Every now and then a dps comparison pops up somewhere in a warframe forum. I, as a number fanatic, love to roam through those posts, trying to see what people are doing and if I can learn something from them. But then I see quad-elemental modding without elemental advantage purposes, or usage of Shred on a Boltor, or, heck, Thunderbolt on anything but Attica. I'll take it this goes without sourcing, after you've read this post and then read any older dps-posts you'll see my point.
So, I feel like I should share my view on weaponisation. This, I'm going to do with firstly a bunch of numbers and explanations, and then examples for a couple weapon types. Yes, I'll include TL;DRs on every paragraph, just to make reading a bit more friendly for those simply passing by :)
Without further ado, let's dive in!
If you look at how damage is calculated, it's a matter of multiplying factors; Base damage type X * Serration * Critchance * Critdamage * Headshot * Elementals, or something the like.
Knowing this, it seems logical to me that you'd try to maximize your general multipliers. To make that a less abstract idea, look at the following example :
Let's say $ Base * (1+X) * (1+Y) $ represents damage on one shot, 'Base' is base damage, X is damage amplification (Serration, Heavy Caliber), and Y stands for elemental modification (Hellfire and the like).
To keep it simple, we'll deal with integers for now. Let's say the base damage is 100, and we got room for 3 mods. Any mod will add a factor +1 to X or Y (which is the same as +100% damage, or +100% elemental damage). For the sake of our example, elemental combinations are irrelevant, and we have both 3 possible mods that amplify X, and 3 that amplify Y.
Let's first go for the most simple modding; three +damage or +elemental damage mods, no questions asked.
$ 100 * (1+3) * 1 = 400 $ We made X (or Y) worth 3, and with that, the multiplier related to them became 4, resulting in a damage of 400 per shot. I contest this choice, for it could be higher;
let's say we balance our mods as much as possible. Since we have three equal options, this means 2 mods allocated to X or Y, and 1 to the other. This results in $ 100 * (1+2) * (1+1) = 600 $. This is 50% higher than the 'simple' example, by simply moving one mod!
However basal this looks, we have 8 mod slots and varying amplifications in our possession, along with the effectivity of status chance, headshot critical multipliers, and elemental combinations. That makes it a lot harder to mod properly. Still, since we're talking raw numbers for now, I propose we assume elemental factors are irrelevant save for the raw damage, and we forego headcrits till later on.
A key factor to my method is the theoretical impact of a mod on performance. A maxed Serration will boost your damage with 165% (which is the same as the mod's power divided by the original amount of power, 1.65/1), but an additional Heavy Caliber will not give another 165% rise in DPS. Barring the influence of accuracy loss, it will only boost your DPS by 1.65/(1+1.65), which is around 62%. Key to this guide therefore is the relative power of mods, instead of the more traditional (and frankly dumber) absolute power.
The idea is to eventually learn to develop a feel as to what mod is the best add in your situation, and to in the end be able to see which mod is your weakest factor, and therefore potentially replaceable.
TL;DR You get most out of your raw damage weaponisation if you balance your damage-amplifying mods out. Remember the idea of relative mod impact.
Extended to rifle-type weapons
For the real deal, we'll look at a generic rifle type weapon. As much as I care, this could be the MK-1 Braton as well as the Boltor Prime; it's about the idea!
Firstly, I'm going to establish the factors involved :
- Base damage : The raw power a rifle brings, directly influenced by Serration, Heavy Caliber, and (negatively) by Vile Acceleration.
- Raw firing rate : The amount of times a shot can release per second. Directly influenced by Shred, Speed Trigger, Vile Acceleration. Also influenced negatively by Critical Delay and Vile Precision.
- Multishot : The chance of firing an additional shot. Due to the law of large numbers this functions as a raw damage multiplier for calculation purposes. Directly influenced by Split Chamber
- Mean firing rate : The amount of times a shot can release per second if the weapon keeps firing for a while, and reload gets involved. Influenced by the firing rate factors, next to ammo capacity and reload speed.
- Critical chance : The chance that the critical multiplier is applied. Due to the law of large numbers this functions as a multiplier for the critical damage multiplier. Directly influenced by Point Strike and Critical Delay.
- Critical damage : The damage multiplier applied when a crit lands. Directly influenced by Vital Sense and Hammer Shot.
- Elemental damage multipliers : A direct damage multiplier which takes the above damage and then multiplies it by it's own factor, adding the result as its own damage type. Directly influenced by the normal elemental damage mods (Infected Clip), dualstat damage mods (Rime Rounds), and Wildfire.
- Base damage type multipliers : Mods like Piercing Caliber function like elemental damage mods, but only take one of the three base physical damage types (Puncture, Impact, and Slash), and multiply them by their own value (+1 of course). This does not affect the elemental multipliers, though.
In all honesty, whether you're looking at sustained or burst damage, reload speed is nearly never a factor to mod for, simply because Fast Hands does too little to change a lot compared to adding another raw damage mod. This might chance when Primed Fast Hands arrives, but until then, this is solely a factor for weapons like the Vectis which have their reload speed tied to their firing speed fundamentally.
For now (since this is becoming an essay already), I'll forego proving this point, although I might come to it later.
Now, when we look at our factors, we see a couple factors that are equally powerful on every weapon (with the exception of status-based weapons); Base damage, Multishot, and Elemental damage multipliers. I'll come to Elemental damage later, but for Multishot and Base damage, we can safely say we should staple Split Chamber and Serration to every single rifle we own. These add, respectively, when maxed, +1.65 and +0.9 to two different multipliers, without affect weapon usability in the slightest. Also, Multishot has no other mods affecting it, so it's an independant multiplier that is fully maximized with only one mod slot taken.
With that done, we have 2 out of 8 mod slots taken, and our multiplying formula has become
$ Base * (2.65 + X) * 1.9 * C $ where C stands for the remaining factors, and X for the potential effect of Heavy Caliber and Vile Acceleration.
Next, I look at the critical chance of the weapon. If this chance is 25% or higher, it might make modding for critical chance worthwhile compared to raw damage; 25% is a borderline case where empirical testing (using warframe builder or the like) might be best. If we were looking at the Soma or Amprex specifically, we would tack in a Point Strike and Vital Sense immediately, but we're looking at a generic rifle, and most rifles do not benefit greatly from critical modding. Therefore, we skip this factor for now.
Firing rate is a harsh mistress. On the one hand its mods give substantial damage boosts (+0.9, 0.6 and 0.3 (with punchthrough) multipliers), but on the other it impairs your ammo efficiency. However, we're talking raw power, so we will use the largest boost we can get here right away; this is Vile Acceleration or Speed Trigger.
$ (1+1.65-0.15)*1.9*1.9 = 9.02 $ for Vile Acceleration.
$ (2.65)*1.6*1.9 = 8.05 $ for Speed Trigger.
In raw numbers, VA is vastly superior for ST, but it makes each shot worth a bit less, and with that makes your ammo efficiency suffer greater than any other mod in the game. Use it with caution, but for raw damage calculation, you should STAPLE IT TO YOUR BUILD (this being one of the reasons I wrote this lengthy piece).
With 5 slots left, we should look at elemental damage. I will now state three elemental mods are the best combination for raw power, but I will use two examples for your convenience.
Let's assume we use the 90% mods. Three of those will make a multiplier of 3.7 (1+2.7), four amount to 4.6 (1+3.6). This makes the possible damage calculations :
A : $ (1+1.65-0.15)*1.9*1.9*3.7 = 33.39 $ with two mod slots left
B : $ (1+1.65-0.15)*1.9*1.9*4.6 = 41.51 $ with one mod slot left
For these final mod slots, we can look at the Puncture or Slash mods, consider critical amplification again, consider additional firing rate/punchthrough, and consider Heavy Caliber. Since we look at a 'generic rifle', only firing rate and HC are relevant. Heavy Caliber adds a massive multiplier at a hefty cost. However, it only gives about 60% to your damage multiplier, while all other mods we added added over 90% each, which is why I kept it back till now.
With this, B becomes $ (1+3.3-0.15)*1.9*1.9*4.6 = 68.19 $
For A, we can consider adding Shred or Speed Trigger, or another elemental mod still.
Shred would add about 15% to the multiplier, with punchthrough adding more potential (which we cannot calculate).
Speed trigger would add a little under 33%.
Another 90% would add a measly 24%
In practice I would recommend something along the lines of Shred, Ammo mutation, critical chance (if the weapon weren't generic), but for raw numbers, Speed trigger is superior, leading to the following;
A : $ (1+3.3-0.15)*1.9*(1.9+0.6)*3.7 = 72.94 $
That is an amplification difference of little under 5. You may state this as a significant difference, even with reload speed incorporated.
TL;DR : Balance your factors out. Don't slap 90% elemental mods on your weapon one after each other because the number is so high, it's about its relation to the already present multiplier.
Extended to non-conformist rifle-type weapons
To clarify things, I'm not including snipers, launchers, or the Opticor (frankly my most favorite primary) just yet. This extension serves to include Soma (Prime), Amprex, and the Ignis-type weaponry. I will first treat the topic of critical rifles, then the point of 'spraying' weaponry, as I've come to call it. In the course of this 'chapter' I'm going to move out of raw DPS calculation theory and into more practical calculation (which sees the use of Shred, Sinister Reach, Rifle Ammo Mutation and Firestorm surge for rifle-type weaponry). This will be a bumpy transition, but stick with me in the progress.
The example of a generic critical rifle (think Soma, Sybaris)
Critical rifles are an interesting bunch, mainly because their DPS relies not only on your ability to mod and the ability to point in the general direction of an enemy, they rely on you hitting the sweet spot. This is because there is something such as a headcrit multiplier. For those who don't know this special mechanic : if you land a critical hit on a headshot, you gain an additional x2 multiplier to your critical damage. I don't know whether this means x4 damage on a red critical hit, but I'll take it it does.
Inbetween TL;DR Critical rifles are more powerful than raw DPS calculators like warframebuilder suggest. Take that, Boltor Prime zealots.
Example 1 : no red crits, no headshots
Let's assume we're looking at a Soma for now. We won't have red critical hits, only yellows, and besides those, the Soma is a normal rifle with an excessive requirement for accuracy.
Hands down, Serration and Split Chamber are free and massive extra damage, therefore we staple them to our weapon. Next to this we reserve a spot for a firing speed modifier (since we know the Soma has a windup and plenty of magazine size, while not having an excessive reload speed or ammo economy, this is a freecard). Personally I prefer Vile Acceleration, since raw power cannot be argued with, but for the more ammo-conservative amongst us (read, those without restores, carrier, and a valid sidearm to stack rifle ammo for a while), Speed Trigger is also acceptable.
Now, it's time for critical modifiers. The problem about the critical factor in DPS calculation is that it's at best a matter of two factors, and often even one of three. To keep it simple, we will disregard the headshot rate for the time being.
The average critical damage multiplier (law of large numbers again) equals the following formula :
$ Mean DPS multiplier = critical chance*(critical multiplier - 1) + 1 $
When the critchance raises above 100%, the critical damage multiplier is applied directly to the DPS once, and then the remaining critical hit chance (that two digits after the 1 of 100) is used in this formula again.
In other words, say our soma has double the critical hit chance, meaning it has a 150% critical chance, and a 6.6x multiplier on crit. We deduce 100% and multiply the soma's DPS by 6.6 (since it always deals yellow crits now), and then fill in the remaining 50% in the formula above (resulting in another 3.8x multiplier).
For our normal Soma, with a maxed Point Strike and Vital Sense, we have 75%|6.6x, resulting in a mean DPS multiplier of 5.2x (which equals 1+0.75(6.6-1)), coming from 1.6x (which equals 1+0.3(3-1)). This means the combination of PS and VS amplified the Soma's DPS by 3.25. This is, frankly, the highest possible DPS increase for the Soma using only two mods. For those interested, those mods independantly double the Soma's DPS, meaning they, also, pose the highest possible DPS boost for this rifle with only one mod.
With this done, we have three slots left, which allow for triple elemental mods, or two elemental mods and a utility mod like Shred or Ammo Mutation. For logical reasons (a multiplier of 3.7 with an independant mod worth of 0.9) removing an elemental mod is the lowest possible DPS decrease from the maximum.
Now for actual calculations, we truly look at the Soma.
From the Soma page
- Base damage x2.5
- Shots fired x1.9
- Firing rate x2.2 or x1.9
- Mean critical multiplier of 5.2x (as calculated above)
- Corrosive damage of 1.8x base
- Heat damage of 0x or 0.9x of base
Toning this down into less variables, we reach :
- Base damage x26.18
- Firing rate x2.2 or x1.9
- Corrosive 1.8x base
- Heat 0.9x base
Which amounts to :
- Base damage per shot : 261.8, consisting of 26.18 impact, 104,72 puncture and 130,9 slash.
- Corrosive damage per shot of 471.24
- Heat damage per shot of 0 or 235.62
- Resulting total damage per shot of 733.04 or 968.66
- Firing rate of 33 or 28.5 shots/s
- Clip emptying time of 3.03s or 3.5s
And ends up in :
- Mean damage per shot of 733.04 (with Shred) or 968.66 (with a tri-elemental build)
- Mean burst DPS of 24190.32 (with Shred) or 27606,81 (without Shred)
- Sustained DPS of 12155.94 (with Shred) or 14882,38 (without Shred)
This obviously does bar the wind-up speed (which is minimal at best), but without numbers I can't calculate that.
Example 2 : Headshots, still no red crits
I hope you, my dear reader (if you survived to this point) know about the headcrit mechanic. This mechanic doubles your critical multiplier if the hit registers as a headshot. Painful bit : you can hardly aim at every enemy's head unfailingly without cheating. The good part however, is that the big enemies (any heavy grineer and ancients) have clear heads and aren't mobile enough to make aiming very difficult, which means your critical rifle DPS rises to its absolute maximum when it has to count.
To calculate your DPS with a headcrit involved, you'll need to do some self-inspection. You need to know your rate of landing a headshot on said big targets. Let's assume a rate of 60% for now.
This turns your crit multiplier into a matter of chance, different from your mean crit DPS factor.
The new critical DPS factor thus becomes as follows
$ Mean DPS multiplier = critical chance*(critical multiplier - 1) + 1 $ (old formula)
$ Actual critical multiplier = critical multiplier*(headshot chance+1) $
$ New Mean DPS multiplier = critical chance*(critical multiplier*(headshot chance+1)-1)+1 $ (new formula, also a cluster of wibbly wobbly stuff)
This means the DPS multiplier becomes 8.17, from 5.2. This is a 57% increase (!) in power.
In order to use this to settle the Soma Prime vs Boltor Prime debate, I will compare the two weapons.
Actual calculation, BoltorP vs SomaP
Let us keep to the headshot rate of 60%. The SomaP has 20% more base damage than the Soma, and double the magazine size. The Boltor's facts are posted in the windows to the right.
The Soma Prime's shot damage (with a tri-elemental build) is - with the facts we currently have (+20% base damage, +51% shot damage due to headcrits) 1826,23 damage per shot.
this leads to a burst DPS of 52047,67, and a sustained DPS of 36460,72.
The Boltor Prime will be build with three elemental mods, Split Chamber, Serration, Heavy Caliber, Vile Acceleration, and Speed Trigger.
The resulting multipliers are as follows;
- Base damage x4.3
- Elemental damage worth of base x2.7 (thus damage x3.7)
- Firing rate multiplied by 2.5
- Shots fired x1.9
- Crit multiplier (in the same user's hands, assuming Heavy Caliber doesn't influence your headshot accuracy) of 1.11
- Damage per shot of 1828,855, with a firing rate of 25 shots/s
- Burst DPS of 45721,36
- Sustained DPS of 22394,14
Inside information I just realised I forgot to deduce Vile acceleration's 15% damage tax. Might work around that later, but for now imagine BoltorP to be a bit closer to SomaP.
Soma Prime's burst DPS is therefore about 6K higher than Boltor Prime's (which is over 10% more).
And even better, Soma Prime's sustained DPS is nearly 14K higher, which a 75% increase at my best bet. Yes. Soma Prime is our new sovereign deity, even with shred or ammo mutation over an elemental mod.
TL;DR ALL HAIL SOMA PRIME, DESTROYER OF WORLDS
I'm going to start over, for several reasons (not least of them my cornyness in the last few paragraphs, and the messiness of my formulas and mathematical explanations). Here I'll put a little map for the guide for myself, and some sort of version header for you guys. Yes. The Soma and Boltor example is going away. No, I don't agree with SomaP<BoltorP because the Soma is more accurate in any circumstance, but that's a personal discussion, not a mathematical one.
- Basics (Damage/shot, noncritical, nonutilitarian)
- Basic formulas
- Basics with criticals
- Formulas expanded
- New example
- Headshots, headcrits
- More math
- More examples
- Basics with firerate
- Combined with crit, brief expansion
- Formulas expanded
- Basics with hit ratio
- Introduction/header to getting personal hit ratios. Disclaimer as to relative inreliability.
- Formulas expanded
- Elemental multipliers
- Specific formulas
- Total formulas
- On the usage of punchthrough, ammo mutation, range increase
- Explanation as to informulability
- 'Example' (recycled?)
- 'Mousewheeling' (the Amprex, Phage, Gammacor glitch)
- Modding under circumstance
- Introduction to statuses
- Modding for status
- (only named example)Tysis
- Full formula including disclaimers
- General baseline modsets per weapon type (practically a very large TL;DR)
- Brief expansion to melee
V1. Blueprint made 31-12-2014 10:46 GMT+1. Happy new year in advance!
V2. 1-1-2015, begin of revamp made, introduction and basics done
This guide is a project set up to make the system behind your weapon's mods more transparent. My purpose is to have any one reader of this guide develop a stronger feel for the mods he or she could choose, and to then be able to make the best decision for their gameplay purposes.
With that official thing being said, I try to keep the tone light. Math is often a boring topic, so I will try to keep the pure math in its own corner, separate from explanations. Sometimes it can't be helped (especially when stuff like criticals come aboard), but I try to maintain an enjoyable experience.
I will mainly focus on rifles for my examples, but the points given here will obviously also translate to pistols (albeit with the one problem that criticals are far less powerful on pistol weapons, and status chance is far more potent). These facts will also relay to melee, but do note that it's far harder to make headcrits (or headshots anyhow) with melee weapons, and their DPS can hardly be calculated with the current knowledge. However, one can rather easily compare two same-type melee weapons using this guide. Shotguns are a weird bunch, but they can be calculated like rifles, with the caveat that you can barely estimate how much of your damage is going to hit.
Now then, if you're ready, let's dive in :)
In this chapter I will introduce the idea of multiplier balancing, staple modules, potency comparison, and practicality choices. Do note that for now, I will only consider raw DPS as target factor, leading me to use the 90% elemental mods over the 60% dualstat ones.
At the root of your damage is your own weapon. If you take a look at the stat window in-game (or on this wiki), you'll see a daunting amount of variables, varying from Impact to Status Chance, and from Critical to Ammo. If I may spoil a bit of this guide already; every single factor there matters. And then some.
To begin building that pile of math up, we will make a beginning with the damage a separate shot will deal. For any examples in this chapter, I will use a generic rifle dealing 100 damage per shot, along with the mods we usually have in our possession. This rifle will have 5 mod slots.
As to make some sort of logic clear in my choices, imagine you have our example weapon and ten possible mods. Five of those mods will give your weapon +100% base damage (much like Serration or Hornet Strike), and the other five will give +100% elemental damage (like Hellfire or Contagious Spread would).
If one of those base damage boosts would be applied, it would mean the damage of our rifle would be doubled. By base, it deals 1x its base damage, and our degenerate Serration adds a +1 to that multiplier, make the damage dealt 2x 100, or 200.
Since that helped, we could just as well throw in all five, right? That would make the damage of our rifle sixfold (its 1x base plus five times +1), or 600 damage per shot. This means we increased our damage per shot by 500%.
Now, what would happen if you'd replace one of those mods by an elemental mod?
$ Damage = (1 + 4*1) * (1 + 1) * 100 = 5 * 2 * 100 = 1000 $
Which means we multiplied the total damage by 10. That's a nice bit higher than the original 5x base damage mods, right? This gets even better if we balance our mods out as much as we can, which in this case would be 3 of one and 2 of the other;
$ Damage = (1 + 3*1) * (1 + 2*1) * 100 = 4 * 3 * 100 = 1200 $
Which is a x12 multiplier applied to the base; twice as much as only throwing five +100% base damage mods on!
In actual in-game situations this is not much different; balancing your DPS factors out is the way to get the absolute most out of your rifle. The biggest problem with that is the problems some of those mods would bring; Heavy Caliber makes you miss shots at range, perhaps even reducing your DPS in the end, while Vile Acceleration makes you expend ammo at speeds that makes all but the most efficient of weapons run dry eventually, reducing your DPS by giving your weapon a downtime, or even making you expend credits and materials to keep your ammo pool topped off (which is unacceptable for us treasure hunters).
A couple of the DPS affectors are staple mods, as I refer to them. This is because those mods give major effects without reducing your weapon's efficiency or increasing the complexity of your calculations, being, in (almost) any build an ideal choice.
For rifles, those mods are Serration (165% increase) and Split Chamber (90% increase), along with the first elemental mod (90% increase) you'd choose to put in. For pistols those are - in order - Hornet Strike (220% increase), Lethal Torrent (156% increase), a first 90% elemental mod (90% increase) and Barrel Diffusion (75% increase after Lethal Torrent).
A second 90% elemental would only give a 45% damage amplification (0,9 / 1,9), making it a choice for later.
For shotguns, this order goes Primed Point Blank (165%), Blaze (156%), Hell's Chamber (120%) and then Point Blank (90%). Note that Blaze gives an elemental amplification of its own, making a 90% elemental mod give only an underwhelming 56% increase in damage.
In this chapter I will ignore melee, because melee weapons require criticals and attack speed to be modded for.
If we would mod our generic rifle, we'd thus first throw in Serration and Split Chamber, along with Infected Clip (just to pick one mod). This means our damage per shot is now;
$ Damage = (1+1,65) * (1+0,9) * (1+0,9) * 100 = 957 $ after rounding.
We now have two mod slots left, with only base damage, multishot, and elemental multipliers as modding factors. Multishot is maximized already (since Split Chamber is our only option for it), so we can discard that option.
This leaves Heavy Caliber and the selection of 90% damage elementals for modding. Heavy Caliber would have an impact of (1,65 / 2,65) 62%, another elemental would have an impact of (0,9 / 1,9) 47%. By this logic, Heavy Caliber is our first choice for more power, followed by an elemental mod to top off.
This has us end up with the following;
$ Damage = (1+3,3) * (1,9) * (1+1,8) * 100 = 4,3 * 1,9 * 2,8 * 100 = 2288 $ after rounding. It goes without saying that this is higher than one'd get from only using Serration and four elementals, or not choosing Heavy Caliber.
That calculation being done however, you should be very hesitant to use Heavy Caliber. Any usage of that mod (as well as Magnum Force and Vicious Spread) should be well thought over and playtested for accuracy; some weapons are heavily affected by it (like Ogris and Boltor Prime) while others almost ignore their effects (like Opticor, Synoid Gammacor and Phage). Missing shots might be more detrimental than foregoing a x% damage boost.