[Guide] Optimizing Moze's Damage - Math without Numbers

[Prismatic (Dancing with Jak 'o' the Shadows)]

Whether min maxing or just trying to make an idea work, we’ve all gone looking for more damage in our builds. You might will venture to the Moze Gun Damage thread and see the following:

Gun Damage = Normal Hit x v1 x v2 x Splash x Elemental Multiplier x Critical Damage

Problem solved right? You now know how damage is calculated for Moze, lets all go home. Nice though that may be, for many I think the above is more confusing than helpful. I’m one of the weird ones round this forum that actually cares about the intricacy of the above, not many do. The real question most people have is:

how do I translate that formula into killing things quickly?

I want to tackle this question, but I don’t want to do so by drowning you in numbers. I want to explore the question of getting more damage by approaching guidelines for you to use when constructing a build. To some it might seem black magic when math wizards can eyeball 2 bonuses and know which is best for damage, I want to take a crack at building your intuition for knowing where the biggest damage is coming from.

Damage Modifiers

Unfortunately before we can start we do need to know a bit about the damage formula. Don’t worry about the maths, what you need to know is what type of damage the common bonuses are.

• Normal Hit: All gun damage boosts in Shield of Retribution, click, click and the class mod roll “+% Weapon Damage.”
• v1: There’s 2 notable v1 boosts Moze has access to.
  • C-C-Combo: This is a guardian rank perk.
  • Victory Rush the 18% damage bonus from killing a badass is v1.
• v2: There’s 3 notable v2 boosts Moze has access to.
  • Weapon Type Damage: This is the specific weapon type rolls on class mods, such as “+% Pistol Damage.”
  • 25% OGT: This is the grenade anoint that gives 25% damage on grenade throw.
  • 300/90: A gun anoint that gives 300% damage to enemies above 90% health.
• Splash: Anything that boosts splash or area of effect damage.
• Elemental Multiplier: Stoke The Embers, Old God and any of the gear rolls such as “+incendiary damage.”

Note: v1 and v2 are just names we have given to 2 categories in the damage formula which contain many relevant boosts, the names themselves have no special meaning.

The Clichè

Everyone’s heard that multiplicative damage is the best damage right? It’s fairly common knowledge that splash damage is multiplicative, so therefore when we use an Ion Cannon we want to stack splash damage right?

So let’s experiment then. I’ll grab one of my best Ion Cannons and we’ll play a guessing game about which of the following class mods is going to do more damage:

For Blast Master I’ll let the Splash Boost charge to full, and for the Bloodletter I’ll reduce myself to 1hp with a Front Loader and Thin Red Line. I’m not going to spend any more skill points, so the class mods only get the skills they boost.

We’ll start simple, I won’t activate the annointment on the Ion Cannon. So, my dear reader, which class mod is going to win? My moneys on Blast Master.

Blast Master Produces:

411k!!!

And the Bloodletter produces:

368k

So a round of applause for all who didn’t doubt themselves and stuck to Blast Master. So onto the formality of taking a shot with the annointment active. We’re all holding firm with Blast Master winning right?

The Blast Master with +125% Splash annoint:

668k!!! We’re over half a million damage with Blast master without a single skill point spent, which is insane! So what did Bloodletter manage?

728k!!! Madness, what Black Magic is this? All we did is add the same bonus and suddenly Blast Master is losing, but it was winning before? Ahh my dear reader, you’ve just seen the true intention behind saying multiplicative damage is better.

Let’s go back to the drawing board about where Blast Master went wrong and why adding a splash annoint doesn’t follow the rule of multiplicative damage being best.

What are Additive and Multiplicative Damage?

Before I talk of the Borderlands communities use of additive and multiplicative, lets see what the terms mean from a maths standpoint.

It may have occurred to you that additive sounds a lot like add. There’s a reason for that, the real meaning of two numbers being additive is that when put into a formula, we’ll add the numbers. I hope it’s simple to then make the leap that multiplicative means we’ll multiply the numbers.

So let’s try this in an example. If my first bonus is Purple, my second bonus is Blue and they are said to be additive, when we do the calculation it will appear as so:

Total = Purple + Blue

Now lets add a third variable Red and we’ll say this is multiplicative to our friends Purple and Blue. The calculation thus becomes:

Total = (Purple + Blue) x Red

Simple enough right? Well let’s up it another notch. A 4th variable Yellow is introduced and this is additive to Red.
Well hold on Prismatic, isn’t Red multiplicative?
Glad you caught that, yes Red is multiplicative to Purple and Blue, however that doesn’t stop it being additive to Yellow. Additive and Multiplicative are relative terms, they only make sense when comparing terms or groupings of terms. When I say Yellow is Additive to Red I make no mention of its relation to Purple and Blue. However as we know how Red interacts with Purple and Blue we can interpret how Yellow fits into our overall formula.

Total = (Purple + Blue) x (Red + Yellow)

If we return to Borderlands math, I hope that description just set alarm bells ringing in your head. Something should seem off about what I said earlier

Do you see any errors? Have I not been careful in my wording? If you’re not seeing it lets narrow it down further:

If you think about what I just said about the meaning of multiplicative, this shouldn’t make sense to you. How can Splash be multiplicative if I’m not comparing it to anything?

The answer is we as a community have gotten lazy, everyone used to compare things to Normal Hit, and in that context, yes Splash is multiplicative to Normal Hit. However, the information lost is that splash isn’t multiplicative to itself. So Blast Masters splash bonus and the 125% bonus splash boosts are not multiplicative to each other, they’re additive.

So why did Bloodletter win?

Lets look at the 2 coms we where using and breakdown the damage we where getting from them:

Bloodletter

I didn’t stack Phalanx Doctrine, so we can ignore it. I did however have 1hp, so that’s 50% from Desperate Measures and the 25% weapon damage roll. These both fall under Normal Hit. I then have the 28% splash damage roll which predictably falls under splash.

In summary Bloodletter gave me:

• 75% Normal Hit
• 28% Splash

Blast Master

Again I have a 25% Weapon Damage roll that will fall under Normal Hit. I also have the full 100% bonus Splash from Blast Master.

In summary Blast Master gave me

• 25% Normal Hit
• 100% Splash

When broken down like this we see that Blast Master gave us bigger numbers, and predictably with nothing else applied it won.

So what changed when we added the 125% splash annointment?

Bloodletter became:

• 75% Normal Hit
• 153% Splash

Blast Master became:

• 25% Normal Hit
• 225% Splash

Blast Master still gives us bigger numbers, but notice how much more lopsided the damage is. The two numbers vary by 200%! The Bloodletter set up is not something I’d call balanced but the difference is far less severe with a difference of 78%.

Normal Hit is going to be multiplied by Splash, so we want the combinations that give us the highest numbers from multiplication. As a general rule you want two medium size buffs instead of one big and one small.

The Moral of the Story

If you’re debating between 2 buffs of approximately the same size then you’ll always get the biggest boost by choosing the buff that affects a category you’ve buffed the least.

You want to play a game of buffing each category in turn and keeping them relatively even. So a quick reminder on the main categories Moze has for buffing her damage.

• Normal Hit: All gun damage boosts in Shield of Retribution, click, click and the class mod roll “+% Weapon Damage.”
• v1: There’s 2 notable v1 boosts Moze has access to.
  • C-C-Combo: This is a guardian rank perk.
  • Victory Rush the 18% damage bonus from killing a badass is v1.
• v2: There’s 3 notable v2 boosts Moze has access to.
  • Weapon Type Damage: This is the specific weapon type rolls on class mods, such as “+% Pistol Damage.”
  • 25% OGT: This is the grenade anoint that gives 25% damage on grenade throw.
  • 300/90: A gun anoint that gives 300% damage to enemies above 90% health.
• Splash: Anything that boosts splash or area of effect damage.
• Elemental Multiplier: Stoke The Embers, Old God and any of the gear rolls such as “+incendiary damage.”

We’ve just looked at an example using Normal Hit and Splash, however this applies to any of the four categories. If you’re already using an Elemental Projector(an Elemental Multiplier), then +30% Splash damage is far better than another 30% Elemental damage.

Keeping variety among bonuses is the best thing you can do for your damage.

The more balanced you can have your different categories generally the better you’ll do. This avoids running into diminishing returns. Its important however to remember that any damage is more than no damage, just because you have some of a category don’t begin skipping opportunities to get more of it. You only need to worry about balancing categories in a case where you’re forced to choose between them.

I’ve not included it here for simplicity but Critical Hit bonuses are actually a fifth category

The Odd Birds

Until now I have conveniently ignored 2 large damage sources that Moze has access to, those being bonus elements and Short Fuse. I have not mentioned them because they play by different rules.

Bonus Elements

You can think of bonus elements as a second shot in the new element with a % of your guns damage. The bonus elements however will not receive Splash. Bonus elements from grenade and shield anoints also do not receive the Weapon Type boost, whereas the rest do.

Except Skag Den, but I do not plan to discuss it here.

So a visual reminder of how this looks

Bonus Element Damage = Normal Hit x v1 x v2 x Elemental Multiplier x Critical Damage

Bonus elements and Splash are two separate entities and do not benefit each other in any way. So despite being different modifiers they do not follow the same trend of variety being the spice for death.

They both have the same diminishing returns effect that we get from stacking multiple of the same bonus (like stacking Normal Hit). So, when comparing bonuses for purposes of simplicity, you can often consider bonus elements and splash the same category.

Given the choice, Moze will almost always benefit more from boosting Splash than picking up a bonus element. Splash has a more important and consistent role in Moze’s damage formula. Bonus elements are powerful on their own but do not influence the damage of Iron Bear, Short Fuse, or Mind Sweeper to the same degree that Splash will.

Short Fuse

A 20% chance to add 75% damage does not sound great for a capstone, yet it is her best capstone due to how it actually functions.

Short Fuse does benefit from mayhem scaling but, for simplicity, we will focus on the non-mayhem scaled Short Fuse.

Short Fuse is based off the total damage that triggered it, so anything that boosts the actual bullet damage of your gun will boost Short Fuse. This is all nice but is not why I call Short Fuse an odd bird. The wacky mechanics come with how Short Fuse boosts the damage that triggers it.

Short Fuse Damage = Trigger Damage x SF Modifier x Splash x v1 x v2

SF Modifier is an abbreviation for mayhem scaling and the base 75% damage. Since these do not influence player decision making I have combined them into 1 modifier for simplicity.

This highlights the categories that we want to pay the most attention to but it does not show us how to balance our other bonuses. So lets look at the formula when Trigger damage is written out in full.

Short Fuse Damage = [ Normal Hit x v1 x v2 x Elemental Multiplier x Critical Damage ] x SF Modifier x Splash x v1 x v2

2 Important Things:

• There are a lot of categories here.
• Splash, v1, and v2 are listed twice.

Having this many categories hints at how powerful Short Fuse can be. Having the Splash, V1, and V2 modifiers listed twice also gives us a place to start our hunt for damage. Since these categories are opportunities to select a buff that you’ll be benefiting from twice. So what are our options to improve these 3?

v1

Since Moze has nearly no access to this modifier, it is something that will always be in your best interest to maximize.

• C-C-Combo: A guardian rank perk that you should always have enabled once you get it. It is a significant damage boost, especially for higher fire rate weapons.
• Victory Rush: This is a really handy bonus to receive and in harder content where you want the damage bonus most it will be nearly always on.

v2

Another bonus that Moze lacks in her skill trees, you should generally take this modifier on your gear whenever able.

• 25% On Grenade Throw: This is Moze’s primary grenade anoint as she has the grenade regeneration to keep it up and will be throwing grenades anyway for Vampyr and Redistribution. This damage bonus also counts twice for Short Fuse making it even more powerful.
• 300% Damage to enemies above 90% Health: For One-Shotting or phase skipping weapons this anoint is unrivaled on Moze as it results in the highest Short Fuse procs. For general use few weapons can make good use of it due to enemies falling below the 90% threshold. This anoint is worth having in your backpack for burst damage but is rarely the best option for general use.
• Weapon Type Damage: This is the only v2 that Short Fuse does not double dip but it still remains a valuable damage boost anytime you are not using 300/90.

Splash

Among the categories that Short Fuse double dips, Splash is the easiest to invest in and will often be one of the highest stacked modifiers in any build. Splash also increases Iron Bear’s damage, when using splash hard-points, making this modifier even more important.

Splash or Area of Effect damage rolls on your class mod and artifact are always best in slot for damage rolls in a Short Fuse build. These are bonuses that should be hunted with high priority.

The Splash bonus of Torgue Cross-Promotion is always worth the investing in if you are going as far as Short Fuse.

The anointments for Splash damage are second only to 300/90 in their damage potential for Short Fuse. They are excellent choices when seeking the highest consistent DPS but do require cycling Iron Bear frequently.

Wrap Up

Well, here we are. Hopefully by this point I’ve hammered into your head that diversifying boosts is the most efficient way to boost damage, and I’ve given you ideas on where to look for this multiplicative damage. The Bloodletter Ion Cannon example should be a shock to your system about why different boosts are better than bigger ones of the same type.

I’ve done my best to avoid throwing numbers around as I realize most don’t want to do math in their gaming down time. Feel free to ask if you want me to show any numbers, otherwise head over to my Intro to Borderlands Math if you want to see a more numbers intensive breakdown of multiplicative damage and how to compare bonuses.

You can also find a full breakdown of all the multipliers in this game in the General Breakdown of Borderlands Gun Damage or if you want to see the Moze damage formula written out in one long equation you can find it in The Moze Math Compendium.

Acknowledgements

I want to say a massive thank you to @twoPIZZA and @Mahtyo who both proofread multiple early drafts of this thread and gave me valuable feedback.

[Mahtyo (Meowze)]

Greay write up, as always!

[plenipotence]

one of my pet peeves is throwing around the “additive” and “multiplicative” without context, since the words express the relationship between things. And can give people the impression that gun damage is undesirable or something.

Also I’m curious why you reworded your bullet damage formula to just list Weapon Type Damage by itself instead of Special Multipliers. Since most characters do have special multipliers (FL4K is the best character to illustrate them with, but Moze has Target Softening for example). And class mod type bonuses should be additive to some of them

[choskison (xCaliburxxx)]

You rock, i don’t even play Moze and read through this. It is great information.

I do have a few of questions -

1. Where would Guardian points be added into this formula, at what point?
2. Seems to me, as i have always suspected, it is better to have more normal damage before any modifiers, correct? Like i use a +25% weapon dam , +18% cirt, + 31% AR Dam mod on Zane?
3. Have you ever or can you do something like this for Zane?

[Prismatic (Dancing with Jak 'o' the Shadows)]

This.

This is a case where I believe Weapon Type Damage is more relevant to this discussion on Moze. The formula above is by no means complete, as I also don’t include guardian rank or amp damage. I prioritized including the bonuses that people are likely to be picking between.

I actually never double checked that target softening is a special multiplier, so again am hesitant to include it.

I have nearly zero knowledge on how Flaks damage works, I just know he has 2 big special modifiers. I know Amara’s Personal Space is additive to weapon type damage, but I’m unsure if there’s anything else.

They’re a category on their own and would be multiplicative to everything discussed here. For damage comparisons they’re equally effective in all set ups.

30% normal damage is as valuable as 30% splash damage. The difference is normal damage is generally easier to acquire so people take it for granted.

I’ve not been as technical in my time with Zane. In order to do this I’d first need to do the groundwork of working out the damage formula and actually analyzing Zane.

However that said if there’s enough interest in it I will look into creating either a Zane specific one or even just generalizing this for all 4 characters.

To expand on Zane, I also don’t think I could do as effective a write up. The archetypes I write about for Moze are not something I’d have the faintest clue about for Zane. From what I’ve seen of his meta it’s already pretty good about encouraging multiplicative boosts with things like barrier and ice breaker. Moze on the other hand has the 2 mammoth damage type boosts that so often I see people needlessly stacking.

[plenipotence]

Have you seen any of the work the discord has done on damage formulas? I pretty much lurk everywhere but I am not sure if there has been much math-nerd-cross-communication. The basic idea is that most of the multipliers in the game fall into two categories, if you saw the video demonite made on FL4K math they are what he called“V1” and “V2.” Almost all the skills that increase Damage as well as items that increase damage like Victory rush, Icebreaker, Piss, Eruption, etc fall into one of those two categories

I think some stuff on the sheet is still wrong (everyone here always says barrier amp is a multiplier for example), I have only really double-checked FL4K math. But Spy is good about correcting stuff and it’s usually being updated toward further accuracy

[Prismatic (Dancing with Jak 'o' the Shadows)]

I had not seen that, thank you I’ll take a look through it.

[roboteconomist (Probably the dumbest Moze player...)]

Based on this information, I have actually specing away from the DW tree when using the Best Master since it gives you the splash damage boost and points into the tree’s two most important utility skills. If I can afford the 8 points, I will go down to MoD, but that’s it.

[twoPIZZA]

If I can afford the 8 points, I will go down to MoD, but that’s it.

I wish I could get away from PtHP and MoD.

[olivier_shady]

Whoa thanks a lot as one who struggles to get damage I understand better how this works. I have a question how annoitment like “the next 2 mags will have 50% elemental damage” stands compared to the 50% elemental on ase ? Are they different? Are they multiplier or added ?

[Prismatic (Dancing with Jak 'o' the Shadows)]

I’d need to double check to be totally sure. However if memory serves if they’re the same element then they’re directly added.

Elemental damage annoints as a whole will follow all the same principles as additive bonuses do.

[twoPIZZA]

This would be because they’re 50% of gun damage, right?

[Prismatic (Dancing with Jak 'o' the Shadows)]

Not quite. It’s because the bonuses don’t enhance each other. If I am dealing 100 damage as cryo because of an annoint and I add a radiation annoint the new annoint has no effect on my cryo annointment and also doesn’t benefit from it in any way.

Whereas If I have a normal hit boost and then add a splash, the splash boost will do more because it also boosts the normal hit bonus.

If you want I can show a bit of maths to demonstrate why these annoints follow similar principles to additive boosts.

[twoPIZZA]

My bad actually, I reread this:

I might have misunderstood what the question was. I thought the question was are the 2 different anointments in the same spot of the formula, being an elemental multiplier. And would they be multiplicative or addative I would have thought multiplicative to splash and addative to other elements.

But

I thought you meant it was additive to normal hit because it’s based on gun damage. Come to think of it, I don’t know if I understand that anointment that well as anytime I use it with blast master it’s weaker than the 120 splash anointment by a large margin… Might be my gear though.

[olivier_shady]

You understood the question right.
Now let s see if I understood Prismatic answer well, basically the two annointments are additive

So is your formula something like that?

Gun Damage = Normal Hit x Weapon Type Multiplier x Splash x Elemental Multiplier x Critical Damage + elemental annointment dmg

elemental annointment dmg = half (50%) base gun damage X Splash X Elemental multiplier X crit dmg with no difference whether it is a magazine annointment or a time based one

[Prismatic (Dancing with Jak 'o' the Shadows)]

with no difference whether it is a magazine annointment or a time based one

That’s my current understanding, but as I said earlier I need to double check this. I’ve barely done any math with the bonus element annoints.

[plenipotence]

The difference I got when I looked at it was that the elemental grenade & shields anointments ignored weapon type damage on class mods. The elemental magazine anointment took it into account. Otherwise they seemed to be the same. They take your final damage before element matching and add half of it as a new element, which gets whatever specific penalties or bonuses the new one has. Also, the grenade/shield anointments apply to some things that are not actually “weapons” like rakk attack & grenades.

[Steeveyb]

I believe grenades are counted as weapons; as they take that role in regards to artifact passives; grenadier (grenade), deadeye (pistol), greasy (smg), long range (sniper), hulking (heavy), …etc;
i haven’t found any relics that have more than 1 of either of these and ive seen quite a large amount so far

[N8d0ggz]

Amazing thread. Thanks for making this. I can confirm, I’ve found Blastmaster to cause greater damage with a class mod that boosts SMG or Assault or Shotgun damage vs Splash Damage.

Mind Sweeper is interesting. You can go either way, IMO. The micro-nades are an explosion, therefor have splash damage. At the same time the micro-nades are spawned in quantity by normal bullets. I find Mind Sweeper to be most powerful with the following combination: fast firing splash damage weapons like the Kybs, a class mod that boosts your weapon type, an artifact that boosts AOE and Grenade Damage (incendiary damage too if all 3 exist), and anointments that boosts splash damage 100% ASE. Grenade that has either 25% weapon damage on weapon throw or 50% incendiary damage on ASE. Shield that drops 10% damage boost. This combo is insanely powerful. I have seen damage in the 100’s of millions on bosses when the grenades start to crit and proc off each other. Graveward can be taken down on M4 in 1 clip of the Kybs using the incendiary version with 100% splash damage on ASE applied.

Interesting take on the Bloodletter. I’ll have to give mine another shot that has +splash damage.

[plenipotence]

They aren’t very consistent with descriptions. For example Zane’s life-steal kill skill says “weapons” but they hotfixed it so that it does not work with grenades. meanwhile Amara’s lifesteal is supposed to work with elemental weapons and still works with grenades. Zane’s new Seeing Dead class mod says it trigger when you damage an enemy with a “weapon” but works with all sources of damage including your summons. shrug

I’m not 100% on the details of artifact rolls but i have heard there are some that are mutually exclusive. And grenade damage is mutually exclusive with the the weapon type damage rolls like you say.