Read this.Follow

I saw that last night...yeah, it's a bit complicated for me (and I had a nightmare afterwards about my high school math teacher yelling at me), but the pretty graphs do help make it a little easier to understand.

Fairly straight forward. Well written and laid out. This was part of the discussion that went on in the very long thread about AP vs Agi we had in TBC, and it's why AP is now better for non SV specs.

It's essentially a nice visual representation of some of the math in the spreadsheet. Thanks for the link

No it doesn't.... it says anything but that.
In fact, nowhere is there a comparison between the values of different stats in that thread.
The only thing he shows is how stats scale and how they affect/are affected by other stats.

I was just saying what i saw from that thread , but hey i am not good at working out that stuff as i never ever did anything in maths at school that included anything they show on EJ that is why i wait for you Aethien or a few others to explain it in simple english so i can understand it.

I'll quote my high school math teacher here "You've got talent for math and you could become good at it, if only you did something"
Which is true.. I just couldn't be bothered doing homework, paying attention or in general doing anything but goof off and listen to music during math classes as I got good grades anyway.
I get the idea behind it, but since I picked the easiest version of math I could Δ is a completely alien thing to me.

The fact that it's been 5 years since I last attended a math class doesn't help much either.

edit: and feel free to explain the formula he uses in detail, I'm interested to see if my thoughts are going in the right direction.
And if anyone doesn't care to read it they can skip the text.

Edited, Apr 10th 2009 9:50pm by Aethien

Nah, he just uses 3.1 versions of talents :P

I wanted to ask this in that thread, but tbh I'm too scared to because I get an infraction every time I post on EJ it seems...

Anyway, do you know if he used the 3.0.x or 3.1 ArP value? If ~1200 is the live cap, the 3.1 cap would be ~1000, which might be achievable with Grim Toll proc (desirable? I dunno, would have to run it through the spreadsheet, but could be interesting, and Toll proc seems to have good uptime from what I've seen).

I think he uses 3.1 everywhere.
Simply because doing all the work for 3.0 when things change in a patch that will hit soon is kind of foolish.

Been very busy, sorry I haven't come back to this

I'll quote his original stats and then work it into longer terms. Since this is kind of 'for dummies' I'll just state that you need to remember the order of operations, and know that this -> Δ <- symbol is "delta" which simply indicates "total change". Finding this value is usually a matter of newcalc - oldcalc, where newcalc and oldcalc are fully encompassing calculations given your comparative values. Think of it like firing two separate copies of the same shot using the specific stats listed and comparing the outcome.

And I apologize for the table breaking but I can't seem to get it down even without pre tags into a format that still preserves the ability to actually read the formulas...if a mod sees this and really needs it changed, please let me know and I'll find another way to post it (I've got the entire post in a text file since it's taken me a few days to compose it in its entirety :P)

Onward!

4000RAP  Δ    4010RAP   = (        500          +     4010     *       .2        ) - (        500          +   4000   *       .2        ) = 2 
Base RAP Δ Adjusted RAP = ( Base Ability Damage + Adjusted RAP * RAP Coefficient ) - ( Base Ability Damage + Base RAP * RAP Coefficient ) = Total change in damage output for this ability with new stats.

All he does here is demonstrate that a linear function has the same delta value, or change, given the same amount of input (in this case, 10 AP). This rule applies to all his linear demonstrations. Using his equation as an example, simply plug your figures thus and you can use this for any meaningful comparison...but be careful using tooltip values ingame as these often apply calculations for you beforehand; you have to make sure you're using the BASE values. Wowhead can usually help with this. His mention of the reduced formula is convenient as it eliminates the "common denominators"; if you're comparing the same information, they're very useful to save yourself some extra math.

20%       Δ      21%      = (         .21        *           2.378            +       .79         ) - (         .20        *           2.378            +       .80         ) = 0.01378 
Base Crit Δ Adjusted Crit = ( Adj. critical hits * Critical damage multiplier + Non-critical hits ) - ( Base critical hits * Critical damage multiplier + Non-critical hits ) = Total change in damage output per-attack

Linear function, same rules as before. The calculation is evenly distributing 100% of all hits made (meaning, this is not like a WWS report; it's only looking at hits that connect successfully and make a critical strike roll) and multiplying the critical ones by the total critical damage multiplier to give a proper value to those hits made at the increased amount. An actual damage value input is not needed because we're not weighing the impact the stat has on any particular thing, and since the calculation is linear it will have the same result on the total output whether we're talking about Autoshot or Aimed Shot. The reduced forumla seems to conflict with the long one, but it's correct; total crit % difference multiplied by crit damage multiplier minus total crit % difference. This is because for every 1% crit you add to the distribution, you remove 1% from your noncrit.

5%         Δ       6%       = 500 *       2.9         / (       2.9         /             1.15             /      1.06      ) - 500 *       2.9         / (       2.9         /             1.15             /    1.05    ) = 5.75 
Base haste Δ Adjusted haste = DPS * Base weapon speed / ( Base weapon speed / "baked in" haste on autoshot / Adjusted haste ) - DPS * Base weapon speed / ( Base weapon speed / "baked in" haste on autoshot / Base haste ) = Total change in damage output per-shot.

Linear function, blah blah. We use division here because haste reduces the weapon speed value (which thereby inversely increases dps output). And unlike critical hits, the percentage values for are tacked with a 1.0x because we're looking to find the total outcome of the change, not just the difference applied. His reduced formula here has a typo, the last function should be ΔHaste%, not ΔCrit%.



I can't verify the formulas here, but if I were to guess at what he's doing, his first formula is using a quick integer conversion from the ArP rating number to an actual percent value of armor reduced. Then it's being multiplied by 25% for the 3.1 patch adjustment to ArP values. So in other words (sorry, this one is long-winded xD)...

EffectiveArmor                                  =                   BaseArmor                      * (                            1                             -           ArP            /                           1523                                 *          1.25          ) 
Effective mitigation value after ArP is applied = Armor before ArP (but after Sunder/Faerie Fire!) * ( "100%" of base armor value represented as a whole number - Armor Penetration rating / Integer conversion from rating to static armor reduction value * 3.1 patch 25% ArP buff )

Once you have that value, you can apply mitigation to your attacks, per his second formula...

Armor                                  / ( Armor            + (               467.5                               *     AttackerLevel       -            22167.5             ) ) 
Effective Armor value as defined above / ( Same as previous + ( Static value applied to scale "target difficulty" * Attacker's level, so 80 - Static reduction for armor cap ) ) = Total amount of mitigation applied to incoming attacks.

To demonstrate how ArP "accelerates" as target armor gets lower, check out this formula I wrote a while back...I wrote it for Faerie Fire, but the numbers are still applicable; just assume you have enough ArP to remove 610 armor. :)

Assume 3000 damage per second, performed against a target with 10,000 armor and then against one with 20,000, both with 4,320,000 Health (note: the 10k one is somewhat applicable to PvE purposes, as boss monsters have approximately 10,000 armor before buffs/debuffs; the 20,000 is just to provide a contrast.) As an interesting aside, this math demonstrates another odd fact that I'm not sure if Blizzard is accounting for: for a given value of armor reduction and a given amount of incoming damage per second, the target's time to live is decreased by exactly the same amount, regardless of their base armor value.

-10,000 Armor-  
Damage output after mitigation: 3000 * ( 1 - ( 10000 / ( 10000 + 15232.5 ) ) ) = 1811.057168334489  
Time to death 100-0: 4320000 / 1811.057168334489 = 2385.347119645495 sec  
  
Damage output after mitigation, with FF(-610 armor): 3000 * ( 1 - ( 9390 / ( 9390 + 15232.5 ) ) ) = 1855.924459335973  
Time to death 100-0: 4320000 / 1855.924459335973 = 2327.68094534712 sec  
  
Delta-damage: ( 1855.924459335973 - 1811.057168334489 ) / ( ( 1855.924459335973 + 1811.057168334489 ) / 2 ) * 100 = 2.447096580082%  
Delta-time: 2385.347119645495 - 2327.68094534712 = 57.666174298375 sec  
  
  
-20,000 Armor-  
Damage output after mitigation: 3000 * ( 1 - ( 20000 / ( 20000 + 15232.5 ) ) ) = 1297.026892783651  
Time to death 100-0: 4320000 / 1297.026892783651 = 3330.694239290991 sec  
  
Damage output after mitigation, with FF(-610 armor): 3000 * ( 1 - ( 19390 / ( 19390 + 15232.5 ) ) ) = 1319.878691602282  
Time to death 100-0: 4320000 / 1319.878691602282 = 3273.028064992614 sec  
  
Delta-damage: ( 1319.878691602282 - 1297.026892783651 ) / ( ( 1319.878691602282 + 1297.026892783651 ) / 2 ) * 100 = 1.746474840742%  
Delta-time: 3330.694239290991 - 3273.028064992614 = 57.666174298377 sec 

The oddity of the time adjustment is likely being "accounted for" in the fact that most armor reduction tools now reduce by a percentage of target armor, as per the earlier formula; this prevents a simple 200 armor reduction from suddenly becoming a massive DPS increase when targets are already perilously low on armor...in effect, the percentage adjustment is probably supposed to "steady" the effect of ArP so it doesn't accelerate, but it seems to continue doing so anyway, albeit at a far slower pace than before. Perhaps because we're dealing with integers in the tens of thousands? I don't know and don't really care. It works for Blizzard, apparently, and that's good enough for me.


So there you have it. I hope this is useful to some of you and doesn't just come across like a raving lunatic babbling on :P

And of course if you still have questions I'll try to clear up what I can, just ask

Edited, Apr 15th 2009 1:26pm by Norellicus