HS: Aura or Critical?

[greek]

Still continuing on my math analysis of notd combat.
This time I went with a simple subject: What is the best combination for damage regarding the HS skills of aura or critical.

say base damage 100 for easier results
The equation is Damage = (100 + Aura) * CritMult * CritChance + (100 + Aura) * 0.85

1 Skill Point
1st level aura: 112
1st level crit: 100 * 2 * 0.15 + 85 = 115

2 Skill Points
Aura 1 with Crit 1 = 112 * 2 * 0.15 + 95.2 = 128.8
Crit 2 = 100 * 2.5 * 0.15 + 85 = 122.5
Aura 2 = 118

3 Skill Points
Aura 2 with Crit 1 = 118 * 2 * 0.15 + 100.3 = 135.7
Aura 1 with Crit 2 = 112 * 2.5 * 0.15 + 95.2 = 137.2
Crit 3 = 100 * 3 * 0.15 + 85 = 130
Aura 3 = 124

4 Skill Points
Aura 2 with Crit 2 = 118 * 2.5 * 0.15 + 100.3 = 144.55
Aura 1 with Crit 3 = 112 * 3 * 0.15 + 95.2 = 145.6
Aura 3 with Crit 1 = 124 * 2 * 0.15 + 105.4 = 142.6
Crit 4 = 100 * 3.5 * 0.15 + 85 = 137.5
Aura 4 = 130

5 Skill Points
Aura 3 with Crit 2 = 124 * 2.5 * 0.15 + 105.4 = 151.9
Aura 2 with Crit 3 = 118 * 3 * 0.15 + 100.3 = 153.4
Aura 4 with Crit 1 = 130 * 2 * 0.15 + 110.5 = 149.5
Aura 1 with Crit 4 = 112 * 3.5 * 0.15 + 95.2 = 154
Crit 5 = 100 * 4 * 0.15 + 85 = 145
Aura 5 = 136

6 Skill Points
Aura 5 with Crit 1 = 136 * 2 * 0.15 + 115.6 = 156.4
Crit 5 with Aura 1 = 112 * 4 * 0.15 + 95.2 = 162.4
Crit 4 with Aura 2 = 118 * 3.5 * 0.15 + 100.3 = 162.25
Aura 4 with Crit 2 = 130 * 2.5 * 0.15 + 110.5 = 159.25
Aura 3 with Crit 3 = 124 * 3 * 0.15 + 105.4 = 161.2
...and so on

Crit 5 with Aura 1 vs Aura 5 with Crit 1 -> 3.8% increase

As you can see what makes a real difference is having both skills against having only one of a kind. So whenever you are the only HS of a team, it pays of a lot better to get at least one level in both skills.
Now lets not forget that the above equation does not take into account ANY damage modifiers due to items.
In that case its best to get aura, since the increased overall team efficiency is a lot more important than the increased maximum damage that a high crit on HS can give. Even more so when there is a marksman around that can benefit from it.
Now, when there are items that modify damage, the equation becomes different.

The equation is Damage = (100 + Aura + Item) * CritMult * CritChance + (100 + Aura + Item)*0.85
Which means that the Aura modifier becomes much less important since it does not multiply the Item damage, whereas Critical does.
The greater the damage increase, the less important the aura skill.

EDIT: I'll get back to this later with specific math results.

A typical HS has a damage of 40
Minigun gives a damage bonus of 10 -> 20%
U238 gives a damage bonus of 10 -> 20%
AP gives a damage bonus of 12 -> 24%

So, for a typical hs who has mini and ap:

1 Skill Point
1st level aura: 156
1st level crit: 144 * 2 * 0.15 + 122.4 = 165.6

2 Skill Points
Aura 1 with Crit 1 = 156 * 2 * 0.15 + 132.6 = 179.4
Crit 2 = 144* 2.5 * 0.15 + 122.4 = 176.4
Aura 2 = 162

3 Skill Points
Aura 2 with Crit 1 = 162 * 2 * 0.15 + 137.7 = 186.3
Aura 1 with Crit 2 = 156 * 2.5 * 0.15 + 132.6 = 191.1
Crit 3 = 144* 3 * 0.15 + 122.4 = 187.2
Aura 3 = 168

4 Skill Points
Aura 2 with Crit 2 = 162 * 2.5 * 0.15 + 137.7 = 198.45
Aura 1 with Crit 3 = 156 * 3 * 0.15 + 132.6 = 202.8
Aura 3 with Crit 1 = 168 * 2 * 0.15 + 142.8 = 193.2
Crit 4 = 144 * 3.5 * 0.15 + 122.4 = 198
Aura 4 = 174

5 Skill Points
Aura 3 with Crit 2 = 168 * 2.5 * 0.15 + 142.8 = 205.8
Aura 2 with Crit 3 = 162 * 3 * 0.15 + 137.7 = 210.6
Aura 4 with Crit 1 = 174 * 2 * 0.15 + 147.9 = 200.1
Aura 1 with Crit 4 = 156 * 3.5 * 0.15 + 132.6 = 214.5
Crit 5 = 144 * 4 * 0.15 + 122.4 = 208.8
Aura 5 = 180

6 Skill Points
Aura 5 with Crit 1 = 180 * 2 * 0.15 + 153 = 207
Crit 5 with Aura 1 = 156* 4 * 0.15 + 132.6 = 226.2
Crit 4 with Aura 2 = 162 * 3.5 * 0.15 + 137.7 = 222.75
Aura 4 with Crit 2 = 174 * 2.5 * 0.15 + 147.9 = 213.15
Aura 3 with Crit 3 = 168 * 3 * 0.15 + 142.8 = 218.4

Crit 5 with Aura 1 vs Aura 5 with Crit 1 -> 9.2% increase

Not that much, if you consider the decrease of the overall team's firepower. Aura level 5 compared to level 1 gives 4*6% = 24% damage increase to the rest of the team.
In the case that we have a PVT HS with no medals, the effect of items is even greater. But on the other hand the really low damage of that marine does not allow for him to pump criticals to his already low damage.

To conclude:
Unless there is a serious need for the HS to increase his max damage limit, to combat armored units, the best build is to go for 1 level of critical, and then max aura. Considering the rarity of the need of the hs to max the damage limit, and the inefficiency of the hs to fight armored foes, I would say that in 99% of the cases, maxing aura with one level of critical is the best damage combination for the HS.

EDIT: Slight mistake in calculations will fix it ASAP. Thanks to Faultline for pointing it out. FIXED

[FrodoPL]

Who is HS? =]

[greek]

Heavy Support (http://grilledfish.be/index.php?n=32&mod=basic2&class=hs)

Now some further refining of the Item results.
In the above calculations I did not take into account the Minigun's critical chance, because we don't know for sure how 2 or more criticals combine.
With Faultine's help I've done further tests and I have gotten close to how they combine.

Will take into account 4 possibilities.
Mini before Critical:

Aura 5 with Crit 1 = 180 * 2 * 0.15 + 180 * 2 * 0.17 + 180 * 0.68 = 54 + 61.2 + 122.4 = 237.6
Crit 5 with Aura 1 = 156 * 4 * 0.15 + 154 * 2 * 0.17 + 154 * 0.68 = 93.6 + 52.36 + 104.72 = 250.68
That's a 5.5% Increase

Critical before Mini

Aura 5 with Crit 1 = 180 * 2 * 0.2 + 180 * 2 * 0.12 + 180 * 0.68 = 72 + 43.2 + 122.4 = 237.6
Crit 5 with Aura 1 = 156 * 2 * 0.2 + 154 * 4 * 0.12 + 154 * 0.68 = 62.4 + 73.92 + 104.72 = 241.04
That's a 1.4% Increase

Therefore its clear that Maxing aura first is even more important. Since its not a 9.2 damage increase, but only a 5.5 in the best case scenario. And the team loses that 24% aura damage bonus.