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Short answers (in red):
Incoming Wall of Text and Theorycraft:
With 1.5, each round of a nano gun does the nano's type of damage, in addition to the DoT effect procing. So, the perks, effectively, can add damage both to the gun and the DoT damage of a nano proc (with the appropriate conditions).
Example 1:
I have EGO 4996 Purple FRC Assualt Carbine Fire w/ a x1.05 DMG roll. Without the Fire perks from DLC5, it does 3677 DMG per bullet (+35 to Health, -50% to Shields). With the perk Conflagration, each bullet does 3677+1286.95(35% DMG to health, Fire Nano)+551.55(15% DMG to health, Perk)= 5515.5 DMG to health, 3677-1838.5 (-50% to Shields)=1838.5 DMG to shields. (Take off 10% for each armor plate on the enemy.)
Example 2:
I have a 5345 Orange VBI TACC Assault Rifle, w/o DMG roll or Power Bore. It does 5199 DMG per shot. With the perk Radiation Burns, each shot does 5199 + 15% dmg= 5978.85 DMG/shot. As this is Radiation nano, it ignores 2.5 Armor plates of the damage reduction (adding Gamma Rays increases that to 3.125 Armor Plates).
When the effect procs, it does damage over time. This DoT is effected by the appropriate perk in the same way as bullet damage is increased. Additionally, the effect adds the bonus of it's element (i.e. Bio breaking armor, Electric breaking shields, etc.) to ALL the bullets hitting the target from other sources. However, the perks on your loadout increasing the damage of your shots does not increase the effects of the other sources shots. Nor are your shots nano "converted" to the Nano effect currently proced on the enemy.
Example A:
You are shooting an Electric shotgun and the Fire effect procs on an enemy from another player hitting it, and you have Conflagration perk on your current load out, your shots are NOT increased by the perk as your shots are still Electric, not Fire, although they gain the added boost of more damage to health. In this case, your Electric Shots are doing more damage to shields AND health, instead of less damage to health, while the guy is on fire, but not doing extra damage to their armor plates.
Example B:
Same as above, except you are using a Nanoless gun. You are still doing extra damage to health (+15%), but no other increases to damage to armor or shield.
Example C:
You are using a Bio Gun, otherwise same as above. You do more damage to armor and health, but not shields.
Because of all of this, when working as a team, it appears to be more advantageous to use a faster firing weapon, with slightly lower damage (like an SMG over a AR, or a Mazu Blast over a TACC Assault). This is because the chance of the nano effect proccing on the enemy is based on the round, instead of time. Additionally, perks such as Insult to Injury (increases chance of nano effect procing on crit hit) become more valuable.
For a well coordinated, lower EGO fire team, having three guys each with a single fast nano weapon and a non-nano high damage weapon can be quite effective. To make the most of perks and nano proc effects, a good tactic would be for shooter 1 (bio) to hit the guy first to get the bio effect proced, and then the other join in with their non-nano weapons. Once the armor is down, shooter 2 (electric) switches to his nano weapon, and shooter 1 and 3 go nanoless. Finally, armor and shield are down, so shooter 3 (fire) switches to his nano, and 1 and 2 go nanoless. (The fourth is the medic.)
Make sense?
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