# [Guide] Forceful Expression, Infusion and Sustainment - Details and Math

These three skills have weird interaction with each other and don’t necessarily work as you would expect. Therefore I decided to create another guide and offer some test results, numbers and formulas so that anyone can make some informed decisions when choosing skills.

# Table of Content

Here’s a neat little chart created by @MentalMars with all the elemental multipliers for easy reference, we’ll use it later on for the calculations:

# Infusion

Let’s start with Infusion. It technically does what it says, it converts damage, 8% per point allocated skill point. But…

On non-elemental guns, you lose 8% non-elemental gun damage but gain the same amount as shock/corrosive/fire elemental damage. This can be favourable if you attune yourself to the element an enemy is weak against (fire for flesh, corrosive for armour and shock for shields) because those elements get multiplied as shown on the chart above and also benefit from Amara’s Tempest skill.

Cryo and Radiation guns fall in between non-elemental and elemental corrosive, fire and shock guns. They have more average/consistent multipliers then the other three elements across the three defence types but are slightly more specialised than non-elemental guns. With those two elements Infusion can make sense if you run them exclusively. But as soon as you also run the other three elements Infusion would be detrimental.

If you’re using corrosive, fire and shock elemental guns your almost always better off not using Infusion and instead switch guns depending on weaknesses. 100% corrosive damage against armoured targets is always better than 60% corrosive (with 5/5 Infusion) and a bit of additional shock or fire damage that’s significantly reduced by the multiplier shown on the chart.
You could argue that this can be countered by just switching elements in the skill tree to have both gun and Infusion set to the ideal element. That’s true but that has also two downsides:

1. Both the base elemental damage and the conversion from Infusion are calculated separately by the engine and therefore they apply DOTs individually. The base DOT that is usually stronger gets applied first and the DOT from Infusion afterwards. But when both elements are the same the weaker Infusion DOT will override the stronger base DOT. Not a big deal for the most part since DOTs are usually weaker than the front-loaded direct elemental gun damage.
2. You invest valuable skill points in order to get exactly the same result as if you’d just ignore Infusion.

IMO the only reason to use Infusion on those elemental guns is if you want to stick to a certain gun/element because you like that gun/element or you don’t want to switch weapons. But you have to keep in mind that you’ll lose damage/DPS and will need more ammo to get the same result.

It’s also important to mention that DOT damage is not only tied to elemental damage and its modifiers but also directly to gun damage. If you increase gun damage you also increase DOT damage. Some guns have higher special multipliers for the Gun Damage to DOT Damage conversion but the same rule applies here as well: when increasing gun damage on those guns with a special multiplier you also increase the DOT relative to the special multiplier. By splitting damage via Infusion you’ll always end up with weaker DOTs.

Here are some screenshots for comparison to show the difference and make it clearer what I described above. I used a corrosive weapon on an armoured target to represent the ideal case. First the damage without Infusion. The 408 is a DOT tick that can be ignored.

And now with 5/5 Infusion and attuned to Shock. Everything else stayed the same.

In comparison, 40% or 444 less corrosive damage was dealt (removed) while the shock conversion from Infusion added just 165 shock damage.

In this scenario, if the target would also have a shield I’d deal more damage to the shield but way less to the armour part. If you’re facing shielded enemies regularly and don’t have any other easily accessible source for shock damage (e.g. grenade) one point in Infusion is usually enough to strip shields quickly. That way you can retain the majority of base elemental damage. Or you could just use a radiation gun which makes quick work with both shields and health bars. That way you could spend those skill points elsewhere. For beefy boss shields, you want to carry a shock weapon anyway.

## Damage Formula

[GunDamage] * ( [GunElementMultiplier] * [InfusionMultiplier1] + [AttunedElementMultiplier] * [InfusionMultiplier2] ) = [ResultingDamage]

while

[InfusionMultiplier1] = 1 - 0.08 * [InfusionRank]
[InfusionMultiplier2] = 0.08 * [InfusionRank]

Examples

Non-elemental gun, 500 base damage, attuned to fire, flesh target, TVHM, Infusion 5/5:
500 * ( 1 * 0.6 + 1.75 * 0.4 ) = 650
Without Infusion it would be only 500 damage, not accounting for Mayhem modifiers, elemental damage bonuses, etc.

Now do the same thing for an elemental gun but with dual-element (having both gun and Infusion set to the same element doesn’t make any sense as described above).
Shock gun, 400 base damage, attuned to fire, flesh target, TVHM, Infusion 5/5:
400 * ( 0.65 * 0.6 + 1.75 * 0.4 ) = 436
For comparison, by using a fire gun with 400 base damage, without Infusion and on a fleshy target you’d deal:
400 * 1.75 = 700

# Forceful Expression

This skill doesn’t convert damage but you’ll get 18% bonus elemental damage on top of the damage you’re normally dealing with your gun. In this case, it doesn’t matter that much (compared to Infusion) what type of element your gun has by default, it’s always 18% of your gun damage that gets multiplied. Having both gun and elemental damage bonuses increases its potential significantly due to them interacting multiplicatively with each other.

It’s best used when you attune yourself to the element an enemy is weak against. While mobbing it’s great for stripping shields (attuned to shock) if you don’t have any other source of shock or radiation damage. For bosses, you should switch to fire/corrosive unless the boss has a beefy shield.

## Damage Formula

[GunDamage] * ( [GunElementMultiplier] + [ExpressionMultiplier] * [AttunedElementMultiplier] ) = [ResultingDamage]

Examples

Non-elemental gun, 500 base damage, attuned to fire, flesh target, TVHM:
500 * ( 1 + 0.18 * 1.75 ) = 657.5

Fire gun, 400 base damage, attuned to fire, flesh target, TVHM:
400 * ( 1,75 + 0.18 * 1.75 ) = 826

# Combination of Infusion and Forceful Expression

So far I can say that it’s always beneficial for non-elemental guns. And when using a non-favourable gun element (shock on fleshy targets) with Infusion the additional damage from Forceful Expression outweighs the loss in damage to some degree but it’s still worse than just using the correct gun element respective to an enemy weakness.
I haven’t yet figured out how the combined formula for both skills looks like. I’ll update the thread in case that changes. If you think you know how it works send me your data and I’ll include it.

# Sustainment

Sustainment uses the default element of your gun and 100% of its damage for its calculations. That means if you’re using a non-elemental gun with Infusion you won’t get any life steal. But you get the full amount with elemental ones, even when using Infusion on top of that. Neither Infusion nor Forceful Expression make a difference when it comes to life steal from Sustainment.

For a more in-depth analysis check out @DocStrangelove’s guide: Sustainment Analysis

# Mayhem Modifiers

Some mayhem modifiers apply before and some apply after elemental conversion/bonuses (mathematically). To determine whether a modifier is beneficial or detrimental for Infusion I ran some tests.
The tests were done with 5 points in Infusion and a non-elemental sniper rifle. The left damage number is the base damage without modifier and the right image shows the damage with the modifier applied.

## Modifiers that apply before conversion

So, all gun damage modifiers apply before the conversion. They directly apply to the [GunDamage] variable in the formulas above. Because of that they also affect the converted elemental damage

## Modifiers that apply after conversion

All the modifiers that affect elemental damage types seem to apply after conversion. That’s good because it means reductions to “Normal bullets” (non-elemental) won’t also reduce the converted damage.

23 Likes

Nice post. Do you think having just 1 point in infusion is worth it for the double DoTs on elemental weapons with the right spec or is it just a damage decrease on the original DoT?

Also, vs multiple healthbar enemies, like shield/armor/health types, I remember reading that infusion helps a lot with those since you have a bit of each (kind of like the Thunderfire laser from TPS) and switching weapons in-between health bars is also a dps decrease. Although I think that post is from before the game’s release so it might be incorrect.

In my opinion it depends on the enemy. If it is a weaker enemy with two bars infusion will help a little but you’ll kill the target regardless. For the really tough ones I prefer to just switch guns. You’ll have to switch guns at least once anyway if they have three health bars.

That said, this could be where having a anointed gun with bonus element damage could help. Because when you switch guns you lose the effect. But if you can’t kill the target in the 8 seconds it is activated then you’ll lose the effect anyway.

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Bonus element is actually for 2 mags after action skill use and refreshes each action skill use. that’s why I really like it with my brainstormer rhat has 16 in the mag thanks to my relic and comp

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If i’m using a phasezerker class mod it’s better 10 more rush stacks (3% more damage for every stack) from avatar or the 18% damage from forceful expression?

18% always on is cool but you can heavily invest in action skill cooldown and have all the bonus from 10 more rush stacks flowing

It depends on the bonuses you already have. The more gun damage you stack via class mod (Phasezerker’s unique bonus and the three affixes at the bottom), artefact and skills the more valuable Forceful Expression becomes while additional gun damage becoming less valuable. Gun damage is calculated like that:

[BaseDamageItemCard] * ( 1 + [GunDamageBonuses] ) * ( 1 + [GunDamageGuardianRank] ) = [ResultingGunDamage]

Then insert the result into the formula for Forceful Expression as the [GunBaseDamage] variable.

I’d say that in most cases* FE adds more damage if the element matches enemy weaknesses due to it being multiplicative instead of additive like gun damage.

*when using Phasezerker with at least one skill point in Do Harm or Violent Tapestry and some bonus from either COM, artefact, Wrath, Samsara, Jab Cross and/or Dread

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I just used a very basic setup for comparison, without any gun damage bonuses other than those from Phasezerker:

25 Rush stacks (Avatar): 1.75 * 1.75 = 3.06
15 Rush stacks (FE): 1.45 * ( 1.75 + 0.18 * 1.75 ) = 2.99

Now the same calculation with Dread and Wrath:

25 Rush stacks (Avatar): 2.3 * 1,75 = 4,025
15 Rush stacks (FE): 2 * ( 1,75 + 0.18 * 1.75 ) = 4,13

The difference isn’t that big. If you don’t feel like constantly switching action skill elements I’d recommend going with Avatar. If you don’t mind switching elements from time to time and want max DPS, go with FE.

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Thanks for all the responses, , it will be very useful in the future builds

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Thanks for this post, it explains some of Amara’s Skill Tree in far greater depth, especially for those of us who aren’t all too mathematically inclined. Amara was my 2nd toon but she has certainly become my main, as FLAK struggles to clear anything on M3 (at least the way I have played him and what gear I have for him in endgame). I struggled ridiculously to level Amara up because i stubbornly refused to leave the elemental tree before i got capstone, but once i did that and began to branch into Mystic Assault things began to fall in place.
A question, if you feel so inclined. I typically keep Fire on as my default element, does the capstone reward stacking the same element as your action skill (fire gun + fire augment specced) versus differential effects?

If you use it on fleshy targets without shield and armour you’ll definitely benefit from having both gun and action skill element as fire. By using it the same way on shields and armour both the base elemental gun damage and elemental damage from FE will suffer from vastly reduced damage. In normal mode this isn’t that big of a deal since the elemental multipliers are more forgiving but in TVHM it can become problematic.

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So meaning that it is a damage loss when used upon an element it is not strong versus? I.E. Fire specced versus Eirdians?

Thanks for the correction. The others are 8 seconds and any bonus damage would be lost switching weapons.

Correct. In TVHM fire damage vs shields and armour is halved.

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Aye I am nearing the end of my playthru on TVHM, has been much easier than leveling up had been thus far. I didn’t die on a single boss encounter up to Troy… But that being said i feel like Mayhem mode is going to absolutely wreck me

If you don’t want to use shock very often, it can be nice to have 1-2 points in infusion with shock element. Between your 50% buff to shock and shock having 250% bonus vs shields, it can really make a difference in other elemental weapons still taking down the shields quickly if 8-16% of your gun damage is shock.

That’s just if you don’t want to constantly switch to shock for shields.

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Yeah guess that was their way of balancing it since less damage. It led to some pretty broken stuff with flakker Moze and that buff tho (RIP).

Whether it’s lost on switching I’ll still need to test (and should be easy to just never came to mind) since I only ran it on my brainstormer only build but yeah the mags were essentially unlimited since I had action skill again before the 2 mags were up and having 16 in the mag.

The one use I have found for infusion is that it allows me to run The Transformer shield with an Elemental Projector and still electrocute myself. When running infusion, you always apply a DOT corresponding to your selected element if you apply another DOT. This will bypass the Transformer’s ability to negate all shock damage for some reason. One point in infusion is enough to allow this interaction.

It’s a niche use but running Transformer and Elemental Projector is pretty common for Amara.

That’s probably a much better idea than leaving Fire default . i used to run Shock figuring the damage buff from Tempest, but it seemed like most cases it was underwheming. This was while leveling though I’m gonna give it a try now that I’m nearly done with my TVHM playthrough so i can attempt Slaughter Shaft etc on TVHM mayhem mode. I’ve accumulated a few good items on her and run a glass cannon build. Wish me luck thanks for helping me learn a little y’all

Interesting… I’ve found that investing 5/5 Infusion (with 5/5 Anima and 5/5 Tempest) on my Phasezerker/TTB Amara gives me a huge edge in battle.

Mostly using a elemental Rad weapon, and keeping SoulFire augment for most of the enemies, I melt shields, armors and obviously flesh WAY faster than when not using Infusion.

I know that in terms of numbers, it might not be the best option, but in term of “time taken to kill things”, I swear it’s really faster

The thing is, with TTB, the DOTs pass from the phasegrasped target to the other linked to it, and having Rad+Fire DOTs on them, they do damages to themselves all together. With this, I chomp on shields and armor like nothing !
Same for bosses : yesterday on my tvhm (not finished yet) it took less than 2min to destroy Agonizer 9k

I don’t have the numbers, but I’m sure things die REALLY fast. Has anyome else noticed that ?

All in all, very interesting post ! Thanks a lot for this great work

If Infusion does not count as weapon damage - does it not benefit from weapon damage buffs then? Or does it apply after the weapon damage buff has applied to the base damage - so it mathematically still benefits?