Saryn - Living Artillery

Saryn is typically considered a priming frame to spread Corrosive and Toxin procs through her Spores ability and others, but she has a different, more powerful strength: Saryn is the only frame I know of that can have three simultaneous % weapon damage buffs on at once, AND still have a self-heal ability to help keep her alive. Paired with the right weapons, she becomes an abject damage-dealing powerhouse the likes of which can be matched by very, very little.

The following build can be used with any Primary, Secondary or Melee weapon that you please, even an Arch-Gun called via an Archgun Deployer (and you can cast the buffs while the Archgun is deployed), however it is built based on my Akarius-Run and Gun Death Cannons build with one adjustment: Convulsion is swapped out for Deep Freeze and sequenced to give it a Viral/Heat proc.

UPDATED AUG 24 2021 with Roar calculations

The Build

First Arcane: Arcane Pistoleer
Second Arcane: Arcane Energize
Exilus mod: Primed Sure Footed
Aura: Corrosive Projection, but you can adapt this as you see fit
Helminth Transfer: Xata's Whisper from Xaku, or Roar from Rhino, replacing Miasma (the only viable option. The other skills are either a weapon buff or a heal, and even at high ability strength its damage is still way too low for killing high level enemies).

Given the admittedly high energy costs of the abilities this will cause, you will also most likely need to have the Zenurik focus school active with both Energy Pulse and Energizing Dash active, and possibly energy restore Gear items. In a pinch, if you can handle the inbound damage, replacing one of Adaptation or Rolling Guard with Hunter Adrenaline can also help.

The Frame Toughness

On a standard Saryn, this gives a final Health of 1337, Armor of 658 (68.7% damage reduction), the protections from Rolling Guard and Adaptation, and Molt gives a 138 base HP/second regeneration for 10 seconds, a 2.38 speed multiplier for 5 seconds, and a decoy with 1380 health that will explode for 1104 damage.

The Damage Boosts

Calculating the actual final damage on any particular weapon setup is rather tricky given how the three damage buffs interact (or not) with base damage and elemental damage (or not) modifiers on the weapons. But through extensive testing, the following can be stated.

Base Damage mods and Crit mods: Multiplies everything
Elemental Damage Mods: Venom Dose IGNORES them, it just adds extra damage based only off of Base, on its own hit (However, see below for special interactions). Toxic Lash, Roar and Xata's Whisper MULTIPLY normally
Toxic Lash + Xata's Whisper simultaneously: NO multiplying effect between them, they are fully independent
Toxic Lash + Roar: DOUBLE multiplies the Toxic hit, and then the 50% strength DoT tick is also multiplied again
Venom Dose + Xata's Whisper simultaneously: MULTIPLIES, the extra hit from Xata's Whisper is fully scaled on Base damage mods, and PARTIALLY on Elemental damage mods; Xata's hit appears to be calculated after Venom Dose's damage is additively stacked.
Venom Dose + Roar: MULTIPLIES similar to Xata's Whisper, the main hit fully scales off of Base damage mods, and Roar is multiplied after Venom Dose is additively stacked on Elemental mods
Venom Dose + Toxic Lash simultaneously: MULTIPLIES, the Toxin hit and DoT ticks are fully scaled on Base damage mods, and PARTIALLY on Elemental damage mods: The Toxic Lash extra hit and DoT tick appear to be calculated after Venom Dose's damage is additively stacked.
ALL THREE BUFFS, XATA: You get the base shot fully multiplied by Venom Surge, + the scaled bonus hit from Xata's Whisper multiplied by Venom Surge, + a Toxin strike and 50% strength DoT ticks from the Toxic Lash x Venom Surge value.
ALL THREE BUFFS, ROAR: You get the base shot fully multiplied by Venom Surge x Roar, + a Toxin strike double-multiplied by Roar, + a Toxin DoT of 50% the multiplied Toxin strike x Roar again

At the 276% ability strength of the above build, Venom Dose gives a 276% boost, Toxic Lash gives an 82.8% boost to guns or 165.6% boost to melee, Xata's Whisper gives a 71.76% boost, and Roar gives an 82.8% on their own.

FINAL DAMAGE PER SECOND OF ANY WEAPON = (Venom Dose DPS) + (Toxic Lash DPS) + (Xata's Whisper DPS if used) + (Toxic Lash DoT ticks)
Venom Dose DPS = (Modded Base DPS) x (Venom Dose + Elemental Mod modifiers) x Roar (if used)
Toxic Lash DPS = [(Modded Base DPS) x (Venom Dose + Elemental Mod modifiers)] x Toxic Lash multiplier x (2 x Roar multiplier if used)= Venom Dose DPS x Toxic Lash multiplier x 2 x Roar multiplier
Xata's Whisper DPS = [(Modded Base DPS) x (Venom Dose + Elemental Mod modifiers)] x Xata's Whisper multiplier = Venom Dose DPS x Xata's Whisper multiplier

FINAL DPS XATA = Venom Dose DPS x (1 + Toxic Lash Multiplier + Xata's Whisper Multiplier)
FINAL DPS ROAR = Venom Dose DPS x (1 x Roar multiplier + Toxic Lash Multiplier x 2 x Roar multiplier)
Toxic Lash DoT DPS = 50% of Toxic Lash DPS x (Roar multiplier if used) x number of seconds fired, up to max duration (6 seconds by default)

WITH MY AKARIUS: With all three buffs active, my tweaked Akarius build AoE blasts will proc Blast, Viral, Heat, Corrosive, Toxin with guaranteed DoT ticks, and Void if Xata's Whisper was used, at long range. (Gods, if only Galvanized Shot worked properly to boost the damage per status effect on the blast...).

AKARIUS RUN AND GUN DEATH CANNONS FINAL DPS, option B)

Venom Dose DPS = 2069.75 x 8.45 x (4.45+2.76) x 3.9 x 1.6 = 786,855 Direct, 676,986 Area
TOTAL DIRECT DPS XATA = 786,855 x (1 + 0.828 + 0.7176) = 2,003,018
TOTAL DIRECT DPS ROAR = 786,855 x (1.828 + 0.828 x 2.656) = 3,168,797
TOTAL AREA DPS XATA = 1,723,336
TOTAL AREA DPS ROAR = 2,726,336
TOTAL AREA TOXIC TICK DPS ROAR = 676,986 x 1.828 x 2.656 x (1 to 6 seconds) = 3,286,880 TO 19,721,285

The DoT ticks are more difficult to calculate an effective DPS given how many of them stack or can be sustained, will be calculated later.

And since the above weapon can inflict Viral procs at range to an area, we can include its increase in Health damage in the calculations.

DIRECT DPS XATA, FULL VIRAL PROCS = 2,003,018 x 4.25 = 8,512,826
DIRECT DPS ROAR, FULL VIRAL PROCS = 13,467,387
AREA DPS XATA, FULL VIRAL PROCS = 1,723,336 x 4.25 = 7,324,176
AREA DPS ROAR, FULL VIRAL PROCS = 11,586,928

For the Toxic DoT ticks, Viral works slightly differently; it does not appear to modify the damage of already-applied ticks if Viral was applied after the toxic DoT, but if Viral is applied first it WILL modify the damage of the base Toxic hit which in turn increases the damage of the DoT ticks accordingly.

TOTAL AREA TOXIC TICK DPS ROAR, FULL VIRAL PROCS (1 to 6 seconds of fire) = 13,969,240 TO 83,815,461

Plus the Corrosive and Heat procs drop armor hard. Xata's Whisper strips resistances off of Sentients, Acolytes and the Stalker as usual, but the higher base damage with Roar could make it unnecessary.

FINAL NOTES

There are no damage-inflicting attack abilities on any frame that can match these kinds of damage numbers, if you pair it with the right weapons, bar maybe one or two very specialized exceptions that are slow to use. And it works on anything and everything Saryn is carrying. So choose the weapons that project damage the way you like be they melee or ranged, and LET RIP.