World of Warcraft - Evaluating druid tank gear

As various bonuses have different values depending on both how much you already have in a stat and how much you have of other stats, one cannot just define that this bonus is worth a fixed amount compared to another. Thus, my approach is to use a given set of gear (and talents), and then calculate relative values of adding one of each type of stat.

Picture an N+1 dimensional graph, where N dimensions each represent one slot we can equip an item, and the last dimension being how good our total gear is. By getting proper values of each stat with a given set of gear, we should be able to detect the direction we need to go to get a better set of gear. We might need to re-evaluate the weights as we go a few times, and we might even reach a local maximum on the graph, but we should be able to do fairly well.

Hopefully, the weights will not vary too much as we move, and thus, if we get a best in slot item, it is hopefully also best in slot once we get to the global maximum. To prevent us going into a local maximum we will try to compare our result with the best gear we can identify that blizzard seems to have intended us to use for tanking. Such as the highest tier set.

Firstly, this calculations will only be confirmed for night elf druid tanks with my set of talents. But I might extend it a bit later. I'm not expecting it ever to be valid for other classes though. I don't tank with other classes, so got no intention of doing that work. If someone wants to try, I can give you my perl code for this page.

A note about rounding. The values here aren't 100% correct. WoW rounds of many numbers. For instance, there is no gain in having 0.8 defense points extra, and stamina is rounded down before multiplying with 10 to calculate health for instance. But, as I want to evaluate how much gain you'll get by adding a single point in an attribute on average, I do not round of any values, as one would get artifacts such as getting one more defense rating would have no effect at this time, but at another time would add a whole new point of defense.

The following formula tells us how much damage we can take without healing before we die. Updated to version 3.0.9.

Health here is merely the amount of health you have in bear form, which can be calculated based on stamina, your current level, and your talent choices. As we want to optimize for raids, we also assume we have relatively common buffs.

The mitigation factor is a bit more complicated. It factors in your armor, dodge, resistance, talents and skills. Even more complicated for other tanks factoring in parry and block, which we will ignore. It is also different for different types of damage. Armor and dodge is skipped for magic damage, while resistance is only used for magic damage.

The damage part is different for each type of encounter, but in general, each encounter has a given percentage of the damage as physical damage, and another percentage as spell damage.

As far as I know the WoW combat system, a single roll is used to decide whether boss hit, miss, crit or get dodged. Thus the avoidance factor just adds and removes from 100%. Each percent crit represents a double damage hit. Each percent dodge or miss represents a percentage of attacks that doesn't do any damage.

The armor reduction factor is given by a formula I found at wowwiki that I hope is still correct. Note that for calculations done here, we use mob level of 83, and values thus differ from what you see in game which shows versus level 80 mobs.

I use this formula for calculating total armor. Note that this is only valid after patch 3.0.8 which has not yet come on live servers.

The effect of expertise is counted into the boss parry increase factor. If the boss parry, he cuts down his swingtime with 40%, if he has at least 60% of the swing time remaining. Thus, he can only get a speed increase once for each swing. The idea here is to calculate the chance of a parry happening in the boss swing, and use that to calculate the average time of a boss swing, and create a damage increase factor based on the relative difference between the no parry attack time, and the average attack time with parries.

We assume that only the auto attack swings from boss gets a speedup from the parry, and that the damage from these auto attacks is only a part of the total damage from the boss.

Savage Defense adds some mitigation if it is up. How much varies with your critrate and boss attack speed, and sadly boss DPS. Thus we also have to set a boss DPS amount in order to make this value count.

• You're more than able to keep threat, so survival is the limiting factor. In my experience, I have never had any trouble to keep threat. When we in addition now are forced to use lots of DPS gear to tank in, with lots of DPS stats, I don't see any reason to include threat generation in loot consideration, as I don't think threat generation will be the limiting factor.
• You're a night elf druid tanking in bear form, having night elf +2 miss chance.
• Mobs critting do double damage. (Do they do +50% on spell damage?)
• Mobs have 5% base chance of missing any player. (I guess this is a bit wrong, as they probably have less chance of missing a player when they are higher level than them). This is increased by 0.04% for each point of defense above 400.
• Mobs have 16% base chance of parrying any player attacking in front, minus bonus from expertise. With 433 expertise rating boss can no longer parry.
• Boss cannot parry anyone but the tank (others are at range or behind)
• You're decently buffed, having mark of the wild, blessing of kings, blood pact, power word fortitude and 30 stamina from food buff.

The paperdoll caster values here can be mined from armory or similar. Note that you need to scan equipment to figure out how much bonus armor and health one have. The adjusted values gives raw values for the stats. That is, values unaffected by talents and unaffected by each other. That is, effects by agility and bonus armor is removed from the armor, such that armor is base armor. Using the adjusted values simplifies calculations later on.

Agility = (Base agility + MotW bonus + Food bonus) * SOTF bonus * BoK bonus = (631.13 + 51 + 40) * 1.06 * 1.1 = 842.00358

Strength = (Base strength + Mark of the wild bonus) * Survival of the fittest factor * Blessing of Kings factor = (273.58 + 51) * 1.06 * 1.1 = 378.46028

Stamina = (Base stamina + MotW bonus + PowF bonus + Food bonus) * BoK bonus * SotF bonus * HotW bonus * Bear bonus = (1841 + 51 + 214 + 40) * 1.1 * 1.06 * 1.1 * 1.25 = 3440.5745

Health = 10 * (Stamina - Naked stamina * Bear bonus) + Naked Bear Health + Bonus Health + Blood Pact + Elixir bonus + Commanding shout bonus = 10 * (3440.5745 - 97 * 1.25) + 8447 + 0 + 0 + 650 + 2255 = 44547.745

Armor = 2 * Agility + Bonus Armor + Base Armor * Thick Hide bonus * Bear Armor Bonus * SOTF bonus * Meta Gem Armor + MotW bonus = 2 * 842.00358 + 2440 + 3399 * 1.1 * 4.7 * 1.33 * 1.02 + 1050 = 29013.308338

Armor reduction = min(75, 100 * (Armor / (Armor + 400 + 85 * (Mob Level + 4.5 * (Mob Level - 59))))) = min(75, 100 * (29013.308338 / (29013.308338 + 400 + 85 * (83 + 4.5 * (83 - 59))))) = 63.5583428922991 %

Defense = Defense Rating * Defense per defense rating = 114 * 0.203314099 = 23.177807286

Chance to be missed = max(0, 5 + Defense * 0.04 - (Mob level - Player Level) * 0.2) = max(0, 5 + 23.177807286 * 0.04 - (83 - 80) * 0.2) = 5.32711229144 %

Chance to dodge = Naked dodge + FS bonus + NR bonus + Dodge Rating * Dodge per dodge rating + (Agility - Naked agility) * Dodge per agility + Defense * 0.04 - (Mob Level - Player Level) * 0.2 = 7.04 + 4 + 6 + 218 * 0.02541425997 + (842.00358 - 87) * 0.024 + 0.04 * 23.177807286 - (83 - 80) * 0.2 = 41.0275068849 %

Diminished chance to dodge = (Dodge - Base Dodge - FS bonus - NR bonus) / (K + (1 / C) * (Dodge - Base Dodge - FS bonus - NR bonus)) + Base Dodge + FS bonus + NR bonus = (41.0275068849 - 7.04 - 4 - 6) / (0.972 + (1 / 116.890707) * (41.0275068849 - 7.04 - 4 - 6)) + 7.04 + 4 + 6 = 35.073942021737

Boss parry chance = 16 - Expertise / 4 = 16 - 21.10094895 / 4 = 10.7247627625 %

Boss swing parry window = Boss Attack Speed * Infected Wounds factor * 0.4 = 2.4 * 0.4 = 0.96 s
Probability of auto-attack hit in window (PAA) = Window / Druid attack speed = 0.96 / 2.5 = 0.384
Probability of global cooldown attack in window (PGCD) = Window / Druid Global Cooldown = 0.96 / 1.5 = 0.64
Chance of no hit in window = (1 - PAA) * (1 - PGCD) = (1 - 0.384) * (1 - 0.64) = 0.22176
Chance of two hits in window = PAA * PGCD = 0.384 * 0.64 = 0.24576
Chance of one hit in window = 1 - Chance of no hit in window - Chance of two hits in window = 1 - 0.22176 - 0.24576 = 0.53248
Chance of boss parrying any of two attacks = 1 - (1 - Boss parry chance) ^ 2) = 1 - (1 - 0.107247627625) ^ 2 = 0.202993201618809
Probability of boss parrying single swing = Boss parry chance * Chance of one hit in window + Chance of boss parrying any of two * Chance of two hits in window = 0.107247627625 * 0.53248 + 0.202993201618809 * 0.24576 = 0.106994825987599
Average boss attack speed = Probability of boss parrying single swing * (Boss attack speed * 0.6) + (1 - Probability of boss parrying single swing) * Boss attack speed = 0.106994825987599 * (2.4 * 0.6) + (1 - 0.106994825987599) * 2.4 = 2.29728496705191 s
Boss parry damage increase factor = Boss auto-attack damage coefficient * (Boss attack speed / Average Boss attack speed) + (1 - Boss auto-attack damage coefficient) = 1 * (2.4 / 2.29728496705191) + (1 - 1) = 1.04471148961546

Chance to crit = (Naked crit chance + Crit Rating * Crit per Crit Rating + Agility * Crit per Agility) / 100 + Sharpened Claws bonus + Leader of the pack bonus = (7.47 + 96 * 0.0217817468961011 + 842.00358 * 0.0120048019207683) / 100 + 0.06 + 0.05 = (7.47 + 2.0910477020257 + 10.1080861944778) / 100 + 0.06 + 0.05 = 0.306691338965035

Attack Power = ( Base Attack Power + Predatory Strikes attack bonus + Weapon Attack Power + 2 * Strength + Bear attack bonus ) * Protector of the Pack bonus = ( 532 + 567.8 + 2239 + 2 * 378.46028 + 240) * 1.06 = 4557.8637936

Average attacks = Boss attack speed / Druid auto attack speed + Boss attack speed / Global cooldown = 2.4 / 2.5 + 2.4 / 1.5 = 2.56
Chance any crit = 1 - (1 - crit chance) ^ average attacks = 1 - (1 - 0.306691338965035) ^ 2.56 = 0.608463583666491
Damage blocked by Savage Defense = (Attack Power / 4) / Mitigation factor = (4557.8637936 / 4) / 0.320686582547768 = 3553.20743183969
Average damage blocked = Chance any crits * Damage blocked by Savage Defense = 0.608463583666491 * 3553.20743183969 = 2161.99732748758
Savage Defense Factor = (Boss damage per attack - Average damage blocked) / Boss damage per attack = (40000 - 2161.99732748758) / 40000 = 0.94595006681281

Physical avoidance factor = (100 + Chance to be critted - Chance to dodge - Chance to be missed - Night Elf bonus) / 100 = (100 + 0 - 35.073942021737 - 5.32711229144 - 2) / 100 = 0.57598945686823
Boss crit factor = (100 + Crit chance) / 100 = (100 + 0) / 100 = 1
Physical mitication factor = Physical avoidance factor * Armor reduction factor * Boss parry increase factor * Protector of the pack modifier * Savage Defense Factor = 0.57598945686823 * 0.364416571077009 * 1.04471148961546 * 0.88 * 0.94595006681281 = 0.182540782039867 = 0.182540782039867
Spell mitigation factor = Protector of the pack modifier * Boss Crit Factor * Spell Resistance Factor = 0.88 * 1 * 1
Mitigation factor = Physical damage coefficient * Physical mitigation factor + Spell damage coefficient * Spell mitigation factor = 1 * 0.182540782039867 + 0 * 0.88 = 0.182540782039867
Damage taken = Health / Mitigation factor = 44547.745 / 0.182540782039867 = 244042.698306566

The balanced mitigation weight penalizes stamina as boosting stamina leads the healers to have to heal more per time. However, having plenty of stamina can make the healers able to heal more mana efficient if they otherwise could not use their best abilities due to time constrictions. Stamina also works against all kinds of damage.

The balanced mitigation weight can also penalize spiky mitigation, such as dodge, to prefer constant mitigation such as armor, which is easier to heal through.

How much we should weight these factors is a totally open question though. Some think that stamina is worth close to nothing once you pass a minimum allowing people to heal you efficiently, while maybe the fact that healers have better time can lead them to heal just as easy due to being able to use big heals, and you may also be able to cope with spell damage or healer silence/interrupts better.

Note that, though mitigation like dodge is very useful for healers to use less time overall, during a long fight, the boss will have lucky streaks where he scores many hits in succession without any of them being dodged, so healers have to be able to cope with the undodged mitigation values over a smaller period of time.

• The dodge calculations seems a bit sketchy. I don't get them to exactly match values I see in game. Any input on what is wrong with the dodge formula is expected. The difference is not that big though, so I expect the weights to be fairly correct anyways.
• Mining data from armory sounds cool. But dunno if anyone is interested and even if they are, I dunno if I want the load on my home network, so I don't expect to implement that soon. Easy for me to update my own gear in the code.