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Bluepepper
12-22-2009, 11:46 AM
Wartotem's post from http://www.tankspot.com/forums/f14/60272-prot-warrior-improved-spell-reflection-2.html has a very nice effiecency analysis of Shieldwall and Laststand. In this post I'll try and look at this from a survivabilty perspective. I made my own post for the math behind Last Stand and Shieldwall as my reply did start to become rather lengthy. I'm pretty much reaffirming some of what Wartotem said although I do disagree a bit on his take on the value of improving laststands frequency of use.


MATH

NOTE: Some of the numbers I'm going to be using are anecdotal (Average Tank Maximum Health, Average Raid Boss Damage, and Average amount of incomming damage-magical and otherwise-it takes to Kill a tank). This is going to be from a Ten-man tank perspective, as tanking Ten-mans are what I have the most experience with. When it comes to the numbers I'm aware they aren't entirely accurate, but I'm only using them to illustrate a point on how glyphing, talents, and a combination of both can increase the amount of large hits it takes to kill a tank (I.e., Survival).

One way you can express the amount of hits required to kill a tank (magical damage or otherwise) is in a ratio of Player Health to Average Incomming Damage:


http://latex.codecogs.com/gif.latex?\frac{P}{D}=H



This formula can help give us some insight on the effects of Shieldwall(Glyphed vs. Unglyphed), and Laststand on the amount of hits required to kill a tank.



Variables
P = Player health
D = Average amount of incomming damage
H = Amount of hits needed to kill the tank



Numbers
Player health (raid buffed 10man): 50,000
Average Incomming Damage (10man Boss): 25,000



Input
Baseline (no cooldowns):
http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{50,000}{25,000}\\\\&space;H&space;&=&space;&2&space;\end{array}



Shieldwall (0/1 glyph):
http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{50,000}{25,000\times(1-0.6)}\\\\&space;H&space;&=&space;&\frac{50,000}{10,000}\\\\&space;H&space;&=&space;&5&space;\end{array}



Shieldwall (1/1 glyph):
http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{50,000}{25,000\times(1-0.4)}\\\\&space;H&space;&=&space;&\frac{50,000}{15,000}\\\\&space;H&space;&=&space;&3.\bar{33}&space;\end{array}



Laststand (at 100% HP):


http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{50,000\times&space;1.3}{25,000}\\\\&space;H&space;&=&space;&\frac{65,000}{25,000}\\\\&space;H&space;&=&space;&2.6&space;\end{array}



Laststand (at 35% HP):


http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{(50,000\times&space;0.35)+(50,000\times&space;0.3)}{25,0 00}\\\\&space;H&space;&=&space;&\frac{(17,500)+(15,000)}{25,000}\\\\&space;H&space;&=&space;&\frac{32,500}{25,000}\\\\&space;H&space;&=&space;&1.3&space;\end{array}



Laststand (at 100% HP) and Shieldwall (0/1 glyphed):


http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{50,000\times&space;1.3}{25,000\times(1-0.6)}\\\\&space;H&space;&=&space;&\frac{65,000}{10,000}\\\\&space;H&space;&=&space;&6.5&space;\end{array}



Laststand (at 35% HP) and Shieldwall (0/1glyphed):


http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{(50,000\times&space;0.35)+(50,000\times&space;0.3)}{25,0 00\times(1-0.6)}\\\\&space;H&space;&=&space;&\frac{(17,500)+(15,000)}{10,000}\\\\&space;H&space;&=&space;&\frac{32,500}{10,000}\\\\&space;H&space;&=&space;&3.25&space;\end{array}



Laststand (at 100% HP) and Shieldwall (1/1 glyphed):


http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{50,000\times&space;1.3}{25,000\times(1-0.4)}\\\\&space;H&space;&=&space;&\frac{65,000}{15,000}\\\\&space;H&space;&=&space;&4.\bar{33}&space;\end{array}


Laststand (at 35% HP) and Shieldwall (1/1 glyphed):


http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{rcl}&space;H&space;&=&space;&\frac{P}{D}\\\\&space;H&space;&=&space;&\frac{(50,000\times&space;0.35)+(50,000\times&space;0.3)}{25,0 00\times(1-0.4)}\\\\&space;H&space;&=&space;&\frac{(17,500)+(15,000)}{15,000}\\\\&space;H&space;&=&space;&\frac{32,500}{15,000}\\\\&space;H&space;&=&space;&2.1\bar{6}&space;\end{array}



Table

http://latex.codecogs.com/gif.latex?\inline&space;\begin{array}{|c|c|}&space;\text{CD/CD&space;combo}&space;&&space;\text{H(Hits)}&space;\\&space;\hline&space;\text{None}&2\\&space;\text{SW}&5\\&space;\text{SW}_g&4\\&space;\text{LS}_{100}&3\\&space;\text{LS}_{35}&2\\&space;\text{SW}\text{LS}_{100}&7\\&space;\text{SW}_g\text{LS}_{100}&5\\&space;\text{SW}\text{LS}_{35}&4\\&space;\text{SW}_g\text{LS}_{35}&3\\&space;\end{array}

note: Rounded up to nearest ones digit because "H" is discrete. H's value will shift based on the variables of the Tank's health and amount of incomming damage.



Inference

1. Using Shieldwall (unglyphed) and Laststand while at full health is a bit much, but very powerful. It can be great for situations where a healer has died and some extra breathing room is needed for a smooth B-rez recovery.

2. Using Laststand while at full health can behave similar, but not equal to, Shieldwall (glyphed).

3. Laststand with enraged regeneration make a powerful combo. A Draenei warrior's Gift of the Naruu can heal on a scale similar to enraged regeneration after raid buffs (LS+ER = OR ~ LS+GotN). With GotN and Glyph of Laststand you can essentially do the LS+ER combo twice within two minutes.