Mathematically optimized flamethrower! I made a heat dmg calculator you can use! 4 million dps!

tldr:

here is the link to my google sheets dmg calculator (for heat+base dmg)
scroll down here to see a screenshot of the chart comparing various builds
I added a 'time to kill' calculator for this build vs [\[Ignis\]](/items/arsenal/908/ignis/) slash varient in the google doc based on inputted enemy armor and hp
basically, this build is vastly better than slash when enemies have low armor and/or large hp pool, and is just as good if they have high armor or low hp pool. (basically, for base sp and normal missions, heat is always better)

        heat build can kill a sp lvl 9999 manic bombard faster than slash build lol 

mods:

use normal bane for primed bane and if u dont like either go hammer shot
‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ- if you dont have weapon arcanes, use [\[Serration\]](/items/arsenal/626/serration/) instead of bane
any ammo exilus works

purpose:

is slower initially (esp before galv ap stacked) than other builds
heat ticks scale infinitely -> building for heat = most damage in the end. (optimal vs tough enemies / sp)
out scales all other builds in about 2-3s when merciless stacked (see chart below)

basic details:

slash bad, crit bad for heat dmg, primed cryo bad for heat chance (full explanations later in guide)
ignis wraith heat ticks benefit from multishot twice - wiki

        ‎the best i can explain it is, first multishot is factored into status chance (as in, how many procs u get per shot), and then it is factored in again because beam weapons combine all the projectiles into one projectile beam (multishot times base projectile dmg) and this is what all the status procs use for their damage calculations. in other words, we get normal amounts of status procs from multishot and each status proc uses a base dmg value of multishot times projectile dmg, so we double dip on it.

the below chart is a part of my fully automated google sheets heat dmg calculator that you can feel free to copy and use (its a bit messy tho srry)
chart assumes full conditionals (ie, viral, merciless) (note these are raw values, before armor mitigation, for total dmg on a single target for 10s) (red is where this build outscales)

(forgor to add slash column in screenshot but dw it is factored into all of the equations)

add me on disc if u have questions: vyxmeow

quick notes:
why [Hunter Munitions] bad:

its not actually that bad but its only slightly better against high armor low hp enemies but alot worse vs low armor high hp (and, for people playing base sp or lower, nothing has high enough armor for slash to kill faster)
scroll to very bottom to see mathematical representation of why exactly it is bad xd
slash procs alone don't do much dmg (even with viral) and really only serve as another status effect for aptitude at best (35 ignis wraith base dmg = small slash procs)
doest proc many of them (expected = almost exactly 2/s)
decreases heat damage (mod slot could be used for something that increases)

why using crit is worse ?

because building for crit uses two mods to make half ur shots do extra dmg but the other half do a lot less since they dont benefit from those two mods, and for heat dmg specifically it turns out to be more efficient to just [Sacrifice] the crit mods to fit in additional heat and base dmg mods which work on all shots. the math says so. we do lose weapon dps but we make up for it with a lot more scaling heat dps. 

why not primed cryo?

doesnt increase heat dmg and makes heat less likely to proc (since viral gets way more share of elemental dmg)

sample equation for heat dps:
status chance = 104.4%
115.3 heat + 55.3 viral = 170.6
115.3 is 67.58% of 170.6
67.58% of 104.4 = 70.56
each projectile has a 70.56% chance to proc heat
heat dmg (see wiki):
35×(1+3.6+1.6)×1.55=336.35
0.5×336.35×(1+1.5)×(1+0.55)=651.68 (2769.63 at 10 viral) (no crit)
0.5×336.35×(1+1.5)×(1+0.55)×2.5=1629.2 (6924 at 10 viral) (yellow crit)
crit chance = 17%
((17×1629.2)+(83×651.68))/100 = 817.86 avg tick (3475.9 at 10 viral)
average expected per projectile:
70.56% of 817.86 = 577.07 (2452.6 at 10 viral)
average expected per shot:
577.07 × 3.3 = 1904.331
expected heat per second:
1904.331 × 15.2 = 28945.8312
total heat dmg/s:
28945.8312 × 3.3 = 93181.42493 (396021.056 at 10 viral)
^heat benefits twice from multishot, once for chance of heat proc and again because the base dmg of beam weapon is multiplied together into one tick

SLASH DMG MATH: (& why u shouldnt use)

solving for when slash dmg (not affected by armor) is equal to raw damage difference between the builds (affected by armor) to see at what armor slash does more dmg than the raw dmg diff between builds (in other words, solving for how much the raw dmg diff needs to be reduced by armor for slash dmg to deal more)

i will use a build designed specifically for slash dmg that uses viral and this is what i came up with. (i couldn't find any other mod combination that gave higher slash - see the description of that build link to see slash + heat + base dmg calculations (results used in calculations below))

5,112.8645233 (slash dmg/s) × 4.25 (viral) × time = (current build total raw dmg - slash build total raw dmg) × (1-(total dmg reduction%))
‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ- "total raw dmg" numbers gathered from my google sheets calculator. the values are the total base+heat dmg totals at the selected time (10s). (already include viral)
21,729.67422 × 10 (example time (seconds)) = (24,832,857.82 - 9,801,457.81) × (1-(armor/(armor+300)))
‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ‎‎‎‎‎‎‎‎ㅤ- for those wondering where (armor/armor+300) came from^
217296.7422 = 15,031,400.01 × (1-(x/(x+300)))
217296.7422 / 15,031,400.01 = (1-(x/(x+300)))
0.01445618785 = (1-(x/(x+300)))

x (armor) = 20,452.36
but this is post 50% pen from heat, so the actual armor the target has is
20,452.36 × 2 = 40,904.72
which is 40,904.72/(40,904.72+300)= 99.27192807% dmg reduction

in the example here, we solved that an enemy who lives 10s of damage from both builds would have to have 40,904.72 armor for the slash alternative to deal more damage. for reference, a level 1000 corrupted heavy gunner only has 35,852 armor.

furthermore, each second longer that an enemy survives further increases the amount of armor the target would have to have for slash to be optimal, because heat ticks scale linearly and therefore there is greater relative increases in raw damage vs slash dmg per second. (so to counter this, the armor value has to be higher to offset the disproportional increases in raw dmg)
this leads to a problem where slash requires a target to have an unreasonable amount of armor to be even worth taking.

out of curiosity, I did the math again for 5s values instead and got
21,729.67422 × 5 = (7,466,165.71 - 3,494,149.52) × (1-(armor/(armor+300)))
108648.3711 = 3972016.19 × (1-(x/(x+300)))
108648.3711 / 3972016.19 = (1-(x/(x+300)))
0.02735345626 = (1-(x/(x+300)))

armor = 10667.54
actual armor (pre heat pen) = 10667.54 × 2 = 21335.08

in other words, for a target to take more damage from slash build vs heat build within 5s, the target has to have 21,335.08 armor... and keep in mind that the longer this enemy survives the more armor it will continue to need to have for it to take more damage from a slash build. so its a cycle, for slash to be better enemies need to be tankier which means they take longer to kill which means for slash to be better they need to be even tankier which means slash takes even longer to kill... etc. therefore, its safe to say, pure slash is basically never better.

enjoy!