Why penetrations are pretty much useless late game, on high health enemies

[Thesiobhan]

The basics here are that penetration should be percentage base. if you want to use a protection rating like you currently are, then what you’re doing is essentially saying that stacking penetration has diminishing returns on dps until the point when you make penetration negative, at which point each point of penetration becomes worth more than the previous point as far as dps increase goes. That’s fiiiiiiine enough but if enemies are getting waaaaay more protection than we can feasibly shred, then it’s not really a great system. Since every point you invest into penetration is actually less effective than previous points until that magic number which as the game currently is, we basically can’t hit.

Seperate but related Marked for death’s increased damage taken should probably more or less be the last calculation for determining damage. Add up all the flat/base dmg modifiers, multiply by increased damage modifiers, then multiply by the more multipliers, then figure in resists/penetration. Then multiply that by increased damage taken modifiers. If people aren’t seeing a noticible difference from 55% increased damage taken something is very wrong with the way the game calculates it, as that should be a very powerful modifier.

[lkodinsson]

I find the math related to Damage Reduction very interesting and it’s something I’ve done lots of math on in all the games of this genre I play. I love finding ways to make characters as tanky as possible.

I’d like to offer some more math on this topic that may help with perspective, because people like to throw around “Diminshing Returns.”

The formula Last Epoch uses is based off a simpler formula found in other games.

Simple formula: Armour / (Armour + Special Value), where Special Value is the number required to get 50% damage reduction. ie: 50 Armour / (50 Armour + 50 Special) = 50% DR.

In this formula each point of Armour is worth as much as the last, even though each point of armour gives you a smaller percentage increase than the last. This is a fact. There are no Diminishing Returns. It is an illusion. Knowing how Effective Hit Points works will illuminate this truth.

Moving on to Last Epoch, the formula is: Armour / (Armour + Max Hit Points). Here you can see that the special value is now variable instead of constant. This changes very little, but some notable differences are:

Each point of maximum hit points are equal in EHP value to increases in Armour. In the simpler formula this is not true. Each point of armour would be worth more than each hit point.

So in Last Epoch increasing HP is better against ALL damage types, and increases Armour (or a specific resistance) is better against that damage type only.

Except… Increasing damage reduction is still strictly better even if your EHP is the same, because of how it relates to healing / regeneration.

In the simpler formula armour gets better the more health you have, making it better in pretty much all circumstances compared to health. In Last Epoch they are more equivalent even though armour still has circumstances where it is strictly better (in regards to healing). In fact your armour value is worse the more health you have, but this is actually an equalizer, rather than a strict downgrade to armour. So even though armour is nerfed, technically, it is still really good.

Moving on we get to penetration. In games where armour (and resistance) is basically the best form of mitigation penetration is really good. Practically the best way to multiply damage. In PoE and D2 it’s basically broken because resistances are too effective. Even worse when you get into negative multipliers because assuming each percentage is better than the last, you get exponential increases from 0% to negative percentages.

All games that use a formula based on the same one that Last Epoch uses has the same problem. Negative armour/resistance values have exponential effect where as positive values have linear effect. That’s not even getting into the divide by zero problem.

In order to fix this all of these problems, the formula needs to be changed to:

Armour / ( |Armour| + Special )

or in Last Epoch’s case: Armour / ( |Armour| + Hit Points)

Regardless, we’re talking about the value of penetration in Last Epoch’s current iteration.

I did some math and I think you’ll find that 200 armour shred is better than you think, even at a “2%” increase in damage.

Enemy has 10k HP, and you do 1k damage. Let us assume it has a positive armour value that doesn’t go below 0. If it did, we can assume damage even better, but we’ll ignore that.

200 armour shred is definitely an increase of 2% damage from 1000 to 1020. But you know what else is?

If you had a base damage of 100 it would take 900% increased damage to get 1000 damage. Or 1000% total damage. +20% damage is the same 2% damage jump.

As far as I’m aware 20% is pretty good.

If you had a base of 200 it would take 400% increased damage to get to 1000. That’s still a single 10% increase to get that same 2%.

So if you spend points and you get 200 armour shred, that’s about the same as a 10%~20% damage increase if your base damage is anywhere from 100-200. If it’s any less, it’s better. Not to mention it gets exponentially better if your target goes to negative armour.

So the complaint here is really that late game scaling slows down (which it should). Not that penetration is bad.

Edit: Also it’s hard to scale penetration when it’s effectiveness changes depending on how strong you are, unless it scales with your character.

Another possible solution is to give enemies less health scaling and more armour/resist scaling just like a player. Then give you a penetration of a percentage of their armour/resist. To make your damage numbers look like they scale properly they could just report the enemy’s average EHP instead of real HP.

Edit 2: Dev confirmed the formula is functionally Armour / (|Armour| + Health Pool); negative armour values scale at the same rate as positive ones. So you actually don’t get an exponentially increase from negaitve values. I’m going to update the wiki to reflect this.

[grimlock9999]

I’m confused. The game refers to ‘shred armour’. Which reduces armour by 100, I assume, for each time the monster is hit. So will 20 minions hitting a target each second reduce armour by 2000 each second?

Is shred different to armour penetration?

From the combat calculations wiki, if we have a 1000 physical hit vs a 10K monster with 10K armour (is there any way to find the realistic estimate of monster armour?)

damage mitigated = 10K/20K = 50%
So we hit for 500 damage.

After 2K armour ‘shred’ , I assume the monster has 8K armour,
damage mitigated = 8K/18K = 44%

So we hit for 560 damage

If we manage to shred all the armour over, say 5s , then:
damage mitigated = 0, so we do full 1000 damage

Then what happens if the shred goes into negative armour?

mitigation = -2K/12K = -17% (is this 17% more damage?)

or even further into negative

mitigation = -10K/20K = -50% (this doesn’t seem linear?)

[lkodinsson]

Penetration has a linear effect on reducing your targets EHP, not a linear effect on your damage. This is true until your target’s armour becomes negative value where it has a diminishing multiplier effect on their EHP.

Here’s a calculator I whipped up if you want to use it:

Desmos | Graphing Calculator

Edit: fixed part of the calculator.

[grimlock9999]

Cool calculator, thanks. So assuming armour shred is the same as armour pen, on a 10K HP, 5K armour target, 2000 pen results in 20 hits to kill them, instead of 22! In other words, armour pen becomes close to useless, as the title of the thread suggests.

[Thesiobhan]

ok So the first formula you have essentially Warframes Armor function which is Armor/armor+300 =DR. So for a value of 300 we have 300/600 or 50% dr. Now, while this does scale This can be written as Y = X/X+300
For simplicity sake you can make this Y=X/X+1 because the graph is easier to see.
http://www.mathsisfun.com/data/function-grapher.php?func1=X%2F(X%2B1)&xmin=-2.709&xmax=2.891&ymin=-1.549&ymax=1.913
Here we see that at the value of X =1, Y =.5 or 50% damage reduction. We also see that the value of Y=1 is an asymptote to the curve. This is the very definition of diminishing returns. For each point of armor we get less damage reduction. NOW If we flip this to damage taken we can examine the point where we are at say, 80% damage reduction. We then increase our damage reduction by 1%. We are now taking 19% of damage. However we were taking 20% damage before, so by increasing our nominal damage reduction by 1% we’ve actually reduced the damage we take by 5%. Since we have gone from 20% to 19% which is a 5% reduction in the damage taken. In this way every point of damage reduction is actually worth MORE than the previous point. % based damage reduction scales at an accelerating rate once you hit positive numbers of damage reduction. However. If you have NEGATIVE damage reduction, each point of damage reduction is actually worth LESS than the point before it until you hit 0 and then it flips. The math for this can be seen as let’s say -10% damage reduction is 10% increased damage taken. Say we get to -5% damage taken. Well we increased our damage reduction by 5% but we took 5/110 reduced damage which is 4.5% reduction in the damage we actually took.

Now on to penetration. your math doesn’t really add up there. 200 armor shred on enemies with presumably thousands of armor based on the numbers I’m seeing is not going to be very effective. Let’s put it this way, I have 18 minions all of which are hitting presumably about 2 times a second with 100% chance to shred 200 armor, and there is not an appreciable difference in the damage an enemy is taking before and after if they have a decent chunk of armor. Now the way Last epoch works at least as described is that Armor is flat =EHP vs that damage type. so 1 armor =1 hp vs physical damage. That means this scales additively with your health pool which is kinda blech feeling, and really awful for healing and such. Since in most games your mitigations scale multiplicatively with your health to give you an EHP that is a product of your health pool. This same multiplier is also essentially a force multiplier on any healing or recovery to make them more effective.

I’m actually not entirely certain how the armor is supposed to work in this game, even just now sitting down it doesn’t make sense. I think the tooltips are wrong. It can’t just be EHP vs a damage type because EHP is always a function of Health and mitigation, and if 1 armor is always 1 ehp, that’s just not possible. IT would have to assume a standard value of health.

Penetration is literally the opposite of resist though so it follows the exact same math just in reverse. At this point every point in penetration is worth less than the point before it until you get to a point where you have reduced enemy resists to 0.

For example. You go from 200 to 300 penetration, You’ve made them take 2% more damage to for arguments sake 3% more damage. Well you’ve increased the damage they take by 1/102 or .98% And when you go from 3 to 4% you’re doing it by 1/103 and 1/104 and so on. Until you hit the point of negative resists. Then the formula flips. and we go from increasing damage at a decreasing rate to increasing damage at an increasing rate.

[Thesiobhan]

Also looking at your calculator even based on the most basic assumptions there’s some problem, with your calculations. If you set the Armor pen to the level of the armor, Say 1k armor 1k armor pen 4k hp and 400 dmg. it gives you 12.5 attacks to kill. which if you’re completely ignoring all armor they should have 0 damage resistence and die in 10 hits since you do 1/10 of their health per hit.

[lkodinsson]

You were right about my caculator being off; it should have been a function of the Target’s REHP instead. That should fix that problem.

Now about diminishing returns. You misunderstand.

Damage reduction is used to calculate Effective Hit Points. This is an abstract value used to tell you how “effectively” tanky you are. This is calculated by dividing your real base health pool by the inverse of your mitigation. This is: (if you treat HP as = 1, then your result is a percentage as a relationship to HP)

HP / (1 - DR)

For simple approximations:

10% DR is +11% EHP, difference of 1%, total EHP 111%.
25% DR is +33% EHP, difference of 8%, total EHP 133%.
33% DR is +50% EHP, difference of 17%, total EHP 150%.
50% DR is +100% EHP, difference of 50%, total EHP 200%.
66% DR is +200% EHP, difference of 137%, total EHP of 300%.
75% DR is +300% EHP, difference of 225%, total EHP of 400%.

If you are paying attention you’ll notice that EHP increases faster with less percentage mitigation each time. This is exponential. You even notice this when you elaborate on Warframe’s formula.

The part that is linear is that for each 1 point of armour/resistance, it gives you the same amount of EHP as the last point. That is the important part.

For example: If you have 100 HP and go from any number of armour to 1 more than that, you will have gained 1 EHP against physical attacks. This is true for every point of armour you add. This is linear. Even if by increasing your armour the actual percentage increases slower. It does not actually reduce the effectiveness of armour the more you have. This is the illusion. The part where diminishing returns is not real. This is proven by the math that determines EHP. Going from 1% to 2% is not linear. It is exponential.

This is true even in formulas that other games use. Let’s say the formula is Armour / (|Armour| + 100). Very similar to other games where your armour value effectiveness is not effected by your health pool. Each point of armour has the same value, but increases in value if your health goes up. Unlike Last Epoch where armour maintains it’s value regardless of your health pool.

For example: If you have 100 HP and add 1 armour you gain 1 EHP vs physical. If you have 200 HP and add 1 armour you gain 2 EHP vs physical for each point instead. This is constant so long as your HP remains the same. Even if the actual percentage decreases.

You said you basically don’t believe how the damage reduction works in Last Epoch. It tells you exactly, and I have even updated the formula on the wiki. It is Armour / (|Armour| + Health Pool). If you use a calculator you can even prove that no matter your Health Pool, each point of armour is always worth 1 EHP.

I don’t know what else to tell you. The math proves the rest.

If we’re still comparing the effectiveness of penetration vs damage increases I can make a more detailed example but I’d like references from someone’s character or the example won’t be that realistic. (All passives and gear. I’m not afraid to do the math manually to make an example.)

Edit: Bonus math to better demonstrate how the illusion of diminishing returns work:

Elaborating on how EHP is calculated: you have HP / (1 - DR) as the base. Let’s pick an arbitrary amount like 5% DR. That would be HP / (1 - 0.05). How do you calculate this if you have 2 instances of 5% DR? 10%? No.

The inverse of an amount of damage mitigated is the amount of damage taken. 5% DR is therefore 95% damage taken. Pretty simple. So what do you do when you have two instances?

It is definitely not addition. As I have already stated each 1% is worth more than the last. So adding them will result in an exponential increase in EHP. So how? If you try multiplying straight up you will have reduced it. (5% * 5% is 0.05 * 0.05 = 0.0025 or 0.25% so that can’t be right.)

You do it by multiplying the inverses of each DR (so multiplying the damage takens), to get a new result of how much damage you take. You can then invert this for your new DR.

(1 - 5%) * (1 - 5%) = 90.25% damge taken or 9.75% DR. This is explained by saying you take 5% less, then you take 5% less of what that result was.

9.75% is the equivalent of 2 sources of 5% DR.

The reason this is, is because the closer you get to 100% the closer to invulnerable you get. You cannot actually reach 100% however. 100% would be infinite EHP. The reason that each percentage is worth more than the last is because reaching 100% is infinite.

This is literally the reason these formulas exist. To prevent you from reaching invulnerability.

Another good example is this one:

If you take 50% less damage it takes twice as many hits to kill you. As in you have double your EHP. If you take 50% less damage again, you double your EHP again.

That can’t be 100% because 100% is invulnerability, or infinite EHP. The real result is 75% DR. This results in quadruple EHP, or double double EHP. You can demonstrate this result yourself with the math provided, and if you keep going you will never reach 100% unless you round.

[Thesiobhan]

Yeah, I’m not saying that armor scales with diminishing returns, I’m saying that Armor pen has diminishing returns. It provides less damage per point up until the point that you get to 0 armor at which point it provides damage at an increasing rate. Just like each point of armor is actually worth more than the previous one. Because it reduces the damage taken by a slightly larger percentage of the remaining damage.
You keep doing math about armor but we’re talking the other side of the equation.

To answer the question on your EHP calculations if you have 2 forms of mitigation it depends on how they interact. If it’s say 2 forms of Resist that affect for some reason the same thing, then They might stack additively, or they might stack multiplicatively. It’s a function of how the game works.
It depends on how the sources of DR work. If you have say Armor and Evasion in this game for example. or Dodge it’s called IIRC. you have a 5% chance to dodge and you take 5% less damage. However note that this is not the same as stacking the same DR and yes you actually see an interesting behavior with this function as well. But it can be Written with words as a 2 step occasion, you have a 5% chance to dodge and over time you will avoid 5% of damage, OF that 95% damage that gets through you will resist 5% of it. which is where you get to 90.25% actual damage taken. Which is 5% of 95. However when you say increase your armor to 10% DR you go from taking 90.25% of the damage to taking 85.5. which is 4.75% change 4.75% divided by 90.25% is 5.26% you increased your mitigation by 5% and took 5.26% less damage than you did before. It’s all about the rate of change where you see increasing or decreasing returns. Essentially what is the 1st derivative of the function. is it increasing at an increasing or decreasing rate?
Yes of course you will get never get to 100 and infinite EHP occurs at 100% DR and that’s literally the point, IF you are moving towards 100 you are gaining ehp at an increasing rate. If you’re moving AWAY from 100 you’re losing EHP at a decreasing rate. Then once you hit 0 you are moving towards -100 and as such you’re gaining damage at an increasing rate again. Think of the DR as a parabola with -100 and 100 as asymptotes and 0 as the vertex. Though generally you can actually get beyond -100 technically and just increase damage by more than 100%.
That’s why I’m suggesting that A change penetration to be % based rather than a flat value, and B based on some of the actual values you see in later in the game the values we get now, just don’t seem to stack up. C You could also flip this as from what I’m guessing and maybe seeing the actual DAMAGE being done doesn’t seem to increase but the enemy health pool decreases based on shred? This makes it essentially an invisible stat and makes it FEEL awful. When I throw out 2000 armor shred twice a second give or take from 20ish minions attacking around twice a second. and I don’t see their damage appreciably increase. going from 1k per hit to maybe 1100 after several seconds of beating on the enemy. I mean it’s a 10% difference but in that time I’ve essentially shred like 10k armor for a 10% increase. Not to mention I have a fully buffed mark for death which should be a massive boost in damage 55% increased damage taken. Which to me should work as the very last modifier on all damage calculated. after resists and everything else. and simply be multiply the number they would have taken by 1.55. However that’s not what I see happening. When I usually go from 1k to about 1300. I’m stacking multiple potentially powerful damage increasing things and they just don’t seem to be working out to actually increase my damage by the amounts it feels like they should be.

The main point here is that even with all the math, it’s basically irrelevant because it doesn’t feel good. and 99.9999% of people are not going to bother to do the math. They’re just going to say, hmmm I put a bunch of points into armor penetration and I don’t see an appreciable difference in my damage. Then not bother with it.

[lkodinsson]

Penetration actual gets worse past 0 because it stays positive below the dividing line.

Also increases to damage get worse (not actually, but relative to your total damage) the more you have because they are additive and not multiplicative. When you already have a bunch of increases it isn’t that good unless you have a high base (melee) or a bunch of more multipliers.

[Thesiobhan]

ugh that’s just awful, an increased damage taken modifier should be different than an increased damage dealt modifier. Increased damage taken is usually a very powerful modifier as in other games it’s basically a 3rd layer or a more modifier AFTER all the more modifiers. That’s what I was expecting too since the only time I’ve seen it is on mark for death, which would make sense since it’s so powerful, you wouldn’t expect to see it everywhere. This is just a poorly worded increased damage done modifier though, and that’s not super nifty at all.

LOL the forums say We’ve been replying too much to each other. Like hey forums we’re discussing game mechanics, this is for everyone to see and weigh in on. It’s not helpful if we take it to PMs.

[grimlock9999]

I’m still reading, and thanks for all the input.

I like these kind of games because you can get complexity in them. But complexity for no reason, and with no rewards is just painful. In addition, only fools mistake lack of clarity for complexity.

Right now, I’m putting armour pen, armour shred, poison, chill, stun, freeze, bleed in the needlessly complex, unsatisfying bucket.

[SlaserX]

This is the greatest reason why I am in favor of getting more data to the players sooner rather than later. The character sheet isn’t bad, but it definitely doesn’t show enough meaningful data for us to make informed decisions. We need PoB-level calculations ingame–it would speed up the process of pointing out the weak points in some of the implementation, as we’ve seen.

+1 to those who did the math.