BunnyAnomaly

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.

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

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

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

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)

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.

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.

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.

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.

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?

When damage is low enough, regeneration will win.

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?

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?

That is incorrect.

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.

There are some very serious problems with this answer, not least of which is that it isn't always correct, and that the assumptions are far stronger than mine. Mine describes what you should do when you face differeing amounts of DPS. This... well. Let me explain.

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.

This is where you are wrong, and the purpose of this thread is shown.

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%.

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.

I can't make people read the whole thread and people will always say "but 5% is really good", which is not the point at all. We know it is good.

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%.

The point it is under debate is that people don't believe me!

This thread hopefully explains it quite succinctly.

Some of the origins of the thread lie in the problem of stating your improvements in % terms. They are fickle and don't serve much purpose unless you can awkwardly state everything in the same term, which is a veritable nightmare.

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%.

The argument that has been posed numerous times is this:

40-45% is worth more than 0-5%.

The problem is... well... it's not really. You can argue a few semantics (I agree that increasing mitigation provides exponential benefits), but the face is you can substitute, say, an equivalent amount of mitigation that was equal to the 0-5%, and it would satisfy you for the 40-45%.

Perhaps that's a bad explanation as it's quite late in my part of the world. I'll say it another way in case that first one isn't clear.

People might assume that because a 0-5% increase in defence is quite small, it is easy to get a similar amount of mitigation to replace it. They might also assume that because 40-45% defence provides a 100% increase to survivability (only half again of the attacks are hitting you), it's very difficult to substitute for that. They would be wrong. You could substitute the same amount of mitigation (I have used Regen consistently because it remains perfectly static, and was the actual question initially posed) that equals 0-5% and it would also equal 40-45%.

To view this, simply do the following.

Set the +defence to 5%
Set the regen to 25 hp/s
This will make the indifference point 500
Set the DPS to 500.

Now you can see that they are just as good at either 0-5% or 40-45%. It doesn't matter.

If you set the DPS higher, it will favour Defence. If you set it lower, it will favour Regeneration.

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.

Now I provide you the same choice but under slightly different circumstances. You are at 40% defence. I offer you either 5% defence, or the exact same amount of regeneration as in the first choice.

According to how I interpret your writing, you would say that when faced with the second choice, the defence is a clear cut answer. If they were just as good at 0%, and you were only adding 5% survivability from defence, then surely when at 40%, where the defence is adding 100% survivability, you should choose the defence?

The problem is: you're wrong.

They'd both give you the same mitigation and so long as they were equal in the first choice, they are also equal in the second choice.

You may test this by using the spreadsheet or some basic maths on a calculator.

This is why expressing it in terms of a % increase leads to false conclusions.

The template is (hopefully) currently saved in such a way to demonstrate this exact relationship. You'll see that the survivability has been set so that 5% defence = 25 hp/s regen, and that both going from 0-5% and 40-45% changes nothing. You still live just as long.

It is essential you view the spreadsheet before posting. That is where the meat of the post is actually contained. I simply don't have time to address people's thoughts on the matter which aren't relevant to the specifics. Such relationships are already presented in the body of the text, however, if you read it entirely. I am concerned by you pointing out what I have already written, it suggests you simply haven't read it.

The question being posed is not actually about layering defence and resistance (although if you look at the spreadsheet, I have given you the capability of doing so), but rather what is the benefit of additional defence, and does this benefit change depending on where you sit with your existing defence, and further if the method of compensation changes too.

Common misconception is that the survivability should favour defence as it approaches the soft cap, and that you are less likely to want regeneration. That however is demonstratably false. It highlights the problem of describing the benefit as a % increase. One would assume a high % increase is better.

Actually Behavioural Economists describe it as the Superstar Effect.

http://gulzar05.blogspot.com/2007/08...ar-effect.html

'tis only a blog site and not a good text book read, but it might be of interest to you.

I would advise you look at my thread on "The Defence Myth". The mathematics in this thread is appalling, and what I have written there quite succintly answers a very key problem that yourself and Werner are struggling with.

This is a study to debunk a myth that has been circulating endlessly and repeated until it has become a false truth. If you don't want to contribute then the game is running right now for you

I have attempted to explain the underlying maths numerous times but unfortunately in the past don't get it. So I have created this spreadsheet so people can set it to whatever they feel like.

I encourage you to be adventurous.

Be aware that the initial defence does not need to be 40. That is just using the default 5%.

You may set the difference in defence to be, for example, 25%, and then it will examine the difference between moving from 0 to 25%, and 20 to 45%. You'll notice that it doesn't matter. The point in fact is that you can select anything under the cap and it doesn't matter. Being close, or being far, from the soft cap is irrelevant

I have purposely selected the most extreme possible results (barring hugely negative defence due to debuffs, but that is outside the scope and would be confusing to people, but still give the same result) so that people might recognise that hitting the soft cap doesn't contribute as much as people think.

As for incoming damage, you should read a bit more on probability theory and you will should come to the conclusion that erratic numbers can be accounted for simply by taking their possible damage and multiplying it by the probability of such happening. This is fundamental to all economics, probability, finance, and likely countless other disciplines.