# Damage Resistance/Reduction does not suffer from diminishing returns

I’ve heard a lot of people complain about the implementation of Damage Resistance/Damage Reduction in Borderlands, and specifically, a lot of complaints about how Damage Resistance is subject to diminishing returns. I wanted to take this time to dispel that rumor, as it is quite untrue. First, let us define diminishing returns:

“[A]ny rate of profit, production, benefits, etc., that beyond a certain point fails to increase proportionately with added investment, effort, or skill.” (http://dictionary.reference.com/browse/diminishing-returns)

The following is the formula by which incoming damage is calculated in Borderlands 2 and Borderlands The Pre-Sequel:

Damagefinal = Damageinitial / (1 + Resistance)

As you can see, incoming damage is divided by the sum of all damage resistance acting on the player, plus 1. If for example one was specced 5/5 into Claptrap’s skill Pain Simulator is Painful, all incoming damage would be reduced by ~17% (100/1.2=83.33). Now, for a lot of people this immediately seems suspect; I have 20% damage resistance, so how come I’m only shaving off 17% of damage taken? Many would assume that because the final number is lower, diminishing returns are reducing the contribution of damage resistance. As an even more dramatic contrast, at 100% damage resistance the actual damage reduction comes out to a mere 50%.

This is not diminishing returns at work. Point-for-point, damage resistance offers the exact same defensive benefit no matter how much damage resistance you have. A more intuitive way to think of damage resistance, is that it increases your effective health by 1% per 1% damage resistance. As an example:

Let’s say you have a health pool of 1000. A bandit pulls out a shotgun and shoots you, dealing exactly 1000 damage (We will ignore health gating so as not to confuse anyone). Now we’ll add 100% damage resistance; at 50% damage reduction, you now take 500 damage from the shot. You have effectively doubled your health pool. Where before you would have went down from exactly 1 shot, you can now take 2.

Same scenario, but with 200% damage resistance; at 66.6% damage reduction, you take 333 damage from the shot. You have effectively tripled your health. And so on, and so forth. No matter how much damage resistance you acquire, it always has the exact contribution of 1% effective health per 1% damage resistance.

I suspect the reason for the confusion is the misleading name that is damage resistance. I personally have always taken damage resistance/reduction to mean 1% less incoming damage per 1% damage reduction. I feel that Gearbox should rename damage resistance going forward, to something that has fewer preconceived notions about it. If nothing else, it would be nice if they stuck with either damage resistance or reduction, as that inconsistency can only serve to add to the confusion. Also of note, the issue is compounded by skills like Jack’s Delegation, which do work in the aforementioned fashion (citation needed). For anyone with a mind for game balance, it should be pretty obvious why implementing readily accessible damage reduction in Borderlands would be tricky. If they allowed it to stack additively, players could potentially find a gear/skill combo that puts them at 100%, which would wreck end-game encounter design. Gearbox would need to either heavily restrict potential sources of damage reduction, or implement a hard cap on how much DR players can stack.

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I think I understand what you are saying.

So if you can…explain in terms of a shield like the Blockade which gives a constant 38% Resistance regardless if partially depleted or not. What does that equate to in actual damage reduction?

Or an Adaptive Shield like the Neo or Evo with their resistances.

If the Blockade confers 38% damage resistance regardless of charge, the persistent reduction of incoming damage comes out to ~27.5% (100/1.38=72.46). Or in other words, your effective health pool increases by 38%.

As far as adaptive shields, I don’t want to provide incorrect information, so someone else will have to verify that they fit into the damage-taken formula in the same way as typeless DR. If that elemental damage resistance is calculated the same way (with the obvious exception that it only applies to the active elemental type), then an OP8 Neogenator with Maliwan parts, which affords 86% elemental resistance on the card, will reduce incoming damage by ~46% (100/1.86=53.76).

Naturally, DR from different sources can stack, so if Gunzerking provides +50% damage resistance (someone please correct me if I’m wrong), and you have also equipped a Blockade, you should see an ~46.8% reduction in damage taken (100 / (1 + .5 + .38) = 53.2) while both effects are active. As a result, you gain 50% effective health from Gunzerking and 38% from your Blockade, in this case.

[quote=“benzillah, post:1, topic:1272236”]specifically, a lot of complaints about how Damage Resistance is subject to diminishing returns.[/quote]I think this comes from people improperly using that to describe the increase in enemy damage that comes, increasingly, with playing at higher levels. In this case (I think), your math is fine, but instead of this same chump Outlaw shooting a Tediore shotgun at you for 1000 damage, they’re now throwing, say, 1300 damage, so people see their equivalent shield being less effective. (Am I reading your bit right?)

[quote=“benzillah, post:1, topic:1272236”]I feel that Gearbox should rename damage resistance going forward, to something that has fewer preconceived notions about it.[/quote]I don’t know… trying to work around the preconceived notions of a large cross section of the public may be an exercise in futility. Whose responsibility are these notions, Gearbox’s or the players’ who generate, maintain, and own them?

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Another thing happening here is that people probably confuse diminishing returns with diminishing marginal utility. Effects such as Damage Reduction, Gun Damage, etc. that scale linearly are always subject to diminishing marginal utility (the % increase of a given bonus is less the more of that bonus you already have, e.g. +10% Gun Damage is a 10% increase to total damage if you have no other bonuses, but only a 5% increase to total damage if you already have +100% Gun Damage from other sources).

If this vocabulary issue is worth trying to solve, I would simply suggest that they drop the % sign from the numbers, so it would read +38 Damage Reduction. A lot of the reason people think that 100% DR would=immunity to damage is because they interpret the % to mean that Damage is Reduced by the stated %, which is not how the math actually works. If it were stated without %, then they’re left at least wondering how DR is calculated, which could be explained by one of those loading screen tips or mentioned the first time you find a piece of gear with DR on it.

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I apologize, I’m not sure I understand the first part of your post. When I say complaints about Damage Resistance being subject to diminishing returns, I’m talking about comments like this:

(http://forums.gearboxsoftware.com/t/the-last-patch-is-it/1064274/27), with regard to Salvador’s skill I’m the Juggernaut.

Not calling anyone out here, it’s just that this comment is a great example of the misunderstanding I have been seeing. Merits of the skill notwithstanding, this line of reasoning is deceptive. If you compare 20% damage resistance added to 50% (yielding a gain of 7.85% actual reduction in damage taken) with 20% damage resistance added to 0% (yielding a gain of 17% actual reduction), it is easy to fall into the trap of diminishing returns. I get the impression that people are getting tripped up in comparing numbers that approach infinity with numbers that approach zero. Obviously zero is finite, and the implementation of damage resistance will treat zero as an asymptote.

Maybe I am mistaken in thinking there is a widespread misunderstanding here, but I have seen too many people cry “diminishing returns” to refrain from starting a discussion on it.

Yeah, I suppose that is as elegant a solution as one could hope for. I really wish Gearbox had an official blog on their website going over game mechanics in detail so the community isn’t left guessing. As far as damage mitigation goes, I feel like it would be a valuable stat to begin including on shields in general, rather than being locked into Adaptive; nearly every RPG out there has an armor stat, and it would make tanking far more robust in Borderlands if you could opt into some avoidance or DR without foregoing the utility of other shield types. Maybe Atlas shield parts could provide DR, assuming they are a thing in BL3.

But I digress. It doesn’t make much sense to me to write off damage resistance in the fashion you describe, as we certainly don’t do that with gun damage or crit to the extent that DR is ignored. Just as gun damage, crit, and firerate synergize and scale with eachother, DR and bonus health/shields synergize greatly together, and provide incredible damage mitigation potential. I hope the people that read this thread gain a better understanding of how DR works, so they can feel good about including it in their builds.

I believe the reason comes from both the focus on the shape of the formula aswell as @Frightning’s point on diminishing marginal utility.

About DR’s value format I guess the ‘%’ helps indicating that the value is a decimal mod… and it’s not that confusing when you go back reading how defense and damage resistances work in something like diablo 2 ._.

Yes, as I said, I could see how those who have less aptitude for mathematics (I do not profess to be a math wiz kid, as they say, I merely have experience with LoL and its armor implementation, which is rather similar to Borderlands’ DR formula) would have difficulty understanding how the damage curve should look. All the same, I have seen and heard many statements that the effects of damage resistance are reduced the more of it that you have, which is a different issue than “the more of it I have, the less value each point adds to the total.” 2 different scenarios may be at work here:

1. I have 100 oranges. I pay for 1 more. Now I have 101 oranges. 1% increase in the number of oranges I have.

2. I have 100 oranges. I pay for 1 more. Now I have 100.3 oranges. .3% increase in the number of oranges I have.

The first is the scenario of diminishing marginal utility, wherein each additional orange has less effect when weighed against the total. The second is the scenario of diminishing returns, which is in this case a fallacy. The fallacy is what I wished to address, as I have seen a number of people profess that damage resistance exhibits similar behavior, which is not the case.

That formula computes damage received after DR, which is not really the correct value to use to judge its effectiveness as an increase to your defenses. The correct metric is effective hit points, meaning how much damage can you sustain before you enter FFYL (in this case). In which case it’s the very familiar formula:
EHP=HP*(1+DR), which shows the additive, linear nature of DR with respect to your survivability. What’s more interesting to me is that DR also increases the effectiveness of health regeneration effects (notably including flat regen effects unlike % health buffs which only affect % regen). All this said, main reason I see for people not valuing DR much is that most of the available DR buffs are honestly really weak, 20% DR for 5 skill points (I’m the Juggernaut) is no better than 20% health for 5 skill points except that it stacks multiplicatively with % health buffs rather than additively. Now if DR values were more like we saw in BL1, where 5/5 Juggernaut was actually 60% DR, then it would be very worth the points.

Overall I think defensive buffs were too weak in BL2 outside of % regen effects, which are adequate and were pretty OP in BL1, and this is part of the reason for the prevalence of DPS builds over tanky builds, especially when you consider the increased clear speed and then the potential for healing off of DPS with grog/moxxi weapons and the asymmetry in scaling between DPS and defense. It creates a situation where you survive better by just doing more damage and even healing off of it, than by actually building tanky.

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Really ? how so ?

Of course, but in the context of my quote, we’re talking about Salvador: a character that has 50% damage reduction AT ALL TIMES.
Evaluating an additional 20% damage reduction with 0 as a basis is completely useless as that resulting value never actually shows up.

I have also NEVER mentioned “diminishing returns” as a reason why I think this skill is bad (“poor yield” might be closer to my point).

I don’t know about some of the others, but you certainly didn’t pick the right guy as your example this time

I get your point, and “diminishing returns” is not the right term to describe what’s at work here, that’s why I don’t use it in that context, but it’s an easy enough shorthand to describe “diminishing overall yield” that it slips by unnoticed by most. At that point though, it’s a lack of semantics comprehension rather than mechanics comprehension that’s going on here, one that many don’t think is important enough to try and correct.

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It’s deceptive because that 7.85% damage resistance has an indeterminate effect on effective hit points (the real measure of the value of a defensive skill). If you had it to the point where you took 90% less damage already, that 7.85% would be an enormous buff to how much damage you could take without going into FFYL, but if you had 0% less damage taken from other sources, then it really isn’t doing much for you. (see what I mean?)

Since Salvador can keep Gunzerking up basically constantly, he basically already has +50% Damage Reduction on at all times, hence the 20% from I’m the Juggernaut puts him up to 70% Damage Reduction, this means effective hit points (EHP) is going from 150% actual hp to 170% actual hp, which is a proportional increase of 13.(3)%, or in other words, DR is effectively 2/3 as strong for Salvador as it would otherwise be because of the ‘free’ +50% DR from his action skill.

Deceptive to whom ?

I refered to that 7.85% value as “damage mitigation”
Which is accurate. The “damage resistance” value is still 20%.

Using hit points as a way of looking at damage reduction is a good idea in theory, but it’s not a perfect method either as it offers no way to assess a situation: a character with 1000 health has 50% DR, so he effectively has the equivalent of 1500 health. That’s true. If he takes 300 damage, how much health does he have now ? How is health regen affecting him ? Isn’t that more deceptive overall ?

It makes for a clean equation when you send all variables on the same side, but it can no longer be used to check anything.

Using damage mitigation as a value may be harder for some to grasp, but it accurately describes the effect in game (in this case, adding 20% damage reduction on Salvador amounts to 7.85% less damage taken)

If he lost 300 health, then he took 450 damage, it he took 300 damage, then he lost 200 health. Does that make sense? There is no ambiguity in how effective health works, regen effects will also be amplified by the stated DR% because those hitpoint are worth an extra DR% in damage that you can actually take. So in this case, health regen effects are 50% stronger in the sense that you can sustain taking 50% more DPS without net losing health. See what I mean?

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Which was my point in that thread: I’m the Juggernaut is a bad skill because it has very little effect in regard to the points invested in it.
By comparison, Krieg has 2 DR skills that are also conditional, and they give 50% instead of 20%, to a character that gets more out of it.

Yea, we are in agreement that I’m the Juggernaut is regrettably weak.

Of all the solutions pointed to here, the best IMO is removing the % sign next to the value, however it creates the same problem: the value can still be confused for something else (like a flat damage reduction value)

The idea of expressing it as a percentage is not so bad as it at least tells everyone that it’s a “proportion” value even if it’s prone to be misinterpreted.

The biggest advantage of the way it’s calculated right now is that you don’t have to pay attention to it (as a designer) because even if you pile up 300% of it, you’ll never be invincible, so they don’t have to watch as carefully if you’ve accidentally created a "god mode ".

One thing to note though: converting damage reduction directly into extra health is a simple solution, but you should state that it’s extra health+shield, as DR affects both. However, health regen only affects health… So a bit of convoluted maths needs to be involved to calculate the real value of health regen.

You say you understand my point, but I already referred to the precise issue with this exact sentence. You are saying that 20% damage resistance results in a 7.85% effective damage reduction. Which is true, while Gunzerking is active. But what about when Gunzerking is inactive? Now 20% is worth 17% reduction. And these values are NO DIFFERENT; In the context of the impact they have on your health pool, they are functionally identical. Which is why it is deceptive to discuss the relative strength of effects that provide DR in the context of the percent damage reduction. It doesn’t make sense to describe DR in this way, just as it doesn’t make sense to consider the power of a gun based on what percent of a boss’s health it deals. Imagine if we said, “the DPUH is a very powerful weapon, because against Pete it deals ~3.7% of his health per shot, compared to the .8% of a standard Torgue Slapper.” Why would anyone discuss a flat value in the context of a percentage? Why would anyone use Pyro Pete’s health as the damage scale for weaponry? It wouldn’t make any sense. Likewise, you are comparing 2 different types of scaling, only the one you’ve chosen to use is nonlinear. Which makes even less sense.

It is not the fault of the developers for implementing damage resistance in this way, it is a perfectly functional system. But many people don’t quite appreciate how it actually works, so they write off damage resistance almost entirely. I honestly wasn’t trying to insult you, but you seem pretty defensive, so I will grab another quote to highlight the logical disconnect here. And I will apologize in advance for its age, I am not terribly familiar with this forum so finding exact quotes has been burdensome, to say the least:

From Ha_Na’s Aurelia Melee/Cryo hybrid build guide. They seem to me to be an intelligent, respected member of the community, but they write off DR in the exact same way as I have been seeing others do.

There isn’t a correct format to use since both achieve the same results, it’s more of a matter of preference between a*x = b or a = b/x.

Sorry for double-post, I just saw your most recent reply. I agree that removing the percent makes it nice and irritating for the curious gamer, who may then be compelled to look it up. But I don’t think Gearbox taking the reins and writing up solid game mechanics guides/blogposts would be a bad thing, either. We could hear it from the horse’s mouth, so to speak, on exactly how they intend their mechanics to function and their vision for gearing.

I had the same thought, it is certainly important to note that DR affects all of the hitpoints the player has.