Five Signs of a Great Warrior Tank

Here are some things that I think set the truly great warriors apart from the merely good ones.

1. Knows where their Intervene button is

Intervene is a very under utilized ability. Yet, it’s also one of the most versatile.The most obvious use is getting to a friendly target before the mob they pulled can reach them. You can even use Intervene just to reduce threat on someone who hasn’t pulled yet. A slightly less obvious use is to move away from a target quickly by Intervening someone out of range (like a healer). This was a skill I honed on Murmur, but it’s come in handy more than once. The last really great use of Intervene is to take some heat off another tank. Keep in mind that it lowers their threat, so use it with care, but you can eat a hit during a big spike (which might even net you some rage, if you are starved at the time).

2. Can turn a mob without showing their back

Turning your back on a mob is dangerous. The moment you turn around, you can’t block/dodge/parry, opening you up to a big spike. However, we often have to turn a mob on a dime rather quickly (especially during pulls). All tanks should practice this trick, which involves mouse turning (keyboard turners need not apply): Run through the center of the mob, and when you reach the middle, do an about face and back up into position.

3. Knows when to pop cooldowns

A big problem that tanks have with cooldowns is popping them too late. Shield Wall can more than double your effective health, but twice 5% is still trouble. Last Stand is better when you are really low. A great tank is aware of the predictable spikes that can be mitigated with cooldowns, the unpredictable dips that can be pulled out with a quick finger, and the cooldowns that other can give them in a pinch.

4. Can build aggro while kiting

For many tanks, aggro falls through the floor when kiting. The combination of moving backwards and hitting a normal rotation is just too much for their fingers to handle. If you really want to kite and build aggro at the same time, practice your rotation until it’s second nature. Building great aggro should simply be what happens when you are on a mob, no matter what else is going on around you.

5. Never misses a pickup

Adds exist. This is a simple fact. Sometimes, the adds can be avoided, but other times they are part of the encounter. A good tank will usually notice them, and pick them up, but sometimes someone will die before that. A great tank, on the other hand, will never miss a pickup that needs to be made. When a mob comes into a fight, the great tank will charge/intercept/intervene/heroic throw/taunt, whatever it takes to get that mpb. No one needs to tell the tank that you have adds, they already know.

The Problem with Block

Blocking. Either it's too good, or it's worthless. There's nothing in between.

Blocking. Either it's too good, or it's worthless. There's nothing in between.

Block is an unusual mechanic. The idea seems simple, while dodging or parrying an attack makes it do nothing, a block just reduces the the incoming hit. Better shields block more damage. The idea is poorly implemented, though.

You see, in the current implementation, which is going to be corrected for Cataclysm, a block reduces the incoming damage by a set amount. For example, if you block an attack, it might do 1000 less damage. The problem is that it blocks 1000 damage whether the attack was 1500 or 15000. In mathematical parlance, one would say that block, as a function, is non-linear.

This problem puts block in kind of an odd place. Block, as a rule, can either be really good or really terrible. Against an enemy that does a lot of little attacks, block is fantastic. However, most bosses make sporadic attacks for massive damage, and block does next to nothing. Tack onto this the fact that block rating stacks very quickly and doesn’t suffer from diminishing returns, and you end up with the off-tanks for Anub’arak that take no unblocked hits and reduce their incoming damage by 97-100%.

How it’s being fixed

In Cataclysm, block will be percentage based. That is, a block might reduce an attack by 30%, regardless of its size. The result will be that block will suddenly be a good stat for raid tanks, where it had been rather worthless in the past. As an added bonus, blocking will be linear and easier to model for theorycrafters.

What to do in the mean time

Consider your needs when considering block. If you are tanking a lot of mobs, chances are good that block will help. Likewise with dual-wielding enemies. If, however, you are tanking enemies that hit hard (Most raid bosses fall into this category) give block stats a pass in favor of Stamina and real avoidance.

Tanking the Coliseum: (Part 4) Anub’arak Main Tank

This big guy is all that stands between you and the tribute chest.

This big guy is all that stands between you and the tribute chest.

Hard mode Anub’arak is a truly difficult boss. He requires a lot of AoE and single-target DPS, precision healing, and at least two solid tanks. In fact, the off-tank requires a special set of gear to successfully handle the encounter. Next week, I’ll talk about how to OT this encounter, but this guide will cover the job of MT.

Make sure your DPS can reach the adds and anub with AoE.

Make sure your DPS can reach the adds and anub with AoE.


Getting Anub’arak in the right place can be tough. You want to make it easy for the off tank to pick up the adds and get them on the ice, while also letting your DPS damage Anub’arak and the adds at the same time. Optimally, he’ll be facing away from the raid (to avoid cleaves), with his back-end on the ice. Remember that you want Anub between you and the off tank, otherwise the adds might jump on to you from thunderclap, or other area threat abilities you put in your standard rotation. This can be very dangerous.

When moving him, be sure to pull him away from the raid. Every moment that he faces the raid is a risk because of cleave. Death Knights should be pulling any ice you need behind you, so you never have to pull him towards the raid. This is key to a clean kill.

Frozen slash is the biggest risk to you as a tank.

Frozen slash is the biggest risk to you as a tank.

Freezing Slash

On a timer, Anub’arak will use Freezing Slash. This the biggest danger to the main tank, since you can’t avoid attacks while frozen. Have enough Effective Health to survive the onslaught in phase 1, but be ready with a cooldown rotation when Leeching Swarm comes into play. Note that percentage based damage reduction cooldowns are best during the swarm, because increasing your health just makes it hit harder.

It's better to lose DPS by moving Anub than to risk burrows from broken ice.

It's better to lose DPS by moving Anub than to risk burrows from broken ice.

Entering Phase 2

Before phase two (the burrow phase) begins, you will want to pull Anub’arak away from the ice. While it is important that you do a lot of damage to him, it’s equally important that the rest of the raid can avoid his impale and the adds don’t burrow. Pulling him away from the raid gives people time to move when he targets them, and also lowers the chance of the add tank’s ice getting shattered.

It is very possible that you will have to move over ice to get Anub away from the raid. Make sure your paladins know this, and have a Hand of Freedom ready for you. Those extra seconds of movement can be the difference between a clean burrow phase and an epic wipe.

Anub keeps aggro between phases, picking him up after a burrow is just a matter of standing in the right spot.

Anub keeps aggro between phases, picking him up after a burrow is just a matter of standing in the right spot.

Leeching Swarm

Leeching Swarm can ruin your day. The healers will have their hands full keeping the raid alive, and you will have a 30% health DoT on you, ticking constantly. Nature resistance will help a lot. Make sure that you have a Nature Resistance Totem, back enchant, and maybe even a head enchant to reduce that incoming damage. Look back at the Freezing Slash section, since he’ll keep doing that even with the swarm going.

Concluding Remarks

All in all, the main tank has a pretty routine job on this fight. Check in next week for off tanking tactics.

Why Cross Server Dungeons Means the Rise of Lowbie Tanks

Enter the tank.

Enter the tank.

I’m just going to throw this out there, I hate questing. Often I’ll frame this opinion in some other way, like “I hate dailies,” “I hate grinding out loremaster,” or most regularly, “I hate leveling alts.” The fact is, though, that it’s not the dailies or the leveling that I hate, it’s the solo nature of questing. I legitimately have fun leveling, when I can do so with a group. Similarly, dungeon dailies are a fun diversion, in the midst of all the solo dailies that feel like absolute chores.

This brings me to the topic of this post, lowbie tanks. Low level dungeons are a different ball game than those at cap level. In general, you don’t even need a tank. Everyone takes damage, and the healer keeps you from dying. In fact, often no one takes damage, because some level 80 is with you, obliterating the whole instance. Of course, this assumes that you can actually find a group. Putting together a party, at least for me, is nearly impossible without a group of friends/guildies all leveling together.

This is all going to change with the advent of cross server dungeons. It’s never been so convenient to queue for an instance, continue questing on your own, and hop in when the queue fires off. For those of us that love to group, it’s a godsend. Moreover, high level characters can’t queue for low level dungeons, so we’ll get to experience them the way they were meant to be played! On top of that, you’ll get level appropriate gear to go with what drops in the instance! I welcome this new era of group leveling with open arms.

The tool, for those unfamiliar with it, will let you pick your role(s) and then assign you to a group. It tries to put together a balanced tank/healer/3xDPS group, and will pull players from multiple realms to make that happen. Those familiar with queueing theory will already be aware of th advantages of such systems, and those who are not should be reminded of how much shorter battleground queues have been since the introduction of cross server queues in that area of the game.

This leaves an opening for dedicated lowbie tanks. The tool simply won’t put together a group without one in the queue. Instead of sitting around all day, you’ll be able to weave instances into leveling. Maybe it’s time for me to dust off that paladin alt I have sitting around.

The Math Behind Effective Health

The phrase “Effective Health” is thrown around a lot among tanks these days. Often, it is touted as the must-have stat for tanks, or as a misleading number in a world full of magic attacks. I will discuss how to calculate effective health in this post and how to determine whether stamina or armor are better at a given point. Determining whether effective health is a valuable stat is a subject left to another post.

What is Effective Health?

Simply put, Effective Health is the minimum amount of unmitigated base damage needed to kill the player. Another way of looking at it is if you could not block/dodge/parry and an attack couldn’t miss, before mitigation from stance, armor, or buffs was applied, how big of an attack would it take to kill you. Since that attack would be reduced by the amount of the mitigation, we get the following formula where μ is mitigation and h is health:


This is the definition of effective health that I will be using.

Note that:


Which will allow us to calculate total mitigation by determining the mitigation of the contributing parts later.

Calculating Effective Health

Suppose, now, that we are in a situation with full buffing available. We have the highest rank of every buff available to us with full talents, and we want to calculate our effective health from our base stats. This is a common situation, and one we consider extensively when gearing.

First off, we want to determine our total health. We will use stamina (s), and base health to determine this, the reasons for this will be shown later. There are buffs that come in to play here: Blessing of Kings, Commanding Shout with talent, Power Word: Fortitude with talent, Mark of the Wild with talent, food stamina, flasks, bonus health from enchantments, and your own health increasing talents. In general form:

h_{tot}=10 \cdot BoK \cdot Vitality(S+PW:F+MotW+food)+h_{base}+h_{bonus}+flask+CS

And with all values inserted in as of Wrath of the Lich King:

h_{tot}=10 \cdot 1.10 \cdot 1.06(S+214+51+40)+8121+275+1300+2812

Simplified as much as possible:


Thus, we have completed the first task in determining health.

Now, we want our total mitigation. For the moment, let’s ignore armor in the calculation. We still have a large number of factors to consider. We need to include stance, Ancestral Healing/Inspiration, Blessing of Sanctuary/Renewed Hope, and talents (if any existed). Thus, before including armor, you get:


After plugging in values:


Finally, we get around to armor. According to Satrina on Tankspot, mitigation from armor is found with the following equation for mobs above level 60, with L being the level of the attacking mob:

\mu_{armor}=\frac{A}{A+K}=\frac{A}{A+(467.5L - 22167.5)}

However, we are more interested in the converse of mitigation, which is found to be:


Now we bring in some assumptions. Suppose we are fighting a level 83 boss mob, and have all of the raid buffs available for armor. Our armor value will be similar to what we found for health. However, armor comes from a lot of places (like agility) and can be hard to track down. Regardless, we get base armor from gear, bonus armor from gear and enchantments, armor from agility, Stoneskin Totem with talent, Devotion Aura with talent, our own talents, meta gems, and Mark of the Wild.

A_{tot}=Toughness \cdot AES \cdot A_{gear}+A_{bonus}+DA+SS+MotW+2BoK(Agi+MotW+SoE)

Plugging in for all those values:

A_{tot}=1.1 \cdot 1.02 \cdot A_{gear}+A_{bonus}+1807+1380+1050+2 \cdot 1.1(Agi+51+178)

Simplifying as much as possible:


Now, we can find K(L=83)=16635 and get that:


Putting it All Together

Now that we have the constituent parts of the equation, we can finally get the full equation for effective health in terms of stamina, armor from items, and agility:


Derivatives and Stat Comparisons

One thing we can do with this equation is find relationships between effective health and additional stats. Suppose we wanted to know if bonus armor from a given piece was better than stamina on a different piece. We first take the derivative of effective health with respect to stamina:


We can do the same thing for armor. First we consider armor on gear:


Then we consider bonus armor:


There are a few things we note here. First off, both stats make the other stat better. That is, the more health you have the more you get out of armor, and the more armor you have the more you get out of health. Thus, we can find a ratio that gives how much armor a point of stamina is worth. Thus, we get:

1 Stamina=\frac{11.66(1.122A_{gear}+A_{bonus}+21303.8+2.2Agi)}{1.122(11.66S+16064.3)} Armor

1 Stamina=\frac{11.66(1.122A_{gear}+A_{bonus}+21303.8+2.2Agi)}{(11.66S+16064.3)} Bonus Armor

While this is correct, we probably want to simplify it. Let’s assume that Agility is around 135 on a warrior, since tank plate doesn’t include that stat.

Now, let’s make some substitutions with easy to find stats. Naturally, we will use unbuffed health and unbuffed armor, since we can just look those up on our character sheets or the armory. We know that h_{unbuffed}=10 \cdot Vit \cdot S+h_{base}+h_{bonus}=10 \cdot 1.06S+8121+275 and A_{unbuffed}=1.122A_{gear}+A_{bonus}+2Agi. So:

1 Stamina=\frac{9.44733A_{unbuffed}+201510}{h_{unbuffed}+6207.8} Armor

1 Stamina=\frac{10.6A_{unbuffed}+226096}{h_{unbuffed}+6207.8} Bonus Armor

To use my unbuffed values as an example, h_{unbuffed}=40836 and A_{unbuffed}=30373 gives us 1 Stamina = 11.6519 Bonus Armor. Using the values of one of my less geared tank buddies, a warrior with 32.5k health and 25.3k armor, you get 1 Stamina = 12.75 Bonus Armor

Tanking the Coliseum (Part 3: Twin Val’kyrs)

The Twin Valkyr is a lot of boring punctuated by a few moments of less boring.

The Twin Val'kyr encounter is a lot of boring punctuated by a few moments of less boring.

You might wonder why I am glossing over Faction Champions. Largely, this is because tanks are often asked to DPS on that fight, so I think that examining it from a tanking perspective is probably not productive. To all those who say you can’t tank faction champs, I submit for your inspection, our World of Logs for last week, which is consistent with our kills in the past. Turns out they hate when you interrupt and chain stun a healer.

Anyway, on to Twin Val’kyrs. First off, which one do you tank? I recommend that a warrior tanks whichever Val’kyr the melee will be attacking. This will ensure that Sunder Armor is always on their target. Additionally, you should grab the opposite color of essence. In my raid, the melee attacks Edyis Darkbane, and I have on Light Essence.

The center of the arena is a great landmark for you and the melee

The center of the arena is a great landmark for you and the melee


You will want to pull your mob to the middle of the arena. You will tank her here, and you never have to move. Easy as can be.

Special Abilities

Once about every 45 seconds, the twins will use a special ability. It can be one of these four, with respect to your attunement: Opposite color shield, same color shield, opposite color vortex, same color vortex. These will be cast at random, but each will be done before it repeats. Think the shuffle function in iTunes. The most important two are the opposite color vortex, and the same color shield.

Shield block makes dual wield look like a joke.

Shield block makes dual wield look like a joke.

Same Color Shield

This is when they mob you aren’t tanking casts a shield. The val’kyr you are tanking will start dual wielding, and her damage will spike. Save Shield Block for this. Her attacks don’t hit hard, there are just a lot of them. Thus, Shield Block trivializes this spike in damage. Additionally, it’s a good idea to keep sunder armor on the other Val’kyr to improve melee damage on that shield.

The vortex can cause a lot of raid damage. Don't make things any harder for the healers than they have to be, use Shield Wall.

The vortex can cause a lot of raid damage. Don't make things any harder for the healers than they have to be, use Shield Wall.

Opposite Color Vortex

The other key ability is vortex being cast by the mob you are tanking. While most of the melee will run off to switch colors, you should just stand there and eat the damage. This is the single biggest spike you will eat. I recommend glyphing and talenting Shield Wall for this occasion. With that on you, you will take almost no damage. The only fear is that you will get hit with the vortex twice before the cooldown can finish. This happens when the vortexes are within two specials of each other. I’m not going to go into the math on it, but that will happen in 18.75% of all attempts. When you do get a vortex with Shield Wall down, call for a healing cooldown, if possible, or pop your Last Stand and call for healing.

General Mindset

Tank damage in this fight is insignificant. You will probably be hit with a Beacon and left to your own devices. This doesn’t mean you can slack off, though. Healers will have their hands full with all the raid damage in this fight, and you should do what you can to not be a burden to your healers. Don’t count on your healers to keep you up through a dual wielding Val’kyr, use Shield Block to reduce the damage. Pop potions and healthstones if you can’t Shield Wall through a vortex. Do everything you can to make their job easier, you owe it to them for all the times they’ve healed your ass.

Circle of Tanks: My Reply

Koriel, over at, posted this survey for tanks. I thought I would share my answers as a nice little Tuesday bonus post.

What is the name, class, and spec of your primary tank?
Markov, Warrior, dual spec 5/15/51 (Cooldowns/Effective Health) 15/3/53 (Threat/Blocking)

What is your primary tanking environment? (i.e. raids, pvp, 5 mans)
25 Man Raiding

What is your favorite tanking spell for your class and why?
Warriors have a huge arsenal to choose from, for tanking abilities. I’m going to have to go with Revenge, though, since it’s so rage efficient and relies on my avoidance to proc.

What tanking spell do you use least for your class and why?
Almost certainly Spell Reflection. While I love the spell in concept, and use it whenever I can, too many spells simply ignore it. I wonder if Blizzard should redesign the spell, increase the cooldown on it (possibly by a lot), and allow it to work on more boss attacks. I doubt that will ever happen, though.

What do you feel is the biggest strength of your tanking class and why?
At this moment in time, with Anub’arak being the biggest foe in the game, I would say our biggest strength is blocking. We can reach unhittable easier than anyone else, and our block value is simply unmatched by paladins. Many guilds rely on warrior off-tanks for Anub, with good reason. We simply are the kings of block.

What do you feel is the biggest weakness of your tanking class and why?
Effective health. Compared to the massive health pools of druids and paladins, warriors are falling behind. This is an issue with gear scaling, since paladins get more out of stamina than warriors.

In a 25 man raiding environment, what do you feel, in general, is the best tanking assignment for you?

Warriors can adapt to any assignment. I can’t think of a single fight where a warrior tank can’t fill any and every tanking role. I tend to prefer being the main tank, though.

What tanking class do you enjoy tanking with most and why?
I can’t say I’ve ever tanked with anything other than a warrior.

What tanking class do you enjoy tanking with least and why?
Same, N/A.

What is your worst habit as a tank?
Biting off more than I can chew. As a tank, my natural instinct is to pick up everything that moves. As a result, I sometimes charge headlong into one more group than I can really handle. This is especially true of trash in instances, since I often go faster than my healers can handle, and wipe my raid.

What is your biggest pet peeve in a group environment while tanking?
Honestly, I don’t have any big pet peeves. Some people complain about trigger happy DPS, but I can’t say I’ve found any that actually pull off me. Some people hate being blamed for wipes, but I own up to it when it’s my fault and have never been blamed when it wasn’t. If I had to choose something, I would say people judging me by my gear, but that’s no longer an issue. When I had just reached 80, I would get people remarking that they didn’t want such a poorly geared tank in heroics, but I never heard a complaint once the ball got rolling.

Do you feel that your class/spec is well balanced with other tanks?
I think warriors are in a good place, right now. We can compete on any fight, and have our moments to shine. I would probably say the same about the other classes.

What tools do you use to evaluate your own performance as a tank?
I use Rawr to evaluate my gear and put together Markov chains to evaluate my survivability. In game, I try to just be objective about my performance and ask myself a few questions. Did I live through the encounter? If I died, could I have prevented it? Did anyone else die in the encounter? If they did, could I have prevented it?

What do you think is the biggest misconception people have about your class?
A lot of people don’t know how blocking works. Those that haven’t played a sword and board style tank often don’t realize that a blocked attack still does damage, and that shield block does very little against the big hits in the Crusader’s Coliseum.

What do you feel is the most difficult thing for new tanks of your class to learn?
How to pick up mobs. Warriors have all the tools to pick up a group of incoming enemies, but knowing how to use them takes time. Bloodrage, Heroic Throw, Charge, Intercept, Shield Slam, Cleave, Thunderclap, Taunt, and Shockwave all play a role in tough pickups. 5-mans really hone this ability, but too many tanks just skip past those on their way to raiding.

Effective Health or Avoidance and why?
Effective Health. The difference in survivability between a boss needing 2, 3, or 4 attacks to kill you is massive. Avoidance is good if you are taking a lot of small hits, but that situation is rare. Moving forward, Effective Health will continue to be good against hard hitting bosses, and Avoidance will continue to be good for trash packs and dual-wielding bosses (if they ever show up).

What tanking class do you feel you understand least?
Death Knights. I know nothing about the mechanics of their class, the sorts of abilities they use, or their strengths/weaknesses. The only experience I’ve had with Death Knight tanks was as my mage, and I was not paying attention to their abilities at the time.

What add-ons or macros do you use, if any, to aid you in tanking?
I’m a big fan of Power Auras for tracking my ability cooldowns. With that and IceHUD, I’m able to keep everything near my character, so I can keep an eye on the battlefield.

Do you strive primarily for balance between your tanking stats, or do you stack some much higher than others, and why?
I try to balance my gear, but I favor effective health. In Rawr, you can set the ratings to favor some stats over others. If Survivability = 1, then Mitigation = 0.8 and Threat = 0.6. That’s the way I normally favor different items.

Why NOT to Tank

Strangely enough, some prefer to hit others, instead of being hit themselves.

Strangely enough, some prefer to hit others, instead of being hit themselves.

Sometimes you wonder, with tanking being such a fun and rewarding role, why do some people actively avoid it? There are many warriors, paladins, druids, and death knights that don’t even know the first thing about their tanking abilities. I’ve thought of a few reasons that people might not be interested in tanking.

Short-term Responsibility

I remember a conversation I had with a mage, once. I told him that tanking was fun, and asked if he’d ever consider playing a class that could tank. His response somewhat surprised me. He said, “You can screw up as a DPS. You can’t as a tank.”

Tanks have a big responsibility, even in a small group. If you don’t have the gear or the skill to handle an encounter, you will cause a wipe. A bad DPS will either not contribute much damage (poorly geared) or just get himself killed (poorly played). Moreover, you can’t really “carry” a tank. You can bring more damage to make up for bad damage dealers, or more healers to make up for insufficient healing. You can’t split a boss’ attacks between multiple tanks to make that job easier.

Personally, I love the responsibility. It keeps me honest, and keeps me focused. Apparently, though, some people shirk from the spotlight.

Long-term Responsibility

Along with the short-term issues in an instance, you also have a greater responsibility to a raid. In my guild, we require a 90% attendance from everyone, but we expect near 100% for the tanks. The reason is simple, it’s hard to replace a well geared tank, and guilds generally focus their gear towards tanks at the start of a tier to make encounters easier. In other words, they are relying on you and you owe it to them.

Ultimately, it’s for the best if you only have tanks you can count on. A no-show tank can kill a night of raiding.

No Big Numbers

Healers try to get big numbers on their heals. A big crit on a tank, a massive group heal, or just a nice HPS on recount. Damage dealers try to get big numbers on their attacks. A big crit on a boss, a flurry of numbers in AoE, or just nice DPS on recount. Tanks try to get small numbers on their damage. A well timed dodge on a boss attack, taking next to no damage from a big group, or just a small Damage Taken number on recount. See the difference, here? Where everyone else is getting bigger and badder, you just make everything else get smaller and smaller.

Can anyone think of other good reasons why people would avoid tanking?

Modelling of Boss Attacks as Markov Chains

A Markov Chain is a way of calculating the results of a random process. You begin in a state, the process acts on that state, and the resulting vector is the probability you will be in each state after the action. This is a simple way of looking at a Markov chain. My character is named after such processes, and coincidentally, they are valuable tools for evaluating tank survivability. Allow me to explain how to construct a transition matrix for an incoming attack, and then how to use this to find your survival.

Building the Matrix

The first thing you should consider in this endeavor is what your states will be. A state should have no memory. That is, it doesn’t matter how you got here, it only matters that you are here now. For this purpose, I use health values. Thus, the matrix for our Markov chain should take us from current health to health after the attack. This seems reasonable.

How the matrix transitions is somewhat easy to describe, if a bit more difficult to calculate. Let’s put max health at the bottom right of the matrix, and death at the top left. Since this is a Markov chain, the entries in the matrix should look like this:M_{ij}=P(X_{1}=j|X_0=i) Which reads as, “the entry in the ith column and jth row is the probability of ending up in j given that you started at i.” Since the boss’ damage will be what causes the transition, we can figure out that damage=i-j.

The structure of the matrix is pretty simple, but changes a bit based on class. Druid is the simplest, since they can only be hit normally, or avoid the attack completely. Their matrix would look like this:

Incoming attacks for a druid are relatively simple

Incoming attacks for a druid are relatively simple

There is a line down the diagonal for avoidance and a stripe for hits, which is spread out because of the natural variance of boss attacks. Note that the hits pile up in the top row, since the attacks that deal greater damage than your current health simply reduce you to 0, instead. Similarly, we can construct a matrix for warriors, which will have a the same structure with added stripes for block and critical block.

Warriors are similar to druids, with block spreading out incoming attacks over a wider range.

Warriors are similar to druids, with block spreading out incoming attacks over a wider range.

We can imagine a paladin matrix would have a shape similar to warrior, without critical block. We’d have to take into account the effect of Ardent Defender which just changes the slope of those stripes when you are transitioning to below 35% health.

Constructing this matrix can take some time. A program like Matlab can handle a lot of it for you, but you will want to approximate the matrix by using % health, or something similar. If you use absolute health, you end up with upwards of a 50000 by 50000 matrix. This would take a very long time to calculate and use. A considerable understanding of theorycraft will be needed to accurately build the matrix, but it can be worth the effort.

Traits of the Matrix

We note that the matrix will have a certain “shape,” as shown above. Different sorts of attacks may take on different traits. A spell, for example, will cue off of your resistances. Additionally, some attacks cannot be blocked, dodged, or parried, and the line down the middle of the matrix will disappear under this rule. For all attack matrices, though, only the upper half will have anything, because the lower half would represent healing.

From a mathematical standpoint, we note that the matrix is a linear map in upper triangular form, and that the eigenvalues of the operator exist on the diagonal. As a result, the vector of the system with the largest eigenvector is the death vector (health = 0) with an eigenvalue of 1. As a result, as the matrix is taken to higher powers, the result is certain death. In other words, if you took an infinite number of attacks with no healing, you would die. This is not particularly interesting, but it does match with what we know about damage.

Another note is that the columns of the matrix all have a sum of 1. An interesting note is that the product of any two matrices with that property will also have columns with a sum of 1. We will use that later when we consider the meaning of specific columns.

Using the Matrix

We want to construct a chain of attacks, and determine if we will live through them. Suppose we were taking the same attack over and over and over again. Then, for n attacks, the transition matrix T over the whole set would be T=M^n. Assuming we start with max health at the beginning of the assault, the last column of T will hold the probability distribution for your health after those attacks. Indeed, the most important value is the upper right-hand value, since P_{death}=T_{max,0} With this in mind, the minimum number of attacks to take you from full to dead is found by finding the minimum value of n such that the upper right value of T is non-zero.

What if we wanted to construct a more interesting set of attacks? Suppose we had a string of n (potentially different) incoming attacks. Once again, we find that T=M_nM_{n-1}M_{n-2} ... M_1. The same conclusion about the probability of death comes in, but now we can have a variety of attacks, like DoTs and spells, thrown into the mix.

Another way to use this is to consider your healers in the equation. Suppose your healers were only healing you when were below 100%. Then we can consider a chain of attacks as starting with the first hit. To do this, reconstruct M with no avoidance, and use that version of M as the first attack in the chain, and follow with n of the original M matrix. That will give you how many attacks after the first hit you can take.

Alternatively, we could construct a healing matrix. In this case, the diagonal would represent your healers not casting a spell before the next incoming attack. Naturally, you would be more likely to receive a heal assuming you started at a very low amount of health, because of talents like Nature’s Swiftness. You could then treat this matrix like another attack that shows up periodically, except that it increases health instead of decreasing it.

Concluding Remarks

As I said in an earlier post, tanks are more interested in distributions than averages. This method of determining the results of boss attacks ultimately gives you the distribution of such attacks, assuming the matrix is built correctly. As a result, you can truly get an accurate picture of your survival.

Tanking the Coliseum (Part 2: Lord Jaraxxus)

Jaraxxus is all about positioning. This infernal, landing on melee, will force me to reposition the boss.

Jaraxxus is all about positioning. This infernal, landing on melee, will force me to reposition the boss.

Now that you’ve tanked Northrend Beasts, you might expect an encounter on par with it in terms of tanking difficulty. You would be wrong. Lord Jaraxxus is a fight that requires little in the way of gear, kiting, or threat generation. The only thing this fight asks for, is a little bit of skill with positioning.

You only have a second to pick him up after the encounter starts.

You only have a second to pick him up after the encounter starts.

First off, Jaraxxus aggros the nearest person to him when he activates. Be that person, and prepare a ranged attack if he runs off at the starting gun.

Predictable placement of portals and volcanoes helps DPS do their job.

Predictable placement of portals and volcanoes helps DPS do their job.

Once you have Jaraxxus firmly on you, drag him into position. The trick here is that you want the portals and volcanoes to spawn in a predictable place for the DPS. My trick is to spawn them in the center of the circle. To do this, note that he always spawns them to the left of where he’s facing. Thus, if you stand with him in front of you, and the circle to your right, 9 times out of 10, the portal will end up in the center of the arena. I say 9 times out of 10, because there is a small chance that Jaraxxus will spawn a portal while he is casting a spell at someone in the raid, and that position will be used for placing the portal. You can’t avoid that, so just plan for the more common situation.

Watch out for these little balls of fun. They can ruin your melee's day.

Watch out for these little balls of fun. They can ruin your melee's day.

The third, and final, tip for this encounter is to keep your melee out of trouble. Keep an eye out for melee getting hit with Legion Flame. When that happens, move him back a little bit, keeping him on a circular path around the arena. I use the second “ring” as a guide here. Similarly, when the infernals fly into the melee, start moving immediately. On heroic, the Fel Inferno they cast can’t be interrupted, so you need to move before people get burned. Note that if he casts a Fel Fireball while you move him, he’ll stay behind. Make sure you have a ranged interrupter (Shaman are perfect for this), for just such occasions.

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