The Defence Myth

I felt this deserved its own thread. The other had far too many points raised for this singular issue to be tackled and dealt with once and for all. Please keep this subject on topic as much as possible, though I know it's remarkably easy to stray on an internet forum and end off in the woods somewhere.

I typically only bother writing very short posts because the point is easily lost in an essay. Inevitably our audience is internet forum goers and so the attention span is naturally short. I know mine is. However given the amount of back and forth, and incorrect information, I have decided I simply must put a considerable amount more effort into this to finally 'close the case'.

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%.

The Origins of the Myth

In short, some bad maths, some troublesome semantics, and some analytical tools used that cause numerous amounts of confusion, which unfortunately have been repeated until it has become a 'truth' of the forum.

The origins arise from the fact that increasing defence gives exponential rises to survivability. This is not a point of contention. The problem lies in the semantics and then the further interpretation into other fields. The original thread which brought this to a head was one which compared an option of having either more regeneration or more defence.

What arose was the argument that the answer would be different depending on the initial defence. This comes from the Myth that it is more useful at or near the cap than at 0%.

What I will provide is a spreadsheet that categorically dispels this myth.

Some final disclaimers before I begin. More defence is always better, up to the cap. Defence provides an exponential boost to survivability. However, this is not some kind of inherent property of defence, but rather an inherent property of mitigation - the protection provided. All kinds of additional mitigation provides exponential benefits to survivability.

How do you compare choices?

The answer is simple: by the mitigation it provides.

An option that provides greater mitigation is the one that is to be chosen.

Why this can be muddled is that different forms of mitigation are applied in different ways.

Defence & Resistance, for instance, are dynamic, and their value is dependent on the damage you will face.

Regeneration is static, a constant amount of effective mitigation regardless of incoming damage.

For the mathematically inclined, it is of interest to note that having a high Resistance actually devalues adding additional Defence, because it inherently decreases the incoming damage by which Defence determines its value.

The Evidence

Here is the spreadsheet.

https://spreadsheets.google.com/ccc?...zUVFnQ3c&hl=en

First of all take some time to examine what is actually written. Realise that it does not consider some extremely difficult to quantify situations such as potential debuffs to your stats, or your ability to actively mitigate damage via kiting, active crowd control, or jousting. It boils the situation down to a few key variables. Hopefully you choose to play with these variable to gather a better understanding of their interactions. By doing so you will reach a number of simple conclusions.

The only initial variable important is your initial resistance. Not your initial health, defence, or regeneration rate, contrary to how you might initially think.

The other important variables are by how much you wish to increase defence and regeneration. These two are the options you have.

The spreadsheet is initially set up with some generic numbers already in. Once again, to appreciate what I have done, please do spend some time to play with these numbers, else you will not understand the significance.

I have completed the spreadsheet quite quickly; it's possible there are errors. Please bring these to my attention and I will correct any. I believe the maths is sound but typos are almost my middle name

One final important point to note when playing with the spreadsheet: The indifference point. The point of indifference is an economic term for when two options are equal in utility to you. In simple terms, it's when you don't care, or are indifferent, to the options. When you change the fundamental terms that decide the model, the indifference point is calculated automatically.

This allows you to test the spreadsheet. By increasing DPS above the point of indifference, you will discover that defence provides better survivability. By lowering DPS beloow the point of indifference, you will find regeneration provides better survivability.

The indifference point is the solution to a question that asks which is better: regeneration or defence.

Please do spend some time playing with the model first before replying. It is much easier to see with your own eyes that the initial defence does not change the decision than it is to explain with long winded mathematics and counter-points that are tangents to the issue.

Thank you and good luck.

-special thanks to je_saist for getting me the google docs link so anyone can open and browse it easily.

um, two quick questions:

A: why didn't you use ISO/IEC 26300 / Open Document to store the spreadsheet?

B: could you please choose a different host. Places like Google Docs will let you upload documents like this without having to run the risk of introducing spyware or other malicious software packages to your downloaders.

I've updated it so anyone can view it... please don't mess with the formula else I'll have to reupload

Much appreciated for the link, that's very very handy je_saist!

Any defense analysis that doesn't consider debuffs is flawed by design.

Any regeneration analysis that doesn't consider burst damage and downtime is flawed by design.

On another note, you're making a thread to argue "initial defense doesn't matter" and your attempt at a proof is a spreadsheet where the initial defense is always equal to 0?... Boy, that sure convinces me.

If you have a question about the functionality I am logged in right now and you can talk to me in real time

Burst damage isn't the same thing as consistent high damage. Burst damage means you will get hit by varying amounts of damage, not a consistent, steady stream of X DPS.

My bad, I didn't understand the spreadsheet well. Let me rephrase my rhetorical question : on another note, you're making a thread to argue "initial defense doesn't matter" and your attempt at a proof is a spreadsheet where the initial defense is always either 0 or 40? Boy, that sure convinces me.

You should spend a little less time telling people what they should do and a little more time actually playing the game, as casual playing would tell you that the probability of burst damage happening is 100%. We call it "jumping into a group", or alternatively "being a scrapper".

Nihilli, the key factors you should be looking for when you explore the spreadsheet are:

First, set an amount of regeneration vs defence to compare. Naturally, set the regeneration to something reasonable, because defence is quite good. Leave resistance at 0% until you get a good feel of how everything else works.

Look at the indifference point, and set the DPS to that.

You'll notice now that regardless of whether you applied the defence to reach a soft cap, or if you added the defence to 0% and 'just started', they are both equal.

This is an important observation. Regeneration is a static form of mitigation. You would expect that Defence would become more useful towards the cap, but it is not. It remains just as useful at all stages.

To test this theory, then increase, or decrease, the DPS by a small amount. You'll notice that if you increase the DPS, the result is that defence pulls ahead. This should be expected, because the value of defence (it's mitigation) is proportional to the amount of incoming damage. Likewise, if you decrease the DPS, you'll find that suddenly regeneration is more effective than defence, because you are reducing the value (the mitigation) of Defence.

Quote:

Originally Posted by Nihilii You should spend a little less time telling people what they should do and a little more time actually playing the game, as casual playing would tell you that the probability of burst damage happening is 100%. We call it "jumping into a group", or alternatively "being a scrapper".

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've just debunked your so-called study in my first post in this topic, much like the question that got you all angry in that other topic was answered by the second post. This thread was rendered useless for its intended purpose past that point, although it still does a good job at providing cheap thrills, such as seeing you trying to deflect a direct answer as invalid because it's based on ingame experience.

Again, you can't resolve a problem through maths if you ignore most of the variables. This is just common sense.

Another basic thing that anyone remotely interested in both probabilities and human behavior should know is that the more people try to refer to hard sciences and external sources in an argument, the less they actually know. Internet only amplifies this behavior through relative anonymity.

While we're on covering the bases, what's the difference between good math and bad math? Bad math twist the facts so they fit the model, good math twist the model so it fits the facts.

There is no myth. Your thesis is flawed.

Assume I have a character with some amount of defense. At that level of defense, whatever it is, I can find a number of some given foe, that, on average, will never kill me. (I might still die if a large number of them manage to hit me at once.)

Now I add defense. I add enough defense to halve the average rate of damage that lands on my character. By definition, I can now survive, on average, twice as many of my chosen type of foe.

We understand that the math of defense means that it is easier to halve the average DPS that lands on a character the closer we are to the "soft cap".

If I go from 40 defense to 45 defense, I halve the amount of average DPS I am suffering, which again means I can double the number of foes I can survive. To do this starting at zero defense I require an additional 25 points of defense. Therefore, 5 points of defense is more valuable starting at 40 than 5 points starting at zero.

The absolute contribution is practically meaningless to the application of how we play the game. The relative contribution is more applicable.

heh heh

nice spreadsheet (seriously). useful for answering the +16.7% vs. HP/Sec argument.

I'm not sure its of as much practical value for the folks that are likely to respond to this thread, simply because incoming DPS for those individuals is typically very, very, very high

So your spreadsheet shows me you're wrong.

All else being equal, going from 0% to 5% defense makes my time until defeat change from 8.33 seconds to 9.30 seconds, a net gain of a whopping 0.97 seconds. Going from 40% to 45 % defense makes my time until defeat change from 50 seconds to 133.33 seconds, a change of 83.33 seconds. I suggest that 83.33 is a larger number of seconds than 0.97, which I can back up with references from my kindergarten teacher. Therefore, in any situation that actually matters, the last 5% is going to keep me alive a lot longer than the first, and the closer you get to softcap, the more of a difference it makes (Kaison, 2009). Conclusion: the last point of defense is worth a lot more in terms of survival time than the first.

Edit: values of spreadsheet not noted, but the experimental results remain similar or identical in terms of increase to survival time.

I'm glad we had this talk.

References

Kaison, D. (2009). Why is reaching the softcap so important? City of Heroes Forums. Retrieved from http://boards.cityofheroes.com/showthread.php?t=185167

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