K, lets see if I can get some info outa here.
First of all lets convert the on use thingy to an added bonus over time.
(We only have to keep in mind that this thing can be used for burst damage, and normally is forgotten against normal mobs. Thus the average effect will be a lot lower since we are not using this thing constantly, but when we use it, it helps more, since we are fighting a mob where every point of damage counts).
150 agi for 20seconds every 2minutes. So 150agi over 1/6th of the time gives us on average 25agi.
The armor is worthless. So basically you compare 25agi with the alternatives for this trinket slot.
For a non SV hunter this would be no good choice, so we can safely assume Expose Weakness and Lightning reflexes.
With LR we get 25agi*1.15 = 28.75agi
With expose weakness, this will increase the AP of every attacker by 7.2AP on average.
So these things we know. What we now need to know is how much DPS do we get out of this trinket and how much DPS do we get out of other trinkets.
Lets compare with another trinket which is standard for a raiding hunter:
-
Bloodlust Brooch 72AP +278AP for 20 seconds, 2min CD.
This trinket will yield 72AP + 1/6*278AP = 72AP + 46.3AP = 118.3AP
Lets assume that 1AP increases a hunters DPS by ~0.4
The Bloodlust Brooch would yield 118 * 0.4 = 47.2DPS Lets compare this with the badge:
The badge increases the hunter's DPS and the raid DPS.
The hunter gets: 28.75AP, 0.7%crit, 7.2AP from EW
The raid gets: 7.2AP for every melee DPS class attacking the same mob.
So we have to know how much Expose Weakness helps the raid. On EliteistJerks I found in the
SV raiding thread that 1AP will yield ~0.3DPS for melee DPSers (though a bit less for feral druids and of course for tanks).
In a normal 25man raid you'll have 3 rogues, 1 dps warrior, 1 enh. shaman, 1 feral druid. Then you will have at least one tank for the mob and some hunter pets which will also benefit a little from EW.
So we can assume that every point of AP from expose weakness will add at least 2 DPS to your raid DPS.
So the EW portion of the badge will yield 7.2*2 = 14.4DPS
So, one component solved, one to go (the hunter's DPS increase)
The hunter's dps increase from AP is rather easy. This should be (28.75+7.2)*0.4 = 14.4DPS
The DPS increase from the extra 0.7crit is a bit trickier.
Lets assume the hunter has 340 tooltip DPS (which is a number a raiding SV hunter should achieve). 40% of his damage is from autoshot, the rest from his steady-shot and other specials.
Thus 0.7% crit give 340*0.007*1.3=3DPS increase for autoshots which is 40% of the total damage. Thus 0.7%crit increase the damage by 3*10/4=7.5DPS
Finally we can estimate the DPS increase a Badge of Tenacity yields:
14.4DPS+14.4DPS+7.5DPS = 36.3DPS
The Badge would yield 36.3DPS I hope I have the most things correct (There are a ton of assumptions in here, but I hope it is close and the calculations are somewhat correct).
All in all it seems as if the badge of tenacity is not that bad a trinket, but it is worth than e.g. bloodlust brooch or other trinkets available for raiding hunters.
So leave this thing to our feral druids which gain 308*4.5=1386 armor and on use ~10% dodge from it.