2H weapons vs 1H weapons + off hand [Warning: Math]

[RiotInferno]

I wrote this up for a wizard friend of mine, and I was hoping that you guys could double-check my logic / math.

Premise: In the case of DoTs (like Blizzard), a 2H weapon is superior due to having a huge minimum damage. I attempt to prove, through absurdity (not in the logical absurdity, but through best-case-possible absurdity), that this is false.

Part 1: Base Damage (not DPS) equation:
Damage per hit = (base weapon damage * skill damage ) * ( 1 + ( primary stat / 100 ) )
For this example, there's no "bonus" damage, but if there was (say, 5% against elites), it's multiplicative.

Part 2: Constants (APS do not matter)
Skill: Blizzard ( http://us.battle.net/d3/en/class/wizard/active/blizzard )

Best base 2H weapon:
Doom Hammer, 2H Mace ( http://us.battle.net/d3/en/item/doom-hammer )
Minimum Damage: 651 (APS: .9)

Best base 1H weapon:
Centurion Spear, 1H Spear ( http://us.battle.net/d3/en/item/centurion-spear )
Minimum Damage: 209 (APS: 1.2)

Weapon Mods:
Minimum Damage (Elemental): +286
Socketed Gem: +20
Minimum Raw Damage: +381
+% Damage: 50%
Intelligence: +101

These 4 mods are able to spawn on both types of weapons. Damage mods have no difference between 1H vs 2H. (some mods, like stun chance, have greater values on 2H weapons )

That brings our new totals to:
Hammer: 2007, 101 int
Spear: 1344, 101 int

Off Hand:
Demilich ( http://us.battle.net/d3/en/item/demi-lich )
+110 min damage.
+200 Int

or
Shield:
+200 Int

Updated Totals:
Hammer: 2007, 101 int
Spear / Lich: 1509, 301 int
Spear / Shield: 1344, 301 int

Plug into equation:
2H Hammer: ( 2007* 2.1 ) * ( 1 + ( 101 / 100 ) ) = 8471.547 Minimum Damage
1H Spear / Lich: ( 1509 * 2.1 ) * ( 1 + ( 301 / 100 ) ) = 12707.289 Minimum Damage
1H Spear/ Shield: ( 1344 * 2.1 ) * ( 1 + ( 301 / 100 ) ) = 11317.824 Minimum Damage

At the end of the day, losing the off-hand slot is costly in Base Damage and defense. That extra 200 Int goes a little way towards resistances, plus you're losing out on +Resist, Armor, and the ability to gain an extra 3s duration on Blizzard (orb affix).

Sources:
D3 MPQ data files,
http://d3inferno.com/affixes/ItemAffixes.html
http://us.battle.net/d3/en/item/
http://www.clicktoloot.com/p/combat.html#weapondamage

[Concillian]

The comparison is a little lopsided if you assume the person is playing a level 60 wizard with NO other intellect other than on their main hand and off-hand slots.

run again at 1000 base INT:
Plug into equation:
2H Hammer: ( 2007* 2.1 ) * ( 1 + ( 1101 / 100 ) ) = 50.6k min damage
1H Spear / Lich: ( 1509 * 2.1 ) * ( 1 + ( 1301 / 100 ) ) = 44.4k min damage
1H Spear/ Shield: ( 1344 * 2.1 ) * ( 1 + ( 1301 / 100 ) ) = 39.5k min damage

run again with 600 base INT:
2H Hammer: ( 2007* 2.1 ) * ( 1 + ( 701 / 100 ) ) = 33.8k min damage
1H Spear / Lich: ( 1509 * 2.1 ) * ( 1 + ( 901 / 100 ) ) = 31.7k min damage
1H Spear/ Shield: ( 1344 * 2.1 ) * ( 1 + ( 901 / 100 ) ) = 28.3k min damage

Like most stuff in the game, what's best depends on the rest of your gear. Since they multiply each other, higher base damage means higher INT has more value. The inverse is also true, as INT increases, so does the value of base damage. You can't give a definitive answer on this without knowing more about gearing than just what's in their hands.

[RiotInferno]

Some quick math shows that for the 1H / Lich, my statement only hold true for non-weapon Int < 406, and for the 1H / Shield, it only holds true for non-weapon Int < 205.

Guess it's a good thing that math isn't my profession .

Thanks for straightening it up, Concillian

[Concillian]

Well, if you add +xx-xx damage rings and amulets, it will shift things more in favor of 1H weapons (because they have more INT and the more INT you have, the more valuable the base damage is). It just shows how important the total gearing package is to assessment of any particular item.

[RiotInferno]

Well, if you add +xx-xx damage rings and amulets, it will shift things more in favor of 1H weapons (because they have more INT and the more INT you have, the more valuable the base damage is). It just shows how important the total gearing package is to assessment of any particular item.

I don't quite follow here...

If you're increasing base damage on both sides (1H vs 2H) by the same amount, then shouldn't 2H stay greater than 1H, at Int > 400?

Edit: Nevermind. Increasing the base damage adjusts the balance point of required INT where 1H = 2H,

[MongoJerry]

Why are you focused on minimum damage? I think most people would consider average damage (half-way in between minimum and maximum) to be the key stat to focus on.

[Lissa]

Why are you focused on minimum damage? I think most people would consider average damage (half-way in between minimum and maximum) to be the key stat to focus on.

If you're going to look at damage, you have to look at it in this method:

+damage (overall) > +minimum damage > +maximum damage

Case in point, looking at a damage range of 2 to 12 (average is 7).

Now, let's add +2 damage, +2 minimum damage, and +2 maximum damage

+2 -- 4 - 14 with an average of 9
+2 min -- 4 - 12 with an average of 8
+2 max -- 2 - 14 with an average of 8

While you don't see much difference here in this example, it does become more pronounced with larger damage ranged.

[RiotInferno]

I focused on the minimum damage as a "control" value. While damage varies based on damage range, the minimum values are constant. Plus, min damage worked well in my case study of damage-over-time. It was just the aspect I chose to look at, and it helped reduce the variance in the answer