AEP and other math stuffs, Lich King edition

[Arcazua]

This is meant to be my attempt to understand the mathcraft behind Lich King era mechanics. I’ve done some surface work here and there, but not enough to truly research it up until now because I simply haven’t had time. With a holiday here, hopefully I’ll be able to put together something meaningful. This page is going to represent all the work that I do. If you want conclusions, without seeing my reasoning behind it, go to the top of page 2.



What is AEP?

AEP (Agility Equivalence Points) was a system designed by rogue players in early 2005 to have a simplistic way of viewing gear. Rogues compared all of their attributes to agility, which was then regarded as their central stat. Agility was worth 1 point, and everything else was worth so many points of agility.

The system was very crude, and it was not very strongly rooted in mathematical origin, but for what it was at the time, it was solid.

Almost two years later, when Burning Crusade was released, a zillion new items were hitting the scene and nobody had any idea what was better than what. So before there was intense research on the 1:1 vs 3:2 (later 1:1.5) rotations, before it was common knowledge that Beast Mastery did the most damage, before Cheeky's spreadsheet and all kinds of other theorycraft, I sought to create a basic point system to evaluate gear. I named it after the rogue's system since hunters also use agility.

AEP, or *H*AEP as it was later known in some circles to imply it was for hunters, met some decent measure of acclaim when it was first released. It was celebrated here on TKAsomething, and not nearly as well received on elitistjerks, where many snooty theorycrafters wrote it off as inaccurate, with wild assumptions and bad estimates and all kind of other nasty things.

And they were right. The first incarnation of HAEP was founded making certain base assumptions that were flat-out not correct. However, for a brief period, while everyone's gear was still relatively low-end, the values of the first system were a decent rule of thumb if you just needed to judge something on the fly that you weren't familiar with.

4 or 5 months later, I revisited the idea, and made a second version for the Burning Crusade era that was more generalist in its approach. It assumed much less, and expected more information from the user. The downside of this was that it required computing by hand of the different weights, and at that point you may have found it just as easy to use Cheeky's spreadsheet, which was in its early days of wide-spread acceptance.

In fact, a few months after that, Cheeky added an item weight and an item upgrader feature to his spreadsheet that one could probably trust a good bit more than either version of AEP.

Well, Cheeky's spreadsheet still exists and is being updated by Shandara, but I have been asked by several sources to make some attempt at an AEP for Lich King-era mechanics. This is that work.

You can certainly say that the spreadsheet, now Shandara's spreadsheet, is a better resource. Overall, it is. It has itemization weights calculated for you. It has an item upgrader feature. It's easy to ask what this is even good for. I give you a few answers:


1. It lets us discuss where our DPS comes from. Even if a few critical errors render this work completely moot, it should generate discussion and knowledge about class mechanics. It's not an easy read, and certainly not written for any particular audience to be able to read it, so new hunters might be daunted, but someone who can understand WTF I'm talking about will probably have a very good handhold on how hunters work.

2. It gives you a simple system to use on the fly. There was a mod for a while that allowed you to put in your own item weights for AEP and it would display the values of both your current item and the one you were looking at, to compare the two.

3. It gives you the freedom to make personal adjustments for what you find superior in an item upgrader. The Gear Planner on the spreadsheet only counts DPS upgrades in the specific ways that it measures. If you deviate from what is chronicled in the spreadsheet, or if you value stamina on an item, or anything else of that nature, you'll be able to make your own adjustments by taking the weights to WoWhead or Allakhazam.

4. It lets you seem knowledgeable and worldly about things hunter-ish. OK, maybe not. But maybe. =p






Change Log and other Comments
This was going to be on the last post of the page until I realized I ran out of posts.

Wall of text crits you for 5,522 characters.


I'll say this much for right now: This is completely unchecked, unrevised, un-anything. I also didn't do as much research as I probably should have, since I am NOT up on the latest shot rotations/priorities and a zillion other things. I'm sure there's errors. I'm sure that someone with a lot more time on their hands than me will find them.

And there's a few things that I didn't finish because I didn't have the information in front of me and didn't care to try to figure it out when I had more pressing things to do. So armor penetration was left out for now, the effect crit has on GFTT is not counted in right now, and I'm willing to bet I could have done a much better job on certain aspects of the other calculations and derivations and other mathy words.

But it's done. Yay.

[Arcazua]

I. Basic Premises

We can’t do anything without knowing the rules of the game. So let’s start off with what we know, from a general level:

1) Most people only care about DPS. As such, we will consider DPS first, foremost, and almost exclusively. Factors related to non-DPS benefits will be mentioned, but not directly factored into any point system generated.
2) A spreadsheet is more effective and robust, but doesn’t give you a quick spur-of-the-moment impulse answer. It also doesn’t tell us anything about how the mechanics work, and only gives us an end result. Part of this process is to take away the curtain masking what makes things go.
2b) I use Shandara’s spreadsheet for a few crude data items, like how much damage I can expect from a pet. And yes, there is a feature on the Overview tab that creates item weights. However, I want a general set of answers, and that only applies to specific hunters with specific gearsets. (Granted, on some level, so will the AEP system derived, but I prefer to deal with things in general terms.)
3) We should really only be concerned with level 80, since eventually everyone will be at that level. Anyone still leveling should find the numbers revealed to be “accurate enough” for picking quest rewards.
4) This is definitely going to be long and painful. To create. To read. To do anything with. But it should hopefully be useful.

And now let’s talk about the actual stat mechanics we need to know about:
Attack Power (AP) - This is going to be the basic building block of our damage. Whereas, in the past, conversions have been made to agility, I believe this is an antiquated relic of the old rogue AEP, and isn’t as useful today as talking about three different stats ALL generating 1 point of attack power. It literally takes 14 attack power to create 1 DPS, without any other modifiers or special attacks present. Shot cycles and other stats will alter this. Pets also get 22% of a hunter’s attack power.
Crit Rating (CR) - It takes roughly 46 crit rating to equal 1% crit. (I’m told it’s actually 45.9060, but 46 will be good enough.) 1% crit adds 1% of a player’s non-crit damage, plus any bonuses like Mortal Shots.
Hit Rating (HR) - It requires nearly 33 hit rating to equal 1% chance to hit. At a standard 5% chance to miss on an even-level target, or 9% on a boss, this means a player will need somewhere between 164 and 296 hit rating to not miss, minus any modifiers they have like Focused Aim or the Draenei racial. Hit Rating is like CR in that it (roughly) adds 1% to your damage per 1%, but it is cheaper in itemization, and has no additional modifiers. It also caps out, after which, extra is wasted. Hit Rating now transfers to pets, which makes it a very useful attribute. (Does Focused Aim? I assume not.)
Haste Rating (Haste) - Haste Rating converts at the same rate as Hit Rating, however the effects are a bit different and more confusing. More on that later.
Armor Penetration (ArP) - About 15 ArP is needed to ignore 1% of a target’s armor. How important this is is very contingent on the target’s existing armor. Armor itself represents a percent loss to your damage output, and ArP helps negate that. More discussion required later when we get into the heavy lifting.

Agility (Agi) - Adds 1 attack power and 83.333 agility adds 1% crit. So effectively, 1 agi = 1 AP + 0.55 CR.
Intellect (Int) - Adds 1 attack power if you have Careful Aim, which WILL be assumed since it has no other direct DPS benefits. If you do not have Careful Aim, ignore it. However, it also adds 15 mana, which means it adds to a hunter’s longevity. This is also worth considering, however past iterations of HAEP have shown that counting mana endurance just proves to be a huge headache.
Stamina (Sta) - Adds 1 attack power if you have Hunter Vs. Wild, which will also be assumed for the same reasons, even though it is unlikely any non-SV hunter would have it. Again, just dismiss the values if you are BM or marks. Stamina also adds 10 health, which is the more important purpose it serves.

Mana Per 5 Seconds (MP5) - Grants the hunter 12 mana per minute, regardless of circumstances. This mana only assists in longevity during a fight, which is a consideration to focus on later in this work.
Spirit - Similar to MP5, but only works during periods of relative inactivity, at a greater rate. Spirit is extremely rare on hunter gear, and will not even be considered.

There are no other attributes on equipment that assist with damage output. There are a few other stats that are worth thinking about, like Resilience and various defensive ratings, but these are less universal, particularly among raiding hunters.

[Arcazua]

II. Shot Mechanics and Other Related Abilities

Auto Shot (auto) (AP scale factor: 7.1%)
Auto Shot is the basic building block for all hunter damage. It represents a bit less than half of the hunter’s personal damage. (That is, ignoring the pet.) Since other shots’ mechanics are at least loosely based on Auto Shot, we’re going to talk about it very carefully.

Basic shot damage is determined by:

Basic Auto DPS = Weapon Damage + (Ammo DPS * Delay) + (AP/14 * Delay), all divided by the attack speed.

Note: Delay refers to weapon speed, and is different from actual attack speed. Delay is the speed the weapon fires with no modifiers, however a hunter should at the very least have a quiver, so they do not actually fire at this rate. Hereafter, attack speed will be referred to as just speed, or spd.

Attack Power: For every second shooting in Auto Shot, 14 attack power will deal an additional point of damage. For simplicity’s sake, we are regarding Attack Power as the most basic attribute to a hunter’s damage. There are a number of other factors that influence this damage, however.

Hit Rating: First, the shot has to hit. So a “roll” is made to decide if a hit occurs. A player normally has a 95% chance against a non-boss or 91% chance against a boss, but hit rating can improve upon this. If the shot misses, zero damage occurs. Otherwise, the damage stays. Effectively, over a long period of time, this means that a hunter will do 95 or 91% of the damage they would if they never missed, and we can raise this to 100 with hit rating, Careful Aim, the Draenei racial, and a few other effects.

Crit Rating: If we have a hit, then we have a percent chance to crit. The player’s crit rate is an amalgam of several influences, but most directly controlled by agility and crit rating. Adding 1% chance to crit adds 1% chance that the shot does an increased 100% damage. (In other words, double.) However, there are also modifiers that increase that 100% bonus damage to a greater factor, such as Mortal Shots, which raises that figure to 130%.

Haste Rating: Haste rating is almost exclusively an Auto Shot attribute. It has some effect on Steady Shot for non-Beast Masters, but essentially 1% haste will increase your attack rate by 1%, and upping your attack RATE to 101% lowers the time you need to shoot by a factor of 1.01. Many players have a misconception over haste rating that it reduces your shot time by a direct amount. Having 100% haste (through Quiver, Rapid Fire, Berserking, Quick Shots, etc.) does not make you attack instantly and do infinite damage. It WILL increase your shot damage by 100% because that is how many more shots you will fire. So, in essence, 1% haste increases your auto shot damage by 1%, but does not affect other abilities that exist independently of your weapon’s delay.

Armor Penetration: TBD. Need the Lich King-era/level 80 armor formula and typical boss armor to be able to comment.


Modifiers which specifically affect Auto Shot

* (general) Improved Aspect of the Hawk only triggers from “normal” ranged attacks. This effect gives haste, and ironically, will be triggered more frequently with a higher attack rate.
* (MM) Wild Quiver has a 12% chance of firing an additional auto shot that deals half damage, but as nature damage. This means it effectively increases auto shot damage by at least 6%. The extra damage is unmitigated by armor, however.
* (Haste) Haste is essentially an autoshot-only effect.


Arcane Shot (AP scale factor: 15%)
Arcane Shot is the most basic cooldown-based ability the hunter has. Press the button, out pops extra damage. Max rank is (492 + .15*AP) arcane damage for 353 damage.

Special characteristics:
* (Armor) The damage is not physical, so the shot is not affected by armor.
* (SV) The ability shares a cooldown with the Survival-only ability Explosive Shot.
* (glyph) Glyph of Arcane Shot reduces the mana cost by 20% when a sting is active.
* (MM) Improved Arcane Shot increases the damage by 15%. Effectively that raises the AP scaling on the ability to 17.25%.
* (MM) Improved Steady Shot gives a steady shot a 15% chance to increase the damage of an arcane shot by 15%. However, this affect can also be applied to higher damage abilities instead.
* (MM/SV) Survival Instincts increases the crit rate of Arcane Shot by 4%.
* (SV) Lock and Load gives 2 free-without-cooldown applications of either Explosive or Arcane Shot. Some marksmen may go deep enough into SV to pick up this talent for use with Arcane Shot. Some survivalists may choose to use Arcane Shot for LnL procs since it does not have an implicit cooldown while the shot finishes its effect like Explosive does. (This is, in fact, not that smart.)

Related: (SV) Explosive Shot (AP scale factor: 24% primary, 8% secondary)
Survival’s ultimate is supposed to replace Arcane Shot. It comes with some liabilities toward things like crowd control, and takes 2 seconds to become fully used, which sometimes inhibits the ability considerably. The ability does, 263 + .08*AP fire damage three times to a target it is shot at. One of the misnomers of this ability is that it does 25% damage on the successive ticks, and thus effectively does 385 + .12*AP damage. In actuality, this damage is what is done to opponents within 5 yards of the target. It still does full damage on all three ticks, assuming the target lives that long, so essentially it does 729 + .24*AP.

Special characteristics:
* non-physical shot, so unaffected by armor
* Can potentially deal many more times its listed damage in AE situations.
* Survival Instincts increases the crit rate by 4%.
* T.N.T. increases the crit rate by 9%.
* Sniper Training increases the damage by 6% if a range of 35 yards is maintained.
* It (or Arcane Shot) can trigger Hunting Party.
* Lock and Load is primarily designed to allow survivalists to re-shoot this ability after either a successful tracking, or occasionally while serpent sting is active. Lock and Load is a tricky talent to work around, especially since the instinct is to want to mash the buttons on explosive when it triggers. See shot rotations section for more details about implications.

[Arcazua]

III. Shot Mechanics and Other Related Abilities (cont.)

Serpent Sting (AP scale factor: 20%)
Can be applied to each target being fought for damage-over-time. Precludes other sting abilities. Max rank deals 1210 + .2*AP nature damage over 15 seconds.

Special characteristics:
* Unaffected by armor.
* Cannot crit. As a result, it’s scaling is much flatter than other abilities.
* (Glyph) Serpent Sting glyph extends its duration to 18 seconds. This increases damage per application by 20% if not overwritten, and thus AP scale factor to 24%.
* (Glyph) Steady Shot glyph increases Steady Shot damage by 10% while Serpent Sting is active. This is considered an essential component of most hunter shot rotations.
* (MM/gen) Improved Stings increases the damage output of the ability by 30%. This, with the glyph, increases the scale factor to 31.2%.
* (MM/SV) Can trigger Lock and Load. This is often the primary means of doing so during boss battles.
* (SV) Noxious Stings increases all hunter damage by 3% when Serpent Sting is active.
* (MM) Has significant interaction with Chimera Shot.


Multi-Shot (AP scale factor: 20%)
Multi is a 10-second cooldown ability that fires at three targets, dealing normal (but normalized to 2.8 delay) damage to up to three targets, plus an extra 408, for 454 mana. In a single-target situation, Multi Shot becomes a free extra attack, although it is questionable whether it is worth the mana to do so. Multi is unlikely to be part of a standard rotation, but may be substituted when secondary targets can be hit for collateral damage. It also shares its cooldown with Aimed Shot and Chimera Shot.

Special characteristics:
* (Glyph) Multi-Shot Glyph reduces cooldown by 1 second. This does NOT affect linked shots.
* (MM) Barrage and Improved Barrage increase the damage and crit rate by 12%.
* (MM) Concussive Barrage can be triggered from multi.

Related: Aimed Shot (AP scale factor: 20%)
Aimed Shot does equal damage to Multi, but for a single target, for slightly less mana. It also leaves a 50% anti-healing debuff and is fired instantly (meaning it can be used on the run, unlike Multi.) It is the 11-point talent for marksmanship, which other specs might or might not have.

Special characteristics:
* (Glyph) Aimed Shot glyph reduces mana cost by 20%.
* (MM) Also affected by Barrage and Improved Barrage.
* (MM) Piercing Shots causes it to ignore 6% of enemy armor.
* (MM) Improved Steady Shot gives steady shots a 15% chance to increase the next Aimed’s damage by 15%. This can also be applied to Arcane or Chimera.
* (MM) Marked For Death increases the critical strike bonus damage by 10%.
* (SV) Sniper Training increases damage by 6% if 35 yard range is maintained.

Related: (MM) Chimera Shot (AP scale factor: 6% with serpent)
Chimera is an ability that interacts with stings. It is essentially worthless without a sting active, however it does refresh existing stings, meaning a single serpent sting can last throughout an entire fight. It does 40% of the damage of a full-term Serpent Sting in addition to a portion of weapon damage, so it effectively scales at a rate of about 6%. Still, it does a tremendous amount of damage before gearing improves, albeit the mana cost is extremely high. (807 mana)

It can also be used with the other stings to produce other effects. Since marks hurts for mana, it can be used with Viper Sting to recover some mana.

Special characteristics:
* Affected by Rapid Killing, Improved Steady Shot, and Marked for Death.


Steady Shot (AP scale factor: 22% with glyph)
Deals 252 + .2*AP for a mere 216 mana. In terms of DPM, this is one of the better shots, however it comes with a 2 second cast time, which is affected by haste. With quiver, this is reduced to the point that beast masters can bring it to the minimum of 1.5 seconds (GCD), but marks and surv hunters will need an additional 15.9% haste (about 525 rating) to achieve this same feat. Considering that steady shot is the ability you will be using in the absence of anything more important, reducing this time is extremely useful, particularly since it can affect the timing of other abilities. See rotations.

Special characteristics:
* Deals 175 additional damage against dazed targets. (Whoopee.)
* (Glyph) Steady Shot glyph increases shot damage by 10% while serpent sting is active.
* (gen) Suffers little pushback with Careful Aim.
* (MM) Improved Steady Shot creates a 15% chance after a steady to enhance the next other single-target special by 15%.
* (MM) Also works with Rapid Killing, Piercing Shots, and Marked for Death.
* (SV/MM) Survival Instincts increases crit rate by 4%.
* (SV) Sniper Training increases damage by 6% if sufficient range is maintained.


Rapid Fire
Rapid Fire gives the hunter 40% additional haste for 15 seconds. This means that the hunter will fire 21 seconds worth of autoshot in the span of what would normally be 15 seconds. So each activation adds 6 autoshot seconds worth of DPS. Assuming steady is haste-capped, there is no additional direct effect.

Special characteristics:
* Adds 6 seconds of auto per 300 with no talents considered.
* Adds 6 seconds of auto per 180 with Rapid Killing.
* Adds 12 seconds per 315 (or 195) with Readiness activated explicitly to reset Rapid Fire. Readiness also has a 3 minute cooldown. Ultimately, this does little to itemization effects, and will not be considered, but is mentioned for posterity. (Someone might try to create overall DPS charts from this info, idk.)


(BM) Bestial Wrath
Pet does an extra 50% damage for 18 seconds. (120 sec cooldown, 100 glyphed.) Also adds 10% damage to the hunter during this period with The Beast Within, which is virtually a given.

Special characteristics:
* Adds 9 seconds worth of pet DPS and 1.8 seconds worth of hunter DPS per 100 seconds.
* Can be triggered from Readiness, which essentially adds an extra activation per 2 normal, or 27 seconds of pet DPS per 200. Effectively, almost a 15% damage increase for the pet. (This requires not using a 51-point Beast Mastery build.)


The only other ability that gets used is Kill Shot, which is not even worth worrying about when it gets used MAYBE twice during a typical boss fight.

[Arcazua]

IV. Pet Damage

In terms of itemization, the central things to consider about pets are the following:

Pets use 22% of your attack power, according to an outside source…this was a different amount before Lich King, so if this is wrong, please tell me. If the pet does not attack with anything that scales, this means 1 hunter AP = .015 pet DPS. For beast masters, this figure will be higher after all effects are considered. Between haste modifiers, damage modifiers, and additional crit, this will probably be closer to .037 pet DPS. Clearly, beast master hunter pets will scale more quickly, but it is extremely dramatic, and BM pets already outdamage the hunter proper at low gear levels. This should indicate that attack power is an EXTREMELY important attribute for BM.


Pets gain 100% of your hit rating. This is not displayed on the tooltip. I have no idea if Careful Aim also adds 1% to pet hit rate; I assume not. Either way, a non-BM pet will deal somewhere around 900 DPS, and a BM pet will do over 1600. (These numbers from plugging my own character into Shandara’s spreadsheet and tweaking talent points.) If 33 points of hit rating add 1% DPS, then 1 hit rating should add 1/3300 of your pet’s DPS, which is roughly .48 DPS for BM and .27 DPS for non-BM…assuming you are not hit-capped, of course.


Pets also benefit from crit rating indirectly through Go For the Throat. This is an essential talent that all hunters should have if they are concerned about DPS. If, crudely speaking, a hunter has 25% crit and fires 8 shots in 10 seconds, they will probably crit 2 of them and add an entire focus bar every 10 seconds. Considering it takes a pet 6 seconds to dump this focus on Claw, Bite or Smack, and they do regenerate some focus of their own during this time, this keeps them from being focus-starved. If an average claw deals 150 damage, this is an extra 60 DPS for the pet. (In practice, it turns out to be much more.) However, the specifics of generating crit rate into pet DPS are about as clear as mud.

Although, technically, there will come a point where crit rate will not add much at all to a pet’s crit rate, let us assume (and assuming is dangerous) that the pet will always be able to use up all its focus and be looking to you for more. That is, Go For the Throat will always generate meaningful focus that lead to 3 claws. (Or bites or smacks.) It should actually be 3.33, but we’re otherwise estimating high since it won’t always be useful focus.

A typical rank 11 claw will hit for around 155 damage for a ferocity pet. So a crit will generate about 465 damage vicariously through the pet.

TBD. Need average shot speeds.

[Arcazua]

V. Shot Rotations

Every hunter spec has a certain shot priority they tend to favor. It differs by spec since some gain abilities from the talent tree they use, and in other cases certain abilities just shine more. What we will be looking at here is shot rotations from an EXTREMELY GENERAL POINT OF VIEW. It might not be 100% accurate, but it should be accurate enough.

The reason we need to know about shot rotations is so we know which shots to accentuate, and recognize the importance of different factors. Marksmanship, for instance, will only fire Serpent Sting once, and let Chimera Shot keep it active. Because SS cannot crit, in this regard, marksmanship gets more mileage than other specs from crit rating, because every shot they fire can crit. As a result, we don’t need to know extreme specifics, but we do need things to be somewhat accurate.

We are going to say for the sake of argument that a global cooldown with latency included will give us approximately 35 GCD’s per minute. (This is about 1.7 seconds.) Everything here will be based on the premise that a certain action will happen roughly so many times per minute, since most actions are on a cooldown cycle that roughly corresponds with X times per minute.


Beast Mastery
Beast Mastery is probably the simplest spec to keep tabs on. A typical beast master’s rotation looks like this:
“Keep Bestial Wrath off cooldown, keep serpent sting up, and mash steady shot.”

Additionally, due to Serpent’s Swiftness, haste rating is a complete non-issue with the firing of Steady Shot. This makes calculating what BM does a lot more painless than other specs.

With a Bestial Wrath glyph and a Steady Shot glyph, a beast master will reactivate serpent sting when it drops, (4 GCDs per minute,) and use Bestial Wrath every 100 seconds. If we include Readiness in our spec, this means we’ll use Bestial Wrath 3 times per 200 seconds, with a fourth global cooldown for Readiness. Without Readiness, this is .6 GCD’s per minute. With it, it becomes .8. A very small difference.

Either way, we can anticipate that a beast master will fire 30 other specials per minute. The bulk of these will be Steady Shot. Depending on mana, the beast master might use Arcane Shot when it is off cooldown. With a 6 second cooldown, Arcane would get fired 10 times, and the remaining 20 would be Steady. We’re going to go with this, but you are welcome to disagree. Ultimately, Steady Shot scales better, albeit it is influenced by armor.

A typical autoshot from a beast master will be 20% faster than other specs thanks to Serpent’s Swiftness. Most weapon speeds are 2.8-2.9. With quiver and SS, this is about 30 autoshots per minute.

Nothing affects specific shot damage

Beast Mastery rotation:
30 autoshots per minute (4.93 damage per minute per AP normally, 5.91 with 20% haste)
20 steady shots per minute (4.4 DPMAP)
10 arcane shots per minute (1.5 DPMAP)
4 serpent stings per minute (.8 DPMAP)
Bestial Wrath
Total: ~12.6 damage per minute from AP, or .210 DPS. Including pet damage, this is .247 DPS.


Marksmanship
Marksmanship relies on a much more mana-hungry rotation. Chimera Shot is a very mana-costly shot, however it rewards the hunter with very good damage when Serpent Sting is active. On the plus side, marks only needs one serpent sting since chimera renews it.

Chimera is on a 10 second cooldown, and will get used 6 times per minute. Around this, Arcane Shot will get used 10 times. The rest will be steady shot. The greatest snag with marks is the mana consumption will lead to more time spent in Aspect of the Viper. We’ll consider that later.

Autoshot gets fired about 25 times per minute.

Two other things to be careful for -- (1) Lock and Load is often incorporated in marksmanship builds. (2) Steady Shot does not fire in 1.5 seconds. With no haste, it fires in 1.74 seconds. The 19 steady shots we anticipate, slowed down, end up being more like 16 steady shots. This is notwithstanding that it may throw timers off by a second, but we’ll ignore this.

Marksmanship rotation:
25 autoshots per minute (4.93 DPMAP, +12% chance of extra half damage shot = 5.22 DPMAP)
16 steady shots per minute (3.52 DPMAP)
10 arcane shots per minute (1.5 DPMAP, *1.15 Improved Arcane = 1.725 DPMAP plus 10% crit bonus)
6 chimera shots per minute (.36 DPMAP, *1.0225 Improved Steady = .368 DPMAP plus 10% crit bonus)
Serpent Sting maintained automatically (.8 DPMAP, * 1.3 Improved Stings = 1.04 DPMAP)
Total: 11.88 damage per minute from AP, or .198 DPS. Including pet damage and 10% Master Marksman bonus and 5% RWS, this is .246 DPS. This is, curiously, almost identical to BM.


Survival
Survival is easily the hardest to model because of Lock and Load. In fact, Marksmanship CAN have Lock and Load, and often does, so we’ll use our modeling of Lock and Load and revisit marks briefly.

Explosive Shot is also a bit of a screwball because of the “over time” component of the shot. This can create havoc on LnL.

Assuming Lock and Load never procs, the survivalist will fire 4 serpent stings per minute, 10 explosive shots, 6 aimed shots, and fill in the rest with steady. Lock and Load has a 2% chance per second to proc, (6% per 3 seconds,) which means it will barely come up once per minute. When it does, it’s good damage, but in essence it leads to an extra 2 explosives rather than steadies per minute. So surv will likely fire 13 steady shots per minute, which scales to 11 when haste is considered.

For marks, this is an extra 2 arcane shots. Since Arcane scales more slowly than Steady, I’m not advocating this, but to each their own. If you can fire serpent stings at multiple targets, you can up your proc rate, I suppose.

Survival rotation:
25 autoshots per minute (4.93 DPMAP)
12 explosive shots per minute (2.88 DPMAP, plus 13% crit chance T.N.T. and Survival Instincts, plus 6% damage Sniper Training = 3.57 DPMAP with Mortal Shots)
11 steady shots per minute (2.42 DPMAP, plus 6% damage Sniper Training = 2.56 DPMAP)
6 aimed shots per minute (1.2 DPMAP)
4 serpent stings per minute (0.8 DPMAP)
Total: 13.06 DPM, or .217 DPS. With 3% Noxious Stings and pet damage, this is .239 DPS per AP. Ever so slightly lower than the other two specs, but remember that surv also has a higher crit rate, which will accentuate the effects.



Conclusion

Each of the specs approaches 1/4 DPS per AP without any crit considered, except things that affect specific shots. With a 20% crit for marks/BM or 25% for surv, they are all around .29 to .30 DPS per AP. For simplicity’s sake, since it appears to be fairly neutral overall, we will say that one point of attack power adds 0.3 DPS. As gear improves, and thus crit rates are higher, this will change, but it’s still a good rule of thumb.

Note that this figure does not include any raid buffs.

[Arcazua]

VI. Effects of ratings and attributes

The difficulty with evaluating the usefulness of various ratings is that it more or less requires an accurate DPS total before crit, before hit, before pet. For different players, these are wildly different numbers, based on gear and performance. Previous versions of AEP have gotten into considerable trouble over this very topic in the past. Therefore, I’m going to do things in general terms so you can plug your own numbers in first, and then use what I consider to be likely estimates for this stage of the game.

White DPS
Just to clarify, the term “white DPS” refers to the DPS on your tooltip when you mouse over damage on your character sheet, which is your extreme basic Auto Shot damage. It has often been extended to the damage also done with specials, with no crits, no misses, or anything else funky. And definitely no pets.

To give you a feel for how much that is, a non-BM hunter that deals 1000 white DPS, and has a 20% crit rate, would deal roughly 1260 DPS personally. Tag on a pet doing around 700 and that hunter is at nearly double what they would have been previously. My hunter was listed at 2667, and working backwards, I found out that that was basically 1300 non-crit DPS. So cutting your overall DPS in half might not be a bad rule of thumb.

For beast masters, it will be different since your pet alone is often more than half your damage. Switching my character’s spec to BM and making an appropriate rotation, 3215 damage was split as 1749 pet and just 1465 hunter. After removing crits, this was just 1163. So one-third may be a better estimate for a beast master that can’t definitely say what their non-crit damage is.

Of course, if you can find the exact figure, that’s a lot better than rule-of-thumb guesstimates. We’ll need this figure for determining the value of crit.



Crit Rating
At 46 crit rating to 1%, but Mortal Shots effectively providing an additional 30% to the effect of crits, it becomes more like 35 crit rating to 1% damage. (35.38 to be specific) So effectively, take your white damage and divide it by 3500 to get the value of 1 crit rating.

Crit rating does depend *slightly* on not missing, since you crit exactly 0% of the shots you miss. (It was once believed that these two did not affect each other, but this has been shown to be false.)

So, it takes a white DPS of about 1050 to match the effect of attack power, 1:1. Considering that crit rating carries twice the itemization cost of AP, one would hope you can do a bit better than this, and I’m sure some day a white DPS of 2100 might very well be reasonable. For me, personally, this appears to work out as about 0.37 DPS per crit rating…right now. I’m still wearing my T6 gear from the last expansion and using a screwball spec.


Hit Rating
Hit Rating is a little bit different from the others, because we actually want to use total damage. Yes, your altogether in-the-end, with-your-pet total damage.

It takes 33 hit rating to equal 1% chance to not miss. That’s 1% of your damage you get back. Assuming you aren’t already hitting 100%, a point of hit rating adds 1/3300th of your damage. So if you were dealing 2500 DPS already, you’d get almost 0.75 DPS per point of hit rating. It takes 1980 DPS to make this better than AP on your items.

Of course, it comes with the catch…too much of a good thing is not always good. You can’t hit 102% of the time. With a 9% chance to miss against bosses, and quite a few ways to improve your chance to hit, you might not need any more hit rating, at which point the value of it is exactly zero. (Other than giving you the insurance to remove other gear without adding chance to miss.)

For simplicity’s sake, let’s use the 2500 DPS figure that I see quoted referring to WWS expectations right now, and say that 1 point of hit rating is roughly .75 DPS.


Haste Rating
Haste Rating only affects your auto shot DPS, which is a relatively minor portion of your overall damage. Specials DPS trounces your auto shot damage these days, making auto probably only 20% of your total DPS once the pet is factored in. Haste Rating uses the same exactly conversion that Hit Rating does, and 1% increase in haste does end up leading to a 1% increase in damage, so basically take the value of your hit rating and divide it by 5.

I’m going to regard Haste Rating as being worth .15 DPS, by that explanation.

However, let’s also remember that haste rating is very important to non-beast master’s for helping tighten up rotations. Steady Shot needs about 16% haste, which is a LOT of haste rating, in order to be firing at the minimum 1.5 global cooldown. So in the end, haste rating might be worth a bit more. Steady Shot is really just the filler shot, and is not necessarily worth a ton of damage in MM and SV builds. Best case, it’s maybe another 50% of the value we just picked out (or 30% of total damage) that were hastening.

One can argue that it makes the other shots fire more in-line with their supposed cooldown timers. I have to refute this claim, however. Unless you had 0.5 seconds latency, and every special took you exactly 2.0 seconds, (but more for Steady Shot,) you are just as likely to squeeze in an extra steady shot before your cooldown-based special and delay the other attack, or fill your rotation with dead time while you wait for it. I don’t think there’s any net effect there.

I’ll give you the 50%, though -- .22 DPS for non-BM.


Armor Penetration Rating

Using Elois's work on the subject, where "154 ArP gives a 2.23% damage increase to a boss with 7000 armor (after sunders, etc.,)" a 2.23% damage increase is, to make up numbers out of my butt, 66.9 DPS for BM or marks, and 55.75 DPS for surv. (Using 3000 and 2500 total DPS.)

But that's 154 ArP. That means a single rating point is worth .43 DPS for BM or marks, or .362 for surv.


Agility

Agility is worth 1 AP and .55 crit rating. So if AP is 0.3 DPS and CR is 0.37 DPS, then 1 agi is .50 DPS.

Of course, surv has to go and muck things up. Lightning Reflexes means you really have 1.15 agility per point on your armor. It also means you get an extra .25 DPS per point of agi. So instead of 1 AP and .55 CR, you end up with (1*1.15*1.25) AP and (.55*1.15) CR = .66 DPS per agi. Effectively, agility is worth 33% more to survivalists, and this actually makes it better to find on items than AP. Again, with no raid buffs considered.


Stamina

Stamina is worth 1 AP to survivalists that have Hunter Vs. Wild. That’s about it. So 0.3 DPS if you got it, and nada if you don’t.

Of course, stamina also adds 10 health. Give that your own value. Because that’s subjective, and theoretically maybe even worth nothing, it will not be regarded here.


Intellect

Same goes for intellect, but for the low marks talent Careful Aim, which most hunters will have. So int will simply be considered worth 1 AP.

However, it also adds 15 mana, and unfortunately, that counts for a great deal. We haven’t discussed mana efficiency yet, which is a completely yucky way to approach itemization, but I think it’s going to need to be done.

[Arcazua]

VII. Mana Efficiency

As with previous versions of AEP, this section will be highly subjective, and depend greatly on your own individual numbers and other particulars. What I’m interested in is not getting an exact answer, merely a decently-acceptable estimate for judging by. Shandara’s spreadsheet says I get .707 DPS per point of intellect, and only .236 for AP -- clearly that work believes that the mana that intellect generates is worth nearly a half a point of DPS. I don’t know how accurate that is, but I want to investigate it a *little*. All told, the spreadsheet is much more likely to be accurate because (a) it’s more comprehensive and exact, and (b) it considers WAAAY more things than I’m sure I’ll think to consider. However, we need to take a look.

Intellect and MP5 indirectly help our DPS because they improve our longevity with mana. Blizzard has decided our route to not being completely out of mana is to switch to Aspect of the Viper and lose half our damage in order to regain a portion of our mana pool. Obviously, we want to avoid this as much as possible.

With all gear, talents and buffs cleared, Shandara’s spreadsheet tells me my hunter at level 80 with nothing equipped would have a mana pool of around 6119. (Let’s just call this 6100 so we don’t bicker over racial differences.) Without clearing those things, I’m listed at 9768. Because gear will improve and my hunter only has 333 int buffed, I’m going to nominally declare an average mana pool to be 12k.

How much mana you exhaust is going to depend on your spec and shot cycle, of course. Using the rotations above, this is the rough expenditure of mana per minute:

BM - 20 steady * 212 + 10 arcane * 339 + 4 sting * 454 + 0.6 bestial wrath * 424 = 9700
MM - 16 steady * 212 + 10 arcane * 339 + 6 chimera * 807 = 11624, -10% efficiency = 10461
SV - 10 explosive * 297 + 11 steady * 212 + 6 aimed * 338 + 4 sting * 454 = 9146. (2 of 12 explosives are free from Lock and Load.)

The rotations suggested in this work are not necessarily the most ideal for a particular spec, however they are a possible and very likely one. What should become immediately obvious to anyone thinking ahead is that marksmanship utterly stinks for mana with good reason -- not only do they have extra mana consumption, but the other two specs also have mana return talents that haven’t been considered. Efficiency has already been factored in (and could potentially be in a BM or SV spec,) so there isn’t much left to tilt MM favorably other than blowing Chimera Shot on a Viper Sting, which costs a tremendous amount of damage compared to the gain. As a result, marks is much more likely to spend time in viper.

Alright, let’s look at mana returned to the player now.

Shandara’s sheet suggests I have more MP5 without buffs than with, for some strange reason, so we’re going to have to work this out ourselves. Let’s forget about hunter regen for a minute. Yes, there are a few abilities we’ll have to look at shortly, and also the possibility of MP5 on gear, but let’s not worry about that and just look at potential buffs.

91 MP5 - Blessing of Wisdom
80 MP5 - Mana Spring Totem
150 MP5 - Replenishment (.25% of 12k each second) with 100% uptime
16 MP5 - Spicy Fried Herring
24 MP5 - Elixir of Mighty Mageblood
19 MP5 - Exceptional Mana Oil (maybe x2)
-----------------------------------------------------
Total: 380 MP5, or 4560 mana per minute

Now, you’re not necessarily going to have all of this. In fact, if you’re cheap like me, you won’t have any of the consumables except when you really need them. But let’s suppose this is offset by any gear you might have and that your actual MP5 is around 380. And I haven’t forgotten about Invigoration or Thrill of the Hunt.

On crittable shots, Thrill of the Hunt returns 40% of the mana. At a modest 25% crit rate (extremely modest for surv, anyway,) you’ll recover 10% of the mana that isn’t from serpent sting. This works out to roughly 733 mana per minute. In actuality, it will probably be more as your crit rate surpasses 25%.

Invigoration is more difficult. With BM talents, Shandara suggests my pet should crit nearly 38% of the time, and there isn’t much I can argue with in the calculations. If your pet uses a special every 1.5 seconds, (and I’m not positive the pet GCD is 1.5,) that’s a trigger almost every 4 seconds for 1% mana. 15 * 120 = 1800 mana per minute.

So the net mana loss per minute for each spec:

BM: 9700 - 4560 - 1800 = 3340 mana per minute. (278 MP5) This should last for about 3.6 minutes.
MM: 10461 - 4560 = 5901 mana per minute. (492 MP5) This should last for barely over 2 minutes.
SV: 9146 - 4560 - 733 = 3853 mana per minute. (321 MP5) This should last for 3.1 minutes.

Ouch, marksmen.

When Aspect of the Viper is activated, Shandara’s says I get over 400 mana per second from it. I have no idea where this number comes from, but if we go easy on mana usage during Viper and it balances outside regen, Viper will refill us in 30 seconds. I’m in favor of keeping this as simple as we can.

[Arcazua]

VIII. Itemization in Mana Efficiency

Oh right, we’re not doing this mental workout to know about mana usage. We’re doing it to know about the impact that MP5 and int would have.

To make this simple and noticeable, I’m going to pretend we add 100 of each stat, and then divide the effect by 100. The benefit should be reasonably linear. Adding a single batch of 15 mana is going to be hard to follow.


Intellect

Adding 100 intellect beyond our 12k mana pool would raise the total to 13650 thanks to Kings. Marksmen would climb to 13716 with Combat Experience.

With that extra mana, it should take slightly longer to burn through it. Let’s assume (eek!) that the additional mana pool has a negligible effect on viper. It doesn’t. However, you’ll also last longer initially and so it should get you closer toward finishing the fight on one viper activation rather than two, or something like that.

Beast Mastery
Formerly: 0.5 out of 4.09 minutes spent in Viper = 12.2% of fight, or 6.1% damage lost.
With 100 int: 0.5 out of 4.59 minutes spent in Viper = 10.9% of fight, or 5.45% damage lost.
Gain of 0.65% of full DPS. At 3000 DPS, this is about 19.5 DPS, so 1 int is worth roughly .195 DPS.

Marksmanship
Formerly: 0.5 out of 2.53 minutes spent in Viper = 19.7% of fight, or 9.9% damage lost.
With 100 int: 0.5 out of 2.82 minutes spent in Viper = 17.7% of fight, or 8.9% damage lost.
Gain of 1.0% of full DPS. At 3000 DPS, this is about 30 DPS, so 1 int is worth roughly 0.3 DPS.

Survival
Formerly: 0.5 out of 3.61 minutes spent in Viper = 13.8% of fight, or 6.9% damage lost.
With 100 int: 0.5 out of 4.04 minutes spent in Viper = 12.4% of fight, or 6.2% damage lost.
Gain of 0.7% of full DPS. At 2500 DPS, this is about 17.5 DPS, so 1 int is worth roughly .175 DPS.

Yes, I put survival at 500 DPS lower than the other two. You’re welcome to argue with these DPS numbers, and scale them up accordingly. If you do 4500 DPS as BM or marks, great, increase the effect by 50%.

There are a zillion reasons why you would disagree with my calculations. I understand this. But this is the best model I can create without a super-mega-ultra spreadsheet that would still probably miss things or get things wrong anyway. I have a fatalistic view toward trying to calculate the game perfectly in simulation. I strive for reasonably accurate. Unless there’s something glaring I’ve missed, this ought to be.


MP5

MP5 regenerates an extra 12 mana per minute. In light of this, I’m leery to add a full 100 MP5, since this will not be truly linear. I’m going to play it a little safer and only add 20. So an extra 240 mana per minute. This will lower the net mana loss by that amount.

Beast Mastery
Formerly: 0.5 out of 4.09 minutes spent in Viper = 12.2% of fight, or 6.1% damage lost.
With 20 MP5: 0.5 out of 4.37 minutes spent in Viper = 11.4% of fight, or 5.7% damage lost.
Gain of 0.4% damage. At 3000 DPS, this is about 12 DPS, so 1 MP5 is worth roughly 0.6 DPS.

Marksmanship
Formerly: 0.5 out of 2.53 minutes spent in Viper = 19.7% of fight, or 9.9% damage lost.
With 20 MP5: 0.5 out of 2.62 minutes spent in Viper = 19.0% of fight, or 9.5% damage lost.
Gain of 0.4% of full DPS. Same as BM.

Survival
Formerly: 0.5 out of 3.61 minutes spent in Viper = 13.8% of fight, or 6.9% damage lost.
With 20 MP5: 0.5 out of 3.82 minutes spent in Viper = 13.1% of fight, or 6.5% damage lost.
Gain of 0.4% of full DPS. At 2500 DPS, this is about 10 DPS, so 1 MP5 is worth roughly 0.5 DPS.

[Arcazua]

IX. Putting it All Together

These are the numbers that the work above would suggest. Along with the many disclaimers I made before, I’ll make one more: This numbers are by no means exact. They were found by cutting quite a few corners, and if you read through the entire work, you’ll probably find a few places where either I took a shortcut you don’t like or picked some numbers that don’t match your’s. So take it or leave it, here’s my results:

AP is worth 0.3 DPS
Agi is worth 0.5 DPS, or 0.66 to survival
Crit Rating is worth 0.37 DPS
Hit Rating is worth at least 0.75 DPS when it isn’t capped
Haste Rating is worth 0.22 DPS, but only 0.15 for beast mastery
Stamina is worth 0.3 DPS for survivalists with Hunter Vs. Wild
Int is worth: 0.6 DPS for marks, 0.5 for BM, 0.475 for surv
MP5 is worth 0.6, or 0.5 for surv
Armor Penetration rating is .43, or .36 for surv.


Well, that’s all good and fine. But how ‘bout some integers?

Rounding a smidge:


Beast Mastery:
AP - 4
Agi - 7
Crit - 5
Hit - 10
Haste - 2
Sta - 0
Int - 7
MP5 - 8
ArP - 6

Marksmanship:
AP - 4
Agi - 7
Crit - 5
Hit - 10
Haste - 3
Sta - 0
Int - 8
MP5 - 8
ArP - 6

Survival:
AP - 4
Agi - 9
Crit - 5
Hit - 10
Haste - 3
Sta - 4
Int - 6
MP5 - 7
ArP - 5


With those in mind, let's also look at gems...(all examples are with WotLK blue-text gems)

BEAST MASTERY & MARKSMANSHIP:
Best overall - Rigid Autumn's Glow: 16 hit rating (160)
Best red - Pristine Monarch Topaz: 8 hit/16 AP (144)
Best yellow - Rigid Autumn's Glow (160)
Best blue - Lambent Forest Emerald: 8 hit/3 MP5 (104)
If hit capped - Bright Scarlet Ruby: 32 AP (128)
Red - Bright Scarlet Ruby (128)
Yellow - Wicked Monarch Topaz: 16 AP/8 crit rating (104)
Blue - Infused Twilight's Opal: 16 AP/3 MP5 (88)
Meta - Swift Skyflare Diamond: 42 AP / minor run speed increase (168)
alternative: Relentless Earthsiege Diamond: 21 agi / 3% crit bonus (147+)

SURVIVAL:
Best overall - Rigid Autumn's Glow: 16 hit rating (160)
Best red - Glinting Monarch Topaz: 8 hit/8 agi (152)
Best yellow - Rigid Autumn's Glow (160)
Best blue - Vivid Forest Emerald: 8 hit/8 sta (112)
If hit capped - Delicate Scarlet Ruby: 16 agi (144)
Red - Delicate Scarlet Ruby (144)
Yellow - Eeadly Monarch Topaz: 8 agi/8 crit rating (112)
Blue - Shifting Twilight's Opal: 8 agi/8 sta (104)
Meta - Relentless Earthsiege Diamond: 21 agi / 3% crit bonus (189+)

I'm gonna say a gem slot is worth the best with hit capped, so a random socket is worth 128 (144 for surv) and a meta is worth 168 (189 surv).







FUTURE SCALING

One of the biggest downfalls of a system like this where a lot of the values used are based on fixed values that will not be the standard six months from now is that the scaling will not stay properly intact, even if you trust it now. The critical thing to remember is that all sources of damage that are not AP-based are going to scale with your damage total, whereas AP-based damage will not. However, AP will scale off the build-up you have of those other ratings.

In other words, if you are doing 3000 DPS, and add a bunch of AP to take you to 3200, and then a bunch of crit to 3350, you could add the same crit to take you to 3125, and then the AP after that to get to 3350. Depending on which order you do it in, the stat added later has increased value. So we'll see how accurate the scaling remains. Note that some of the differences between the surv column and the other two specs are because I regarded surv as doing ~15% less damage.

But remember, regardless of what single stat adds the absolute most damage, don't forget that there is a balance to maintain. If you completely throw it out of whack by doing nothing but stacking attack power, there will come a point where you're better off adding crit rating.

Time will tell, and I will no doubt have to rework the system, but what matters -- for right now -- is that we can pick decent start-up gear for the expansion. I only really hope AEP just does its job for that.