This post is not meant to tell you whether stat X is better than stat Y. Use Shandara's spreadsheet for that. It also does not, and cannot, show how all hunter stats interact with each other - you would need at least a 7-dimensional graph to represent this with an axis for each stat.
If you are interested in the math and data behind the graphs, look here and here. The more complicated math is pulled from Shandara's spreadsheet.
=Basic Stat Analysis (pre-Talents)=
Each stat is not in a vacuum. They have synergy with each other and with certain talents. The first section here is merely taking a look at the most basic operations of these stats to provide a framework for everything else.
Scales linearly. Consider an ability that has 500 base damage and scales with 20% of your Ranged Attack Power (RAP). We can look at the effects of adding 10 AP to a starting point of 4000, 5000, and 6000 AP
1. 4000RAP Î” 4010RAP = (500+4010*.2) - (500+4000*.2) = 2
2. 5000RAP Î” 5010RAP = (500+5010*.2) - (500+5000*.2) = 2
3. 6000RAP Î” 6010RAP = (500+6010*.2) - (500+6000*.2) = 2
Notice that all of these functions can be reduced to 10*.2 or more generally, Î”RAP*Coefficient. The chart below shows that scaling is completely linear
Increasing AP will also increase the value of critical strike rating, armor penetration, haste, and hit. In other words, the harder your shots hit for, the more value they get from being critical, the more value they get from ignoring armor (a percentage reduction), the more value they get from being more frequent, and the more value they get from actually landing. For instance, having 5% crit with 500 AP is a bigger deal than having 5% crit with 300 AP.
All hunter shots and stings benefit from attack power and your pet also gets benefit from this.
Scales linearly. With mortal shots and a 3% crit meta, our special shots do 237.8% damage when they crit compared to 100% damage on a normal hit. If your normal hit is 1000, your crit is 2378. The actual crit modifier obviously changes the value of crit, but has no effect on its scaling. Consider a few examples of adding 1% crit to various crit base values.
1. 20% Î” 21% = (.21*2.378+.79) - (.20*2.378+.80) = 0.01378
2. 40% Î” 41% = (.41*2.378+.59) - (.40*2.378+.60) = 0.01378
3. 60% Î” 61% = (.61*2.378+.39) - (.60*2.378+.40) = 0.01378
Notice that all of these functions can be reduced to Î”Crit%*CritMod-Î”Crit%. Piercing Shots can be considered as an addition to the crit modifier for the appropriate shots.
Similar to AP, crit will also increase the value you'd get from additional AP, armor penetration, haste, and hit. In other words, the more likely your shot is to crit, the more value they get from attack power, the more value they get from ignoring armor (a percentage reduction), the more value they get from being more frequent, and the more value they get from actually landing (see later section).
All hunter shots except for serpent sting and black arrow can crit. Crit has no direct effect on pets but does have an indirect effect with some talents.
This post strongly suggests that hunters are on a two-roll system to determine crits. This means that an RNG first determines if the ability is successful, and then determines if it is a crit. Thus hit will scale your crit until hit capped.
There is no crit cap but because you need to hit to crit your crit percentage is effectively a percentage of total landed (not missed) shots, rather than total shots.
Hit scales linearly in terms of a pre-talent/special abilities look at the stat. Any proc ability that requires a hit (such as Master Tactician), or any interaction between abilities that requires hits (such as serpent sting being on the target) will increase the value of hit. The chart below shows simple hit scaling not including those kinds of cases.
It is effectively a percentage of your damage potential, so the difference in hit will be of greater value the more damage potential you have. In other words, the difference between 97% hit and 98% hit with a shot that does 2000 damage is the same as between 98% and 99%, but the difference between 97%-98% hit of a 3000 damage shot is bigger than the difference between 97%-98% hit of a 2000 damage shot. Again, once talents and other interactions are considered it is more than this.
All shots and stings have an 8% chance to miss that can be countered by acquiring hit rating.
Agility grants both attack power and crit and thus scales like they do. Expose Weakness is affected in two ways; by uptime (due to crits) and the potency of the buff, which is effectively an additional AP component for agility.
Haste needs to be considered in two respects. One, its effect on auto shot which has no practical cap. Two, its effect on special shots which is effectively capped at the GCD of 1.5 seconds.
Let's look at a 2.9 second, 500 DPS gun with 15% baked in haste and the effect of adding 1% haste on top of 5%, 10%, and 15% more haste from gear per shot.
1. 5% Î” 6% = 500*2.9/(2.9/1.15/1.06)-500*2.9/(2.9/1.15/1.05) = 5.75
2. 5% Î” 6% = 500*2.9/(2.9/1.15/1.11)-500*2.9/(2.9/1.15/1.10) = 5.75
3. 5% Î” 6% = 500*2.9/(2.9/1.15/1.16)-500*2.9/(2.9/1.15/1.15) = 5.75
The formula here is DPS/100*1.15*Î”Crit% and again we see it is linear.
However, there is a bit more to it than that in the case of haste. Since haste does not affect each shot individually it has been argued that the fight duration needs to last at least long enough to see that "extra" shot. For instance, if you had a 2 second auto shot and were wondering about hasting this to 1.9 seconds, this point of view would contend that the fight needs to be 38 seconds long to see a benefit. This isn't quite true; there only needs to be a period of combat within that fight where FLOOR(Period/1.9,1) > FLOOR(Period/1.95,1) such as a 1.95 second window. In this way it is seen that haste's scaling can be viewed probabilistically.
For auto shot, haste increases the value of AP, crit, armor pen, and hit, much the same way that AP scales.
The effect of haste on special shots is completely separate from the effect on auto shots, except for some talents. Even then it is mostly convoluted, such as steady shot hasted to increase special shot frequency which will thus have a very slight effect on Expose Weakness uptime which in turn effects auto shot. The only special shots that are affected by haste are steady shot and volley. Volley scales exactly the same as auto shot does with haste, but note that the probabilistic nature here is a matter of volley tick frequency, not fully channeled volleys. Steady shot is soft-capped at 1.5 seconds from haste. It can continue to be made faster with more haste, but you will not see benefit in terms of a rotation because of the 1.5 second GCD limitation.
Assuming you do not have any wait time in your rotation, where you spend time waiting for a cooldown but are not affected by the GCD, haste will also scale your entire special shot rotation until you reach the soft cap of 1.5s steady shots. Beast Master hunters reach this through talents alone. How much it affects this is also affected by how frequent steady shot appears in your rotation. If your rotation consisted exclusively of steady shots (a poor "rotation") haste will scale it exactly the same as auto shot until soft cap, with the same probabilistic nature. The more instant cast shots included in your rotation the less effect haste will have on your special shots.
You need approximately 12.39 armor pen rating to reduce 1% of the targets armor. In actuality, it reduces a percentage of a theoretical armor pen cap which is normally slightly less then the targets actual effective armor. You would need 1239 armor pen rating to achieve 100% armor pen, but the current mechanics leave this at 2% mitigation from armor. Apparently it is possible to continue this and reduce boss armor below 0, doing more than unmitigated damage. For more information on armor pen see discussion here, mostly around page 18.
Armor pen increases the value of AP, crit, and haste for your physical abilities and damage that procs off of physical attacks. The harder your shots hit, the greater the difference between having pen and not having pen will be.
Armor penetration increases the damage of every physical ability the hunter has, which includes auto shot, steady shot, kill shot, aimed shot, and multi-shot. It has no effect on shots and abilities that do magical damage, such as chimera shot, arcane shot, and explosive shot.
For survival hunters with the Hunter vs. Wild talent, a percentage of stamina is also counted as attack power. This makes stamina exactly the same as AP for scaling purposes.
The AP component from this stat (with Careful Aim) scales the same as AP. It also reduces time spent in Aspect of the Viper, but this is beyond the scope of this article.
=Talents and Scaling=
Some talents scale stats in unique ways that may warrant further analysis of that stat's role.
Agility and crit will both increase the uptime of this ability. It should be noted that the role of agility here is complex considering it increases both the uptime of the buff and the power of the buff (25% agility). In most raid instances with typical gear though, 2 points in this talent tends to yield a high enough to keep a uptime. With a 1 second shot frequency, the formula for EW uptime is 1-(1-Crit%*EWPercentage)^7 where EW percentage is 33%/66%/100% per point. The following chart plots EW uptime for two and three points invested with a 1 shot per second frequency
This is a perfect example of diminishing returns, both in terms of getting more crit to increase uptime and adding more ranks to increase uptime. At very low crit levels, crit plays a significant role in EW uptime. With typical gear and raid buffs however, adding a bit more plays almost no role. For the most part, we do not have to look at agi and crit in terms of their effect on EW uptime because it will have such a small impact. The AP effect from agility will continue to be a linear function.
Haste will also effect EW uptime. The below chart shows EW uptime for a fixed crit percentage of 50%.
Again we see diminishing returns. Please note that the x-axis generally requires a significant amount of haste (or a faster weapon) to move very much. As a result we can see that haste and weapon speed does not have a considerable effect on EW uptime.
The spreadsheet gives an explosive shot frequency of roughly 5 seconds and steady of roughly 4.3 seconds with end of T7 gear. The below chart shows HP uptime with varying levels of crit. Glyph of Explosive Shot and 2/2 Survival Instincts are assumed.
All have diminishing returns and crit plays less of a role with more points spent in Hunting Party.
Since this talent no longer requires crits, only shot frequency and hit rating (which can be considered a factor of shot frequency) will increase the value per talent point.
There is a slight diminishing return from shot frequency for every point invested. The more points invested, the more value you will see from increased shot frequency.
The interesting thing about this talent is that the faster you shoot, the more this will be up, increasing your frequency. This also means that the difference between a 3 point and a 2 point difference will be greater than the difference between a 2 point and 1 point investment. However, this is by such an incredibly small amount as to make it a non-issue. For example, the spreadsheet shows me having a a 46.04% uptime of this buff in my current gear with 1/5 IAotH. The uptime of IAotH if I added a second talent point would be 46.91% uptime, an almost trivial amount. The real value would be the increase in haste not the increase in uptime.
The following graph takes a look at auto shot average speed from IAotH with varying base speeds and point investments.
=Weapon Damage and Speed=
Although not exactly a "stat", weapon damage and speed have their own ways of scaling. The information on speed normalizations here is taken from the spreadsheet and has not been independently verified.
Weapon damage is a factor in auto shot, aimed shot, multi-shot, steady shot, chimera shot, scatter shot, and silencing shot. It is notably excluded as a factor in arcane shot, explosive shot, and serpent sting. Since ammo DPS affects the same abilities as weapon damage, it can be considered as an extension of weapon DPS.
For auto shot, faster weapons will do less damage more often while slower weapons will do more damage less often. The net result yields the same DPS regardless of speed, except for some caveats mentioned later. Consider a 150 DPS weapon with X amount of RAP at speeds of 2.7 (405 base damage per shot) and 2.9 (435 base damage per shot). Every 14 RAP gives 1 DPS so DPS would be as follows.
2.7 speed: (X/14*2.8 + 405)/2.7 = X/14 + 150
2.9 speed: (X/14*2.9 + 435)/2.9 = X/14 + 150
This graph shows how weapon DPS increases auto shot DPS for some select values of RAP.
It should be noted that a faster speed will have a benefit on trinkets and talents that are proc based, but do not have a set PPM (procs per minute). For example, Hunting Party and Expose Weakness uptime were shown to increase (albeit only slightly) with more special shots. For information on proc mechanics, particularly PPM abilities like Judgement of Wisdom, take a look at the Proc Mechanics entry in the Theorycrafting Think Tank. Note that the PPM of Judgement of Wisdom is based on auto shot speed although special shots can still proc it, yielding a higher actual PPM. This results in slower weapons actually have a slightly higher gain.
Steady shot is normalized to a 2.8 second speed, meaning that weapon speed is not a factor in base damage.
These shots appear to have their RAP% normalized to 2.8 seconds, but not their weapon damage. Consider Chimera Shot which does 125% weapon damage.
2.7 speed: (X/14*2.8 + 405)*1.25 = X/4 + 506.25
2.9 speed: (X/14*2.8 + 435)*1.25 = X/4 + 543.75
Since Chimera frequency is determined by cooldowns and not weapon speed, the base damage increases with slower weapons. Aimed and multi behave similarly.