Originally Posted by Foxx2405
Not only slow ulduar weapons would be an upgrade. That weapon is about as good as a slow blue reptuation weapon (like [Reaper of Dark Souls]) . If i remember correctly from my deduction a few posts back going from 2.6 speed to 1.5 speed is only worth it if the faster weapon has about 60 DPS more. That means that Lionhead Slasher is upgraded by anything from naxx and beyond with a speed of 2.6 and slower.
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I couldn't find your deduction, in fact I couldn't find any proper calculation of the benefit of weapon speed, just simulation.
A simulation is sort of a black box, nobody can understand exactly how the weight came to be, we just trust it because we hope we fed it the right data. A proper calculation, aka theorycrafting, however is transparent and clean, so here's an attempt, feel free to nitpick.
I'll assume raid buffed, thus about
35% crit,
30% haste (7% personal haste is not unreasonable) and
15% miss chance for white attacks for simplicity. If you want to assume a different hit, just change the miss % in the auto attack calculation, assuming special hit capped should be a given.
I will only compare average weapon damage to average dps.
I will consider neither Boss level (glancing blows etc) nor Armor Penetration, Armor Penetration would only have an effect on Frost Strike (I'm not too familiar with boss armor after sunder and a reasonable amount of armor pen). Glancing blows could have a noteworthy effect, but I'm not sure exactly how the glancing blow mechanics work, so I'll assume that the damage difference can be ignored without influencing the results too much, especially since I always assume Full Subversion and no BCB in my examples. Boss level related reductions to crit would have the opposite effect (since specials scale better with crit) and I know even less about that, overall it should alleviate the absence of glancing blows.
Attack power does not change this calculation at all since Scaling is normalised. Main Hand or Off Hand is also irrelevant since the 50% damage penalty is consistent in all relevant aspects.
I will calculate for both Subversion and BCB, and I assume an Unholy subspec at least including necrosis.
I will first calculate the value of an average point of damage for every ability that uses Weapon Damage, then determine to how much dps that translates and compare to the benefit of dps for auto attacks. Numbers are rounded to 2 decimal points.
Obliterate:
100% weapon damage, 25% diseases, 15% frost fever, 15% (24)% extra crit, 45% crit modifier
(1 * 1.25 * 1.15) * (1 + ((0.5 * 1.45) OR (0.59 * 1.45))) ~= 2.48 OR 2.66 (depending on Subversion)
Blood Strike:
44% weapon damage, 25% diseases, 15% frost fever, 0% (9%) extra crit, 45% crit modifier
(0.44 * 1.25 * 1.15) * (1 + ((0.35 * 1.45) OR (0.44 * 1.45))) ~= 0.95 OR 1.04
Plague Strike:
50% weapon damage, 15% frost fever, 6% extra crit, 30% crit modifier
(0.5 * 1.15) * (1 + (0.41 * 1.3)) ~= 0.88
Frost Strike:
60% weapon damage, 15% frost fever, 13% extra magical damage, 10% razorice, 10% Black Ice, let's say 55% crit with KM (just a qualified guess), 45% crit modifier
(0.6 * 1.15 * 1.1 * 1.1 * 1.13) * (1 + (0.55 * 1.45)) ~= 1.70
In 20 secs, the normal Frost DW rotation (without GoD) uses 1 Plague Strike, 2 Blood Strikes, 4 Obliterates and has space for ~5 extra globals, of which we assume 4 go to Frost Strikes
So every point of average damage yields:
(2.48 * 4 + 0.95 * 2 + 0.88 + 1.70 * 4) / 20 ~=
0.98 dps without subversion and
(2.66 * 4 + 1.04 * 2 + 0.88 + 1.70 * 4) / 20 ~=
1.02 dps with subversion
Auto Attacks:
20% (35%) extra Necrosis/BCB, ~30% haste, ~15% miss chance
((((1 * 1.2) * 1.3) * ((1 / 1.15) + 0.35)) ~=
1.90 OR 2.07 dps (BCB calculation is simply adding 15% of auto attack dmg with haste and miss, but without necrosis or crit, since it doesn't scale with either.)
This means that a weapon needs to have from 1.86 to 2.11 times more average damage than it loses dps compared to another weapon to be better, disregarding stats on the weapon (which are usually in favor of the one with the higher dps).
Applying this to the example you listed
[Lionhead Slasher] vs
[Reaper of Dark Souls], we get (206 + 384) / 2 = 295 average damage and 196.7 dps vs (281 + 422) / 2 = 351.5 average damage and 130.2 dps.
Translated that means 55.8 average damage vs 66.5 dps, or 56.92 dps increase vs 126.35 dps loss, assuming no BCB and full subversion. Apparently
[Lionhead Slasher] is clearly superior no matter the circumstances, the gap only widens if you consider other talent specs and the higher stats on the weapon.
Comparing
[Lionhead Slasher] to
[Grimhorn Crusher] we get 78 avg dmg vs 53.4 dps, 79.56 dps increase vs 101.46 dps loss, again with subversion and without BCB.
[Lionhead Slasher] is still better.
Comparing
[Lionhead Slasher] to
[Aledar's Battlestar], again full subversion, no BCB: 129.5 dmg vs 33.4 dps. This time it's 132.09 dps increase vs 63.46 dps loss. So the slower weapons quickly catch up, but I'm pretty sure if we'd use the heroic version of
[Lionhead Slasher], it would be better again.
Summarizing we can say that if you choose between similar quality items, the slower one always wins, but if you have vast differences in quality (more than 2 tiers), the faster one is probably better and the better weapon is always better equipped in the main hand, regardless of speed.