This was done rather hastily, but the math seems pretty good to me. You'll notice that I pulled a lot of numbers out of a hat (an experienced hat, but a hat nonetheless). However, this shouldn't have an impact on the result; I made a point of making sure things were shifted in favor of slow weapons. Since the result is that fast weapons are superior, my fudging shouldn't have any appreciable impact.
Heroic Strike
Weapon one (W1 for short) will be a 200 DPS weapon with a 1.6s swing speed. Weapon 2 (W2) will be a 200 DPS weapon with a 2.6s swing speed. Let's assume we have 3k AP (215 extra DPS), and that the 30% bleed bonus is present.
In 20.8s, W2 will hit 8 times, while W1 will hit 13 times.
Heroic strikes deal 259 threat + bonus damage. Let's assume the boss has a 30% armor reduction. This gives W1 a 605 Theat * 5 = 3025 threat lead over 20.8 seconds assuming infinite rage.
Devastate
Devastate hits for 83 more damage with the slow weapon. Assuming you put out on average 1 devastate per 4 GCD's, that's an extra 288 threat from devastate with a slow weapon.
Deep Wounds
W1 - 664 per hit * 0.48 * 1.3 = 414 damage/6s = 69 DPS
W2 - 830 per hit * 0.48 * 1.3 = 518 damage/6s = 86 DPS
That's a 17 DPS lead for W2. Over 20.8 seconds, that's 354 threat. However, we need to factor in DW rolling to get the full picture.
Deep Wounds Rolling
Deep wounds rolling obviously makes things more complicated. In total, W2 does 114 more damage per full DW duration. The end TPS result is going to depend on how many times you can crit.
Over 20.8s we have 13 GCD's = 13 abilities being used. I'm going to assume a 30% crit rather than 25%. This isn't too unreasonable if you have an odd piece of gear here and there, along with a couple points in cruelty. In any case, the end result will be skewed towards the slower weapon, which, if you read further, isn't a problem.
Base W1 = 13 * 0.3 * 414 = 1614 damage
Base W2 = 13 * 0.3 * 518 = 2020
Melee W1 = 13 hits * 0.1 * 414 = 538 damage
Melee W2 = 8 hits * 0.1 * 518 = 414 damage
Total difference = 282 damage.
The damage difference is actually normalized somewhat due to the faster weapon getting more crits. If Damage Shield can indeed proc DW then you might see a slight difference depending on boss swing speed. If the boss hits 10 times in our duration, let's assume 3 are avoided. Of those 7, you'll have 1 crit, resulting in 114 more threat for W2.
In total, you're looking at 296 more threat for the slow weapon. This actually decreases as your avoidance increases.
Rage
Rage modeling on this is going to be tough, since it's not just weapon rage you're considering. I'm going to attempt to fudge the numbers a bit to equalize the rage cost across weapons (W1 needs 45 more rage than W2 for those HS's), but those numbers will be very rough. Bear with me
I'm going to assume that each W1 hit generates 15 rage. This means that in order for W1 to not require more rage than W2, we have to remove two HS's (45 rage / 24 rage per HS ~= 2). This removes a solid 1210 threat from what we calculated earlier.
Summary
These numbers are over 20.8 seconds.
W1 (our 1.6s speed weapon) generates 3025 more rage from Heroic Strikes than W2 (our 2.6s weapon). Extremely rough and haphazard rage modeling tells us that unless we have infinite rage, we need to remove two HS's (1210 threat) from W1 in order to have the same rage cost as we would with W2.
Devastate with a 2.6 speed weapon gives an extra 288 threat.
While Deep Wounds does more damage with a slower weapon, the numbers are much closer than they'd appear at first glance due to the faster weapon critting more often - if you were to do only white damage, the faster weapon would do
more DW damage. Interestingly enough, Damage Shield is completely in favor of a slow weapon for Deep Wounds. Summing it up, a slower weapon causes roughly 282 more threat from Deep Wounds.
3025 - 1210 - 288 - 282 = 1245 more threat for W1 over 20.8 seconds, or 60 TPS. With infinite rage, W1 gets 1210 more threat over 20.8 seconds, for a total of 118 more TPS.
Bottom Line
Faster weapons are better.
Please check my math
Note: Yes, I accidentally used 2.6 as my speed instead of 2.5. Fortunately, this should have only a very minor difference. I also didn't factor in HS crits. Seeing as this favors the faster speed anyway, I'm not going to go back and recalculate.
Slow Weapon & Deep Wounds -- Math Challenge
