parry from strength will).

    What this form lets you see is how the waveform will end up. It will be asymptotic and converge at Y(x) = c if you let X go to infinity.

    You're interested in knowing how much parry you get out of each "step" of parry you get, you can actually see that via the derivative (slope of the line) if you know calculus, which would be:

    Code:
    dY(x) (c^2)k
    ----- = ----------
    dx (x + ck)^2
    This tells you how "efficient" your current level of parry DR is. If dY(x)/dx = 0.56, then your next bit of parry (infinitesimally small bit) will only net 56% of it's value.

    Back in WotLK, I plotted these values against the old linear non DR parry for an example:


    The Y axis is in units of the ratio, since you can compare the DR curve to the non DR curve easily.

    Mind you the actual values of that chart are no longer valid (based off the old parry DR constants before CATA), but the trends are the same. What you'll see at X as it goes towards infinity is the DR curve will converge on the value of C, meaning the highest amount of parry you could ever have is 65.63% + whatever your base parry is. The "k" constant affects how quickly it converges to that 65.63% point.

    EDIT: as a side note, back in WotLK, the "c" constant for parry was like 47 or 48 something, so you'll see that chart asymptotically approach 47 or 48% ish. In today's world it would approach 65.63%.
    this is pretty much EXACTLY what i was trying to find out for the current situation, just a few steps ahead of my op. . .So any parry gained via strength does NOT effect the DR slope of the parry gained from rating? is that correct? of did i miss understand?
    Reev: So, do I macro /dance into Shield Slam now? Raysere: Yes, I hear it increases your DPS Gold balance gear quality attractiveness to the opposite gender considerably

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    Quote Originally Posted by jere View Post
    Just to re-inforce, remember that the DR equation does NOT count base parry (or dodge if doing dodge)
    Why would dodge be important? you lost me.
    Reev: So, do I macro /dance into Shield Slam now? Raysere: Yes, I hear it increases your DPS Gold balance gear quality attractiveness to the opposite gender considerably

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    Quote Originally Posted by truculent View Post
    this is pretty much EXACTLY what i was trying to find out for the current situation, just a few steps ahead of my op. . .So any parry gained via strength does NOT effect the DR slope of the parry gained from rating? is that correct? of did i miss understand?
    There is no difference between Parry rating gained from strength vs Parry rating gained from rating. There is only parry rating. The only difference is where it comes from, it all diminishes the same way at the end.

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    nvm
    Last edited by truculent; 04-21-2011 at 03:57 PM. Reason: brain fart
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    Yeah, you gain parry rating at the rate of 1 parry rating per 4 strength (so, for example, if you had 3200 strength, you'd get 800 parry rating from it).

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    Quote Originally Posted by truculent View Post
    Why would dodge be important? you lost me.
    The diminishing return on dodge chance from dodge rating and agility, and parry chance from parry rating is determined by the same expression. Or in other words, the benefit from the two ratings decreases at the same rate when you add the same amount of rating.

    To elaborate on the "base parry and dodge" bit:

    Your base dodge and base parry chances are different, this becomes obvious if you remove your character's armor so that you have no ratings - your dodge chance is lower than your parry chance when naked. Your bonuses to dodge and parry chance are added on to these values after the DR has been calculated.

    While you are not interested in dodge chance as you want to calculate HtL uptime maximisation and this is based on your parry chance, don't forget that both avoidance types work off the same expressions.

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    As stated by those above, parry from STR does count (as long as it isn't base STR).

    Real world example:

    Take the warrior Truculent on the Dark Iron realm (might be you).

    He has the Following:

    2647 STR (192 Base and 2455 from gear, enchants, gems, etc)
    11.67% parry chance (after DR)

    The parry tooltip reads he has 1255 parry rating which would give 7.10% parry (before DR sets in)

    I can tell you that if you take his STR from gear, etc (the 2455 number), you get 2455*.25=613.75 parry rating from STR (notice the 192 didn't come into effect). If you add that to the parry rating on his gear/enchants/etc and round, you will get a total of 1255 parry rating.

    Now let's run the 7.10% parry into the DR equation:

    y(x) = (65.631440*7.10)/(7.10 + 65.631440*0.956) = 6.67% (after DR)
    Add that to the 5% base parry you get and:

    6.67 + 5.00 = 11.67%, which is what your character sheet shows.

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    Deminishing returns is only applied to the change in Parry or Dodge (or Miss, but since Defense Rating is no longer in the game this isn't a factor so much anymore). This is the net difference caused by all the Parry Rating you gain from either Strength or Parry Rating directly. Note that Strength does not convert to Parry directly, it converts to Parry Rating and then is converted to Parry. So functionally, you only need to consider one variable in the case of Parry, what the Parry Rating is from the combined sources. In the case of Dodge however, Agility is in fact converted directly into Dodge, not Dodge Rating as a intermediate conversion. Because Dodge has two variables which contribute to the net change it is slightly more complicated of a formula.

    If your base dodge was say 5% and base parry say 6%. Then the amount of DR you suffer at 6% dodge and 7% parry (difference from base value of 1%) is identical. Meaning the value of 1 Dodge Rating = 1 Parry Rating at the base values of 5% and 6%, but also when the delta is the same the ratio of values from DR remain constant. So at 6% and 7%, 1 Dodge Rating is still equal to 1 Parry Rating in terms of DR (this wouldn't be true if the constants for dodge and parry were different).
    Last edited by Quinafoi; 04-21-2011 at 05:18 PM.
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    Quote Originally Posted by Quinafoi View Post
    In the case of Dodge however, Agility is in fact converted directly into Dodge, not Dodge Rating as a intermediate conversion. Because Dodge has two variables which contribute to the net change it is slightly more complicated of a formula.
    Actually, while Agility does not directly add dodge rating, it DOES count directly into the DR formula (at a value of ~0.41 Dodge Rating per Agility). This is why you need to consider buffs when comparing stats, as an equal amount of Strength & Agility pushes Dodge further into DR than Parry.

    @OP:
    If you want a complete math base, I suggest checking out my spreadsheet (in sig). It has formulas to calculate all your dodge & parry, as well as a derivate on the last page, which shows the gain in avoidance from Dodge/Parry Rating as a result of DR. If you don't understand, feel free to PM me about the spreadsheet, I'll try & explain it as best as I can untill you understand
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    WarTotem, that's what I said in my first paragraph.

    DR is applied to the change in Dodge or Parry from it's base value, not to the stats which contribute to it. However from a formula standpoint in determining your non-DR Dodge or Parry, the formula is different in that Agility converts directly into Dodge where as Strength converts to Parry Rating before converting to Parry. I was discussing the differences in the formulas, but at no point do I say Dodge from Agility isn't subject to deminishing returns. In fact I say the exact opposite in the first sentance of that post.
    Quote Originally Posted by Quinafoi View Post
    Deminishing returns is only applied to the change in Parry or Dodge
    That doesn't say Dodge from Agility isn't subject to deminishing returns.

    Note that at no point in that post is "Dodge" used where "Dodge Rating" was meant and the same for "Parry" and "Parry Rating". I was very deliberate in my word selection to avoid confusion however I believe you may have misinterpreted it. If I don't say "Rating", I don't mean rating.
    Last edited by Quinafoi; 04-22-2011 at 07:19 AM.
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    Quote Originally Posted by Pyrea View Post
    The diminishing return on dodge chance from dodge rating and agility, and parry chance from parry rating is determined by the same expression. Or in other words, the benefit from the two ratings decreases at the same rate when you add the same amount of rating.

    To elaborate on the "base parry and dodge" bit:

    Your base dodge and base parry chances are different, this becomes obvious if you remove your character's armor so that you have no ratings - your dodge chance is lower than your parry chance when naked. Your bonuses to dodge and parry chance are added on to these values after the DR has been calculated.

    While you are not interested in dodge chance as you want to calculate HtL uptime maximisation and this is based on your parry chance, don't forget that both avoidance types work off the same expressions.
    thank you sir. much clearer now.
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    Quote Originally Posted by Quinafoi View Post
    WarTotem, that's what I said in my first paragraph.

    DR is applied to the change in Dodge or Parry from it's base value, not to the stats which contribute to it. However from a formula standpoint in determining your non-DR Dodge or Parry, the formula is different in that Agility converts directly into Dodge where as Strength converts to Parry Rating before converting to Parry. I was discussing the differences in the formulas, but at no point do I say Dodge from Agility isn't subject to deminishing returns. In fact I say the exact opposite in the first sentance of that post.
    I think some confusion may have just came from the way you stated it earlier in the thread. It almost read as if you were saying the DR formulas were different for dodge and parry (which they are not, they are exactly the same). However, from this quote it looks like you are more talking about formulas for calculating avoidance percent, which would then be input into the DR equations. I think yall are talking about two different "formulas" and thinking yall are talking about the same one. Easy to get mixed up in all this stuff.

    I'll be honest, I read your earlier posts as implying that you need to put rating values into the DR equations, but I think (correct me if I am wrong) you really didn't mean it that way. The DR formulas specifically take in avoidance percentage values as inputs. You can convert ratings into those percentage values, but not all avoidance come from rating (well for parry it does, but not for dodge as you stated).

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