The Defence Myth
People that insist on stating 40-45% = x2 survival struggle to grasp that this same amount of survivability can be substituted from different sources, just as perfectly easily, as the difference between 0 & 5%.
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Let's say I surround him with stuff that is going to kill him in 30 seconds. That means they're dealing around 108.3 DPS. Edit: net after accounting for my defense.
If I assume he's at 40% defense and can get him from 40% to 45%, I will halve their average DPS. I will now live 92.1 seconds.
Now, what do you think is easier for my Scrapper: adding 5% defense or adding 54.1 HP/sec regeneration?
Blue
American Steele: 50 BS/Inv
Nightfall: 50 DDD
Sable Slayer: 50 DM/Rgn
Fortune's Shadow: 50 Dark/Psi
WinterStrike: 47 Ice/Dev
Quantum Well: 43 Inv/EM
Twilit Destiny: 43 MA/DA
Red
Shadowslip: 50 DDC
Final Rest: 50 MA/Rgn
Abyssal Frost: 50 Ice/Dark
Golden Ember: 50 SM/FA
Bunny:
The majority of the individuals that will reply to this thread view the following statements as functionally identical: "40-45% is worth more than 0-5%." (Post 20) "The origins arise from the fact that increasing defence gives exponential rises to survivability. This is not a point of contention." (OP) I foresee that this thread will sadly not end well |
Neither approach is fundamentally wrong. The problem is that Bunny's method requires you to have the opponent's DPS, whereas the survivability method uses the character's immortality line -- or 60-second-survivability line, or 30-second-survivability line -- to approximate the opponent's DPS.
Why? Because knowing the theoretical breakpoint (what Bunny calls the indifference point) where DEF outpaces regen (and vice-versa) isn't instructive unless you have an exhaustive and implausible knowledge of what DPS you're likely to face, and under what circumstances your build decisions are likely to matter.
The survivability analysis takes care of that for you. It tells you what to choose for the situations where your build decision (in this case, X DEF versus Y Regen) is likely to matter. The survivability doesn't care what the opponent's DPS, because it already knows what DPS your build can survive.
All the rest is just amusing posturing on Bunny's part. He flat-out admits here that the non-linear effect of DEf on survivability is not a point of contention, but in the original thread he spent several pages saying that everyone who prefers the survivability method can't do simple arithmetic -- over and over again. His arithmetic was never at issue; the practical usefulness of it was.
We're all measuring the same thing. Saying that 10 / 10 = 1 doesn't disprove that 10 / 1 = 10. This spreadsheet is yet another attempt to prove a correct number wrong by asserting another correct number.
If anyone's curious, here's the original thread: http://boards.cityofheroes.com/showthread.php?t=245914
Unfortunately you haven't even looked at what I have written. Please actually read this and come back to me.
The amount of regeneration that you need to substitute for the survivability moving from 0-5% is equal to that needed to substitute going from 40-45%. |
Disproven above: the last five percent defense is in fact far more valuable than the first 5% defense. You have committed a common error; you are completely misrepresenting the position of others in an attempt to make it easier to attack, as well as equivocating regarding your own position.
Actually, I did read what you wrote. To wit:
Disproven above: the last five percent defense is in fact far more valuable than the first 5% defense. You have committed a common error; you are completely misrepresenting the position of others in an attempt to make it easier to attack, as well as equivocating regarding your own position. |
I hope that you read my entire post and can see that I am talking about the relative benefits of attaining different levels. And that is: expressing 100% survivability doesn't allow you to make a judgement on substiting effects.
Blue
American Steele: 50 BS/Inv
Nightfall: 50 DDD
Sable Slayer: 50 DM/Rgn
Fortune's Shadow: 50 Dark/Psi
WinterStrike: 47 Ice/Dev
Quantum Well: 43 Inv/EM
Twilit Destiny: 43 MA/DA
Red
Shadowslip: 50 DDC
Final Rest: 50 MA/Rgn
Abyssal Frost: 50 Ice/Dark
Golden Ember: 50 SM/FA
Aieee poorly worded The answer back is: sort of. They both protect you from the same *AMOUNT* of damage.
I hope that you read my entire post and can see that I am talking about the relative benefits of attaining different levels. And that is: expressing 100% survivability doesn't allow you to make a judgement on substiting effects. |
Let's think about this for a minute. Let's use the example of my Invulnerability Scrapper. His build operates around the softcap, and has 2409 HP and a regeneration rate of around 28 HP/sec with Dull Pain up.
Let's say I surround him with stuff that is going to kill him in 30 seconds. That means they're dealing around 108.3 DPS. Edit: net after accounting for my defense. If I assume he's at 40% defense and can get him from 40% to 45%, I will halve their average DPS. I will now live 92.1 seconds. Now, what do you think is easier for my Scrapper: adding 5% defense or adding 54.1 HP/sec regeneration? |
I'm actually going to say that even if I could get enough regen to equal my survivability increase from 40% Def to 45% Def (assuming I had 40% Def), and actually had to make a choice between the two, I'd pick the 5% Defense, because it is more valuable than the Regen. Sure, the Regen helps just as much against sustained damage, but the Defense also helps me against burst damage. Burst will happen, I know from experience and I know enough maths that I don't have to calculate every distinct scenario where burst might happen and what the odds for it happening are. Point I'm trying to make: the last 5% of Defense count for a lot when you factor in burst damage.
If you want to deal with numbers in a complete vacuum and dismiss facts, sure, do it, I won't stop you. The thing is that your approach isn't practical. Any build I'm rolling doesn't up with just the Defense soft cap. It also ends up with decent regen or a heal, to the point where additional regen bonuses aren't worth looking for. Regen bonuses are quite prevalent in many sets, particularly Defense and Heal IO sets.
In the end, the survivability line method is much more practical way of going about the stuff most people in this forum are interested.
- @DSorrow - alts on Union and Freedom mostly -
Currently playing as Castigation on Freedom
My Katana/Inv Guide
Anyone who doesn't take truth seriously in small matters cannot be trusted in large ones either. -Einstein
Again, flawed, as per UberGuy:
The relative value (your words) of defense and regeneration do in fact differ, by dint of it being much easier to gain defense over regeneration, in the amounts needed to increase survival time at levels of defense approaching softcap. In other words, at 40% defense, in order to double survival time, you can either add another 5% defense (trivial to do, in general) or double your regeneration (likely impossible). |
Comparing based on %'s is flawed.
Please take the time first of all to address the system provided (the spreadsheet). It will highlight some of these mistakes.
You are accurate that you double your survivability by adding 5% defence. What is false is that you'd need to double your regeneration.
I will once again restate the same point I presented to Uberguy.
There are two situations that are identical except for the points I mention. In the first, you are at 0% defence, and are offered either 5% defence, or an amount of regeneration equal to that 5% defence in terms of survivability. In other words, in terms of pure damage mitigation, it doesn't matter.
Then, there is a second situation. You are at 40% defence, and are offered 5% defence, or the exact same amount of regeneration in the first option.
According to how I read what you have writtne, that amount must be double your present regeneration. That isn't the case. The answer is in fact that they both give the same amount of survivability so long as the regeneration is the same as the first option. You don't need to increase the regeneration at all, even though the change in survivability is 100% instead of 5%.
There are two situations that are identical except for the points I mention. In the first, you are at 0% defence, and are offered either 5% defence, or an amount of regeneration equal to that 5% defence in terms of survivability. In other words, in terms of pure damage mitigation, it doesn't matter.
Then, there is a second situation. You are at 40% defence, and are offered 5% defence, or the exact same amount of regeneration in the first option. |
Let's go back to my example. In there, I assumed 40% defense and 108.3 average incoming DPS after defense.
If I dropped to zero defense, that same 108.3 DPS would jump to 541.5 DPS. Adding 5% defense now avoids 10% of this, which (to your point) works the same 54.15 DPS I came up with before. But no one cares, because I'd still be left taking 487.35 average DPS, which means I'm screwed! Edit: I now die in 5.2 seconds.
According to how I read what you have writtne, that amount must be double your present regeneration. That isn't the case. The answer is in fact that they both give the same amount of survivability so long as the regeneration is the same as the first option. You don't need to increase the regeneration at all, even though the change in survivability is 100% instead of 5%. |
Blue
American Steele: 50 BS/Inv
Nightfall: 50 DDD
Sable Slayer: 50 DM/Rgn
Fortune's Shadow: 50 Dark/Psi
WinterStrike: 47 Ice/Dev
Quantum Well: 43 Inv/EM
Twilit Destiny: 43 MA/DA
Red
Shadowslip: 50 DDC
Final Rest: 50 MA/Rgn
Abyssal Frost: 50 Ice/Dark
Golden Ember: 50 SM/FA
You are accurate that you double your survivability by adding 5% defence. What is false is that you'd need to double your regeneration.
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Once again: defense does increase in value as you approach the softcap, contrary to what is stated in your opening paragraphs.
I don't think either of us knows what point you are trying to make, honestly. You are all over the map.
I am loathe to address the survivability method proposed by Werner as it will be a tangent to the thread which is already going everywhere But, I cannot help myself.
If I have misunderstood the method, please correct me, but I will restate it here so that you can clarify any misunderstandings for me
The method is to determine the precise amount of damage that you can take where you are essentially are invincible. That is: you take 0 damage.
Then you add either the amount of defence, or the amount or regeneration, and work out again where you are invincible. Whichever lets you live indefinitely against higher DPS is better.
I have quoted the method for reference:
regeneration and healing = 30 HP/S -> 23.3 HP/S toxic/psionic resistance = 0% other resistance = 20% smashing/lethal defense = 15.5% -> 33% positional defense = 0% fcen defense = 27% -> 33.3% toxic/psionic defense = 0% Given that, here's what my survivability calculations say on the subject, with the usual cautions in regard to immortality-line-based mathematics that I won't go into unless someone wants more background: current build survivability = 111 defense build survivability = 146 So go with the defense. |
It only provides an answer for a single instance, and that is when you are under a very specific amount of damage that precisely isn't enough to kill you.
It has a very good chance of giving you the wrong answer. The answer naturally lies in the numbers of the problem, and sometimes it will say that regeneration is better. The problem is that when you face more and more damage, defence will always overtake it. When you choose to use this method, it is only valuable to calculate when you are invincible. Once you are not, you do not know.
A method that solves the problem under 1 specific set of circumstances, and is likely to give you the wrong answer at any other times, is not a good one. I have used strong language before (it's rubbish!).
It might tell you regen. You go with that because that's what the method says. But then you face a tough fight, and you die, because really you should have had defence for it. If you had have had defence, you would have perhaps lived long enough to defeat all your foes before your defeat.
You might say that mine has limited use because it can be difficult to judge just how hard enemies hit you. But, assuming you can figure this out (Werner did for his calculations), then you can make a decision. A decision rule that is accurate is more useful than a decision rule that is not.
Here's the problem:
Suppose I present you a choice. You are currently at 0% defence. You can slot IOs in such a fashion that you either get, say, 5% defence, or an amount of regeneration that will make you just as survivable as that 5% defence. It really doesn't matter about the specific quantity of regen that this might be. [/b][/color] |
If you make the regen equal to the defense needed to mitigate X, then yes, it's the same. If X=Y, then Y=X. Not a big discovery there.
Thing is... at the incoming damage levels of a level 50 scrapper jumping into a spawn, we're talking about a data point where 3.75% defense may be equal to 2000% regen.
When doing a build, you're faced with choices like do I get 3.75% defense, or 10% regen... easy choice.
But ok...ok... that's not really your point. Your point is you mitigate the same amount of incoming damage with 3.75% defense irreguardless of your initial defense level.
That's true. Absolutely true. This is also true... if you're dieing in 11 seconds vs 10 seconds you won't notice that much. If you're dieing in 5 minutes vs 2.5 minutes... that's big big difference.... both of those times are from adding 5% defense to a build.... one at 0% defense and one at 40% defense.
I gotta make pain. I gotta make things right. I gotta stop what's comin'. 'Least I gotta try.
Similarly, in order to live twice as long by increasing regeneration, you must double regeneration.
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Assume we have character A who regens 100hp/sec. Assume he has 40% Defense and 0% Resistance. Assume he has 1000HP. Assume he confronts enemy group B who deals as a collective 101DPS if they hit 10% of the time.
He dies in 1000HP / (101DPS - 100HPS) = 1000 seconds.
In order to double his survivability to 2000 seconds, he needs to add 0.5 HPS of regen, which is not double. Then again, he'd need less than 1% of Defense to get the same effect. Maybe I should try with numbers that aren't as close to each other, but I won't bother.
It's just a shame mitigation isn't this simple. This only works if we know what the DPS of the enemy is going to be when planning a build. That's why the survivability line calculations are practical.
P.S. If I'm totally mistaken in everything I posted in this post, please take into account I've drunk more wine than what is healthy. Thank you.
- @DSorrow - alts on Union and Freedom mostly -
Currently playing as Castigation on Freedom
My Katana/Inv Guide
Anyone who doesn't take truth seriously in small matters cannot be trusted in large ones either. -Einstein
I think the point Bunny is trying to make is this:
Assume we have character A who regens 100hp/sec. Assume he has 40% Defense and 0% Resistance. Assume he has 1000HP. Assume he confronts enemy group B who deals as a collective 101DPS if they hit 10% of the time. He dies in 1000HP / (101DPS - 100HPS) = 1000 seconds. In order to double his survivability to 2000 seconds, he needs to add 0.5 HPS of regen, which is not double. Then again, he'd need less than 1% of Defense to get the same effect. Maybe I should try with numbers that aren't as close to each other, but I won't bother. It's just a shame mitigation isn't this simple. This only works if we know what the DPS of the enemy is going to be when planning a build. That's why the survivability line calculations are practical. P.S. If I'm totally mistaken in everything I posted in this post, please take into account I've drunk more wine than what is healthy. Thank you. |
We may not know what damage is coming in exactly in a build. But we know it's enough that defense wins these discussion every time.
Here's some real numbers (reasonable ingame numbers IMO):
Scenario 1:
400 dps incoming.... 1800 hp...(note base is 50% tohit, so 200 dps actually hits you) 20hp/s regen. You live for 10 seconds.
Add 5% defense to that (you'll go from 50% tohit, to 45% tohit, so 180 dps hits you). 20hp/s regen. You live for 11.25 seconds.
that 5% defense gave you 1.25 seconds of life... or an improvement of 12.5%.
Scenario 2:
400 dps incoming.... 1800 hp...40% defense (note base is 50% tohit -40% defense = 10%, so 40 dps actually hits you) 20hp/s regen. You live for 90 seconds.
Add 5% defense to that (you'll go from 10% tohit, to 5% tohit, so 20 dps hits you). 20hp/s regen. You live forever.
Conclusion:
The difference between 10 and 11.25 is not the same as the difference between 90 and infinity, therefore initial defense values do matter.
Myth is validated.
edited a bunch for formating... and to add this note:
In both scenarios, the 5% defense reduced the incoming damage by 20 DPS. So it did the exact same thing in mitigation, but mitigation is not directly equal to survivabilty.
I gotta make pain. I gotta make things right. I gotta stop what's comin'. 'Least I gotta try.
Blue
American Steele: 50 BS/Inv
Nightfall: 50 DDD
Sable Slayer: 50 DM/Rgn
Fortune's Shadow: 50 Dark/Psi
WinterStrike: 47 Ice/Dev
Quantum Well: 43 Inv/EM
Twilit Destiny: 43 MA/DA
Red
Shadowslip: 50 DDC
Final Rest: 50 MA/Rgn
Abyssal Frost: 50 Ice/Dark
Golden Ember: 50 SM/FA
. In other words, at 40% defense, in order to double survival time, you can either add another 5% defense (trivial to do, in general) or double your regeneration (likely impossible).
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Starting numbers:
HP: 1000
DPS Incoming: 500
Resistance: 0
Defence: 40%
Regen: 10hp/s
Time to Defeat: 25 seconds (take 40 damage/second)
Case A: Increase defence by 5%
Time to Defeat: 66.6667 seconds. (take 15 damage/second)
Case B: Double Regeneration.
Time to Defeat: 33.333 seconds (take 30 damage/second).
And once again, we come to the highlight the purpose of the thread. You cannot express something as "100% improvement" without being exceptionally careful with your numbers. Shown above is the 100% improvement from defence vs an 100% increase in regeneration. They don't add up.
This is inherent in the very definitions of how the various effects work. Regeneration is defined in absolute HP/sec. Defense and DR are defined in removing a percentage of damage directed at your character. It's therefore impossible to compare Defense or DR to regen without choosing a fixed incoming DPS.
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What's the point if it isn't right?
The survivability line only says: When I am faced with an amount of damage that is exactly at how much I can survive, it is preferable to add (def/regen) to improve this to a new level where I cannot die. Once damage goes beyond this point, I cannot answer this question.
My method says: Given a certain amount of damage, you should choose (def/regen).
Both requires you to make an assumption of the damage. Mine allows you to calculate it at any point. The survivability risks selecting Regeneration and then later leaving you in the dust because...well... you know. You actually fought something tough and perhaps you should have taken Defence?
We may not know what damage is coming in exactly in a build. But we know it's enough that defense wins these discussion every time.
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That point is dependent on just exactly how much defence, or regeneration, you will get.
To simply state "Defence" is wrong. What if there were some kind of example where you were deciding between taking a healing power for yourself, or taking weave? Healing can be approximately translated across to an amount of hp/sec.
Lastly, this thread is NOT about showing how incredible Regeneration is. It's darn hard to get and I don't really advise it at all with the way that IOs currently exist.
Precisely. You simply cannot decide without considering how much damage you face. Call that a weakness of the model but it is an absolute truth. A model that attempts to give you a single answer is going to be wrong under numerous situations. Even though it may be simpler (I say it isn't, my method is remarkably easy), it doesn't give you a correct answer.
What's the point if it isn't right? |
Go back to my example, including my 2nd post on it, for a clear example of why we know with a high degree of certainty that aiming for that last 5% of defense is the more practical goal.
What you may be missing here is the implicit assumption that we're playing under conditions where we will die if we do not defeat our enemies first. If we don't have enough incoming DPS to create that situation, we go find it. Therefore, the DPS output by our foes against a high-defense character is assumed to be immensely high. Per my second post, it is usually quite literally impossible to obtain regen rates that would substitute equivalently given the same pre-mitigation DPS applied to our characters at low defense levels. At least without outside help - attaching an Empath to your Scrapper is not usually considered vogue.
Edit:
The key sticking point is that no one is interested in damage this low.
Blue
American Steele: 50 BS/Inv
Nightfall: 50 DDD
Sable Slayer: 50 DM/Rgn
Fortune's Shadow: 50 Dark/Psi
WinterStrike: 47 Ice/Dev
Quantum Well: 43 Inv/EM
Twilit Destiny: 43 MA/DA
Red
Shadowslip: 50 DDC
Final Rest: 50 MA/Rgn
Abyssal Frost: 50 Ice/Dark
Golden Ember: 50 SM/FA
This is inherent in the very definitions of how the various effects work. Regeneration is defined in absolute HP/sec. Defense and DR are defined in removing a percentage of damage directed at your character. It's therefore impossible to compare Defense or DR to regen without choosing a fixed incoming DPS.
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All you need to know is the character's HP, DEF/RES, and expected healing/regeneration rate and you can figure out what incoming DPS you can survive for X amount of time (or forever). If you want to choose between two different build options, then you just take the appropriate figures and compare.
Bunny would have us act on a number that's divorced from practical context. "Ok, you're better off with the regen when incoming DPS falls beneath [for example] 100 DPS." That's great, except that as a player I have no way of knowing what 100 DPS actually represents in gameplay terms. Would I be able to go AFK indefinitely under 100 DPS regardless of my choice? In the alternative case (where DEF outstrips regen at some massive number) would I be screwed either way at the numerically-approved level of incoming damage?
He's giving us a correct (more correct, he argues) version of the same number that the survivability-line method gives us, but he fails to take into account that number's relevance.
And then he's telling us all we've been misguided to seek the more relevant number.
BA, could you please, for the record, state what point you are trying to make? You seem to be arguing several things, and changing them as you see fit, whenever someone demonstrates you are wrong. I assumed you were arguing this:
The Myth
That when defence is added to a character, it is more valuable to a character near the soft cap than to a character who is at 0%. |
In fact, I am not sure that you even know what you are arguing at this point. I saw your posts in the 16% def vs X regen thread, and I realize your ego was bruised there when people showed you were wrong, but this isn't really going anywhere productive here either.
The survivability line acts as a proxy for the incoming DPS. That's the point.
All you need to know is the character's HP, DEF/RES, and expected healing/regeneration rate and you can figure out what incoming DPS you can survive for X amount of time (or forever). If you want to choose between two different build options, then you just take the appropriate figures and compare. |
Blue
American Steele: 50 BS/Inv
Nightfall: 50 DDD
Sable Slayer: 50 DM/Rgn
Fortune's Shadow: 50 Dark/Psi
WinterStrike: 47 Ice/Dev
Quantum Well: 43 Inv/EM
Twilit Destiny: 43 MA/DA
Red
Shadowslip: 50 DDC
Final Rest: 50 MA/Rgn
Abyssal Frost: 50 Ice/Dark
Golden Ember: 50 SM/FA
Oh, I'm well aware. That still involves picking a DPS (or regen rate) number. It's a number based on quite reasonable information - the character's known HP and regen rate. We can compare what different regen rates and different DEF/RES values do to a build's immortality line, but we still can't compare a given applied regen rate to a given DEF/RES delta in a vacuum.
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Sure, if you want to say that for some reason we don't know the character's starting regen/healing/HP then you might as well pick the opponent's DPS number out of a hat -- but we do know the character's starting values for all of the above. We don't know how relevant a given hat-picked DPS number is.
It wasn't my intention to correct you on a point you didn't understand; clearly you do understand. I was just trying to clarify why it serves no useful purpose to indulge Bunny by admitting that the opponent's DPS is crucial.
The majority of the individuals that will reply to this thread view the following statements as functionally identical:
"40-45% is worth more than 0-5%." (Post 20)
"The origins arise from the fact that increasing defence gives exponential rises to survivability. This is not a point of contention." (OP)
I foresee that this thread will sadly not end well