The Defence Myth

My ego is not bruised; if it weren't, I wouldn't write this thread I know that many people will argue against it, and there are some issues of semantics. I am guilty at times of putting the wrong word in here or there, but I believe that those reading this thread, especially those who have bothered to truly investigate the tools I provided, will understand.

I have watched the spreadsheet carefully over the last few hours and the activity was extremely limited. Most of the posts here would be clearly answered if you read the initial post. For instance, I have stated that it is not a point of contention that increased mitigation provides exponential benefits. That was in post 1. Perhaps, again, I have worded myself poorly at other stages and brought that into question, but I apologise if that is so. More mitigation = exponentially better. The point though is that it doesn't matter where that mitigation comes from, so long as it is equal. That final 5% defence, to move you from 40 to 45%, could be attained by regeneration, and this amount of regeneration is the same that it would require you to go from 0-5% defence.

A key point that I want to show is that a 100% improvement in survivability is not the be all and end all, and that it can be equalled by applying different methods. You have yourself fallen for this concept, by saying when 40->45% = double survivability, you'd need to also double regen. That is false.

The origins of this thread are in statements that suggest that which you have written. The best way of attaining the highest survivability is by calculating the individual mitigation that each method provides and choosing the best. A statement of "100% better" doesn't give you correct information in doing so. As evidenced, it provides false conclusions.

The survivability curve is useless when faced with a situation where you are at a chance of dying. That is, as soon as the damage exceeds your own regen/defence/resistance, it cannot answer. What's the point of it? The indisputable truth is that it may telll you that regen is better (be it from IOs, from Health slotting, from a self heal) but then you get in a situation where you are at risk of dying, and you discover that it should have been defence, because defence is a better choice under high DPS? Again.. what's the point if it isn't correct when you need it most?

The problem is you "decide" long before you go against a group of enemies. You don't get to change your build based on the damage of what you'll be fighting. Even if you did know, the incoming damage will change rapidly.

I don't actually understand how this thread has gone on so long. Was the original +Regen hypothetical value really +200 HP/s in this spread sheet? How in the world could it be just as easy build wise to get 200 hps as it is to get 5% defense? By comparison, using 5 slots to use the +regen procs, a Numina's: Heal, finish enhancing Health and get another 10% (From LotG or Entropic, what have you), only represents about an increase of 10 hp/s on Scrappers. The same 5 slots used for Guassian's get you 2.5% defense. That's almost the best slot:+regen ratio against a middle of the road slot:defense ratio.

Anything better will be centered around a specific power (RttC, IH, etc). Is the question really to skirt slotting on a key +Regeneration power in your defensive powerset or to softcap? If that's the case... use those numbers from actual builds. Even if you want to use pretend builds... imagine a Tanker who doesn't slot RttC with 10 mobs in range and 45% defense vs a Tanker w/slotted RttC and only 40% defense. There may just be a case or two in the game where Bunny has a point.

I've seen on a few other threads that Bunny likes to insert irrational values into mechanical formulas to try to make a point... but all it does is disconnect the arguments founded in hypothetical situations further and further from the actual game. Even when the math is completely wrong and the values inserted are irrational, the argument continues.

Sure, if you know the DPS coming in, and you could achieve a ton of +Regen with the same amount of slots that it takes to get a wee bit of defense, then he might have a point.

We had a similar discussion in another thread about how good IH really is. I made the case that with DP it's just as good as a crashless tier 9, because in order for such a power to match the mitigation of DP+IH you have to be taking so much damage already that you'll be dying quickly. I think this is the sort of case Bunny is trying to make across the board. However, the problem is with crashing tier 9s, it quickly turns on its head. The initial DPS required for something like Unstoppable to match DP+IH only leaves ~8 DPS. Anything much above the 53 DPS that IH+DP can mitigate, and any crashing tier 9 is better. In other words, with lower incoming DPS, +Regen can shine, but it quickly falls apart when the +Def and +Resists are "comparable" and the DPS rises. Comparable in the sense of the same number of powers or slots devoted to a particular form of mitigation.

Anyway, there are no myths about Defense. The claim In the spreadsheet is beyond dead wrong. The math behind this was done a long time ago by folks more suited for it using more realistic numbers.

Please read:
Arcanaville's Guide to Defense 1.10
Arcanaville's Scrapper Secondary Comparisons (from before IOs)
Dechs Kaison's Guide to the Softcap

I am repeating myself here, but the flaw in this method is astounding.

It might chose Regen/Self Heal instead of defence. That's quite possible. There are times where picking up a self heal, or slotting extra regen, or a unique IO, might be easier than finding an amount of defence to a particular position/damage type.

The problem is this:

As soon as you are taking damage greater than what you are guaranteed to survive, the survivability curve is useless. It could be wrong.

Why do you favour something that is demonstratably wrong?

It's better to have a level of complexity (ie: estimate their damage... Werner did that for his tests!) than to have a method that's just flat out wrong sometimes.

Understood.

Why do you insist on building such atrocious stawmen? This is not how you use this information. You use it to determine which build choice is most survivable. The one with the highest survivability line is the one that will live longest on average, and is therefore the one that's best to chose.

You don't use this information to choose what to fight. You use it to determine which build will survive best whatever you're fighting. Whether or not you can actually win the encounter or not isn't actually relevant - it's all about what will last longest.

QFT.

I cannot stress this point enough.

When building characters, I'm not interested in absolute differences between the DPS figures of group A and group B. I'm interested in their relative damage differences, because this is much more practical. This is why Defense soft cap is a primary objective and decent regen is secondary. Regen deals with absolute differences modified by the relation of Defense and incoming DPS whereas Defense just modifies the relative incoming DPS. If I know I'm taking in 5% of the incoming DPS no matter how high it is, I don't have to worry about numbers that are low enough that bumping Regen might be the better choice.

I'll use the spreadsheet to show you why initial defence isn't a parameter. Feel free to do it yourself, or use your own calculations.

Some nice round numbers here:

HP: 1000
DPS Faced: 300
Starting Defence: 0%
Starting Regen: 10 hp/s

Two Choices: Either +5% defence (all), or +15hp/s regen.

With +5% Defence, you'll survive for 8 seconds.
With +15 hp/s regeneration, you'll survive for 8 seconds.

Now according to what you write, if I change it to 40% defence, then .. what happens? Let's see.

HP: 1000
DPS Faced: 300
Starting Defence: 40%
Starting Regen: 10 hp/s

Two Choices: Either 5% defence (all), or +15hp/s regen.

With +5% Defence, you'll survive for 200 seconds.
With +15 hp/s regeneration, you'll survive for 200 seconds.

Clearly,it doesn't matter what your initial Defence was. They were both worth just as much at any stage. Again, the problem with +100% survivability rises. It is a trick!

You can do quite easily test the other calculations, simply imput 299 and 301 DPS. When you put in 301, regardless of initial defence, Defence is better. At 299, regardless of intial defence, Regen is better.

No, it's not.

You cannot tell which is more survivable for the exact reason that you don't *always* fight people who have the precise damage output equal to your mitigation.

As soon as you fight someone exceeds that, you risk having taken the wrong choice (that being, if your survival line said the regen was better) and then ending up having *worse* survivability.

And this is exactly the point. How do I know what kind of DPS a random spawn of, say, Rikti is going to put out? What should I consider the average DPS a random group of any enemy type deals?

This is why we always just consider incoming DPS high, and just use the survivability line.

And to be perfectly honest, I'd bet in a large majority of the cases it is easier to get 5% Defense than 15hp/sec when you're at 40% Defense. I'd argue it is much easier to get 5% more Defense no matter what the position. And this is only when looking at DPS figures of 300 DPS before Defense/Resistance. It's not even that much.

What you seem to be missing here is what we're trying to stress. When calculating the benefits of Defense, people are generally more interested in the relative increase of survivability, because that's how Defense works.

ETA: You should also consider the effects of Regen and Defense in practical terms. Which one is easier to achieve, very high Defense or very high regen? Defense is most of the time the way to go because against very high figures of DPS it always provides better returns than Defense, and against lower numbers it either provides comparable results, or it simply doesn't matter which one you choose, meaning Defense is the way to go. These two things combined make Defense the choice of a survivalist.

This is both true and false. It is true in the sense that no matter where you gain the defense, it is still going to be mitigating 5% of the incoming damage, no matter if it is your first or last 5% interval of defense. It is false in the sense that it provides the same real increase in survivability, and I, like many others, can prove this mathematically.

At 0% +def, 5% +def is going to mitigate 10% of your incoming damage (turning what was a 50% hit rate into a 45% hit rate), which means that you need 10% of your base regeneration to equate the improvement. At 40% +def, the last 5% +def is going to mitigate half of your incoming damage (turning what was a 10% hit rate into a 5% hit rate), which means that you would need 100% of your base regeneration to equate the improvement. At 40% +def, a 10% increase in base regeneration rate would only equal a 10% increase in survivability. Regeneration scales directly (newRegen / oldRegen = survivability increase) whereas defense scales indirectly (survivability increase = ((.5 - oldDefense) / (.5 - newDefense)).

If you plot those two functions, you'd find only 1 point of intersection within the set of numbers we care about (i.e. quadrant 1), which means that there is a single point of equivalence for any specific combination of defense and regeneration. In order for your above quote to be true, there would have to be an infinite number of intersections along those two lines. A single point of equivalence is what you'd actually get, which is direct mathematical proof that your above quote is false.

(From a different response, but I didn't want to split my own response when one will suffice)

There is a reason that the model that you were referred to is called the "immortality curve". It doesn't care if you kill something. It assumes that you never will (i.e. the amount of damage you can indefinitely sustain while never dying). This is not, however, the only measure of survivability ever used. You can calculate for any reasonable time frame rather easily by adjusting the formula a bit and covering that base and still completely supporting the veracity of the "defense myth" (actually, adjusting for time frame actually makes it look way better because regeneration is a direct counter to attrition, which is what you're directly trying to counter with immortality).

The formula is as follows:

(((Regen * Time) + MaxHP) / (1 - Mitigation)) = Damage

Regen is your regeneration per unit of time.
Time is the total number of units of time.
Max HP is your Max HP.
Mitigation is the percent of incoming damage you mitigate (via defense, mez, resistance, etc.).
Damage is the amount of damage you can take in total (in order to determine the DPS needed to kill you within the Time, just divide Damage by Time and you'll get your answer).

Thank you

I am not trying to reinvent the wheel. I do recognise that it's pretty fine to get to the soft cap I tend to aim for that on all my characters. The way that IOs are nowadays makes it a very wise investment.

Unfortunately people still do not recognise that the calculation isn't dependent on the initial defence. For instance, Gillia claiming I am dead wrong, but I can immediately display that I am in fact right.

The origins do stem from people saying a 100% increase is the be-all-and-end-all, when there are other options which may be better. YMMV, and they may not be applicable in as many cases.

This statement makes it clear that you do not understand the topic under discussion.

Why on earth do you think it's relevant what the precise incoming DPS is?

You're thanking him for pointing our that he doesn't know what you're debating? I don't think he was talking about the rest of us...

Bunny, you have not once addressed my example. Please do so and then defend this claim in light of it.

Yes, and the cases where everyone else is working cause defense to almost universally be the more practical choice. Low incoming (pre-mitigation) DPS is not relevant to a discussion about nearly any AT with defenses near the soft cap.

If I can stop you here because this is where you have gone wrong. Your definition of incoming damage has changed.

Incoming damage MUST be determined from the start, else you end up where you are now.

Let's assume the incoming damage is 100.
50 of that is mitigated by an enemies base chance to hit.
With 5% defence, 5 of that is mitigated by defence. That is 5% of 100.
The amount of damage you take is 45. If it mitigated 10%, then you would be taking 40, which clearly isn't so.

Next look at incoming damage of 100.
If 5% defence = 10% mitigation, does 40% defence = 80% mitigation?
No it doesn't. 50 is mitigated simply on the basis that the enemy misses 50% of the time.
40 is mitigated by defence.
That leaves you with 10 damage.

If you go from 40% to 45% defence, you go from 10 to 5 damage. That is 5% of the original attack.

Onto your more key point:

There is one amount of DPS where they intersect. In fact, ALL points intersect, hence why I say they are interchangeable. For a demonstration of that point:

There you go. Both are perfectly interchangeable.

When you are above that DPS, you should always go for Defence. When below, you should always go for Regen.

(I am tempted to stop saying Regen and say "health recovery" so that people can consider self heals as an example, it is causing some side tracking here)

My apologies Umbral, very late and tired now but I enjoy the discussion

This has already been raised before and shown to be false:

Do you understand what percentages represent?

He expressed change in incoming damage as a percent. There is nothing wrong with that statement. He did not change the definition of anything.

You don't have to know the absolute number to know that removing a larger percentage of any number is better mitigation. We don't understand why you can't see this.

The value of defence is entirely dependent on the incoming DPS.

If you don't know it, you cannot decide how useful the defence is.

Do I say you need to be precise? It sure helps. You could estimate, and many of the calculations should be fairly clear cut.

I hope you recognise that I have many many many messages to respond to and quite a few of which are repeats that I can answer by copying/pasting previous solutions too. It's very late here for me too but I do like this conversation

Is your question why defence is a more universally practical choice? The availability of IOs is probably #1.

I have called it Regeneration throughout the thread, but any kind of self heal can be calculated to an amount of hp/sec, so it's worth sometimes considering the benefit of a self heal power choice to a defence power choice. Both will serve under different circumstances - you can calculate which quite easily.

If your point is something else, can you please state it in a single post because I am always 100 posts behind <3

Oh I understand them perfectly. I did not make the mistake of writing that +100% survival through defence = +100% regen rate.

My point is exactly that. You should be careful about your interpretation. Expressing mitigation in these terms leads to false conclusions. It should be written as a quantity of mitigation. That quantity (if defence or resistance) will depend on how much damage you face.

You do realise this is exactly what I have written in the spreadsheet but simply in a different order.

This expresses how much damage you can take, dependent on time.

This is... damage over time.

Run the numbers What I propose is precisely that for determining length of life.

lol Not a cruel lol, but I loved your disclaimer it was funny

If someone wishes to measure their maximum DPS they can survive indefinitely then certainly the survivability line is the way to go.

My issue, stated perhaps ad nauseum, is that it can give you the wrong answer at times.

It might suggest to go with Regen. Your problem is that there is a point where you are taking enough damage that the Defence would have actually been a better choice, and by taking Defence you would live longer. In game terms, that is more meaningful to me, than to determine how long I live if and only if I am under a very specific set of DPS. It doesn't carry meaning outside of that 1 case.