The Defence Myth

I put in 50% defense in the spreadsheet with DPS at 100, 0% resistance, 20 regen, and 1800 maximum hitpoints. The regeneration that compared to this 50% defense was 50 additional points.

Mathematically, this is true. In both instances, such a character will go from 1 hitpoint to max in 90 seconds. Also, going from -5% defense to 45%, or instead from 20hp/s to 70hp/s, the character will go from 1hp to full in 120s. Again, 50% defense = 50 hp/s.

While we have caps on defense, in-game caps, which are subject to change, do not alter the relationship when the survivability mechanics remain the same.

To compare this to something more realistic, look at 100% resistance instead of 50% defense (since I see no one complaining about that relationship in this thread). 100% resistance has been possible before in this game. Using the method applied by the original poster, a level of regeneration can be found that is equivalent to that 100% resistance figure.

Also we have something that mimics the effects of uncapped 50% defense against enemies with a base tohit of 50%: Phase shift. Using phase shift we can similuate these effects and have an apt comparison for survivability purposes. Again, this same method used by the OP can apply a regeneration % that is equivalent in mitigation to phase shift.

edit: So, let's say that since 100% resistance or 50% defense is impossible to reach after caps, what value of regeneration must I have to achieve those effects? I put in those values into your formula, and tada, I can now survive as much as an i0 perma-unstoppable tank.

This method is wanting.

AHA!

I finally worked out what the heck the OP was thinking when they wrote this. It took a while of contemplating it and reverse engineering the thought process.

It comes down to this: the OP makes a critical mistake right up front in terms of what people believe. The OP has heard the phrase that defense gets stronger the more you have, and then made a leap none of us has ever made before. The OP tried to figure out a relationship between defense and regeneration, and compared a given level of defense to a given level of regeneration for different starting points of defense. The OP believes, I think, that if the "myth" were true, then as you started with higher levels of defense, the incremental amount of defense would be worth increasingly larger amounts of regeneration. In other words, if 5% defense is equal to X regen starting from zero, it should be worth more regen if you start from 25% defense, say.

But the problem is that, as most number crunchers know, both defense and resistance amplify the benefits of regeneration. So as you stack defense on top of defense, each time you do the value of that defense increases, but the value of regeneration you're comparing to also increases in value in direct proportion, so they stay equal.

The OP thinks that the "myth" states that if you have enough defense, eventually an incremental amount more will be better than all other alternatives and that's not true. No one states that. The "myth" only states that the value of 5% defense is higher if you start at 25% than if you start at zero. To prove this we need to avoid comparing to standards that themselves shift around, and look at the actual net change in survivability.

If the OP thinks there are people out there that are saying things like "near the soft cap, defense is worth more than any amount of regeneration" then that's false If I was at 40% defense, I would take +400% regen over +5% defense. That's an easy choice. But I would take +5% defense over just +50% regen, because the former doubles my survivability while the latter increases it by only 50% (or less, if I start with slotted Health). The break even point, if you have slotted health, is about +180% regen.

The thing is, we're basically *never* in a position to choose between five percent more defense and +180% more regeneration starting from 40% defense**. So when someone asks "I have 40% defense, should I get 5% more or get some regen" we usually just say "go for the soft cap" because there's probably no way the alternative amount of regen they might be able to get could be comparable to what that level of defense equates to. But if someone offered me toggle instant healing instead of that last five points, I'm taking the regen. The "mythical models" actually do a great job of telling you which to go for most of the time, in that most people would tend to do what the models imply is the better choice.

Ask any SR (defensive) min/maxer, though, and they'll tell you that right after hitting the soft cap, the next thing they go for is health recovery: +regen bonuses or aid self or both. Because at the soft cap, regen bonuses that don't mean much to low mitigation characters mean everything to high ones. When I add a +10% regen bonus to my blaster, that increases recovery by about 30 health per minute. Interesting, but for the most part that is a downtime reducer, and allows me to move from spawn to spawn faster without starting ever lower in the hole. For my soft-capped SR, its not much more: about 35 health per minute. But because I have 90% damage mitigation most of the time, that allows me to erase the equivalent of about 350 points of incoming damage per minute. Per bonus. Five of them equal 1750 damage per minute of incoming damage I can recover from. That's a minion or two that get erased by those bonuses. On average. Because critters die (assuming you're trying to kill them), unless you are in a heavily AoE dominated setting, critters tend to be around attacking you only about half the time (think: start with five critters, then as you kill them that count drops to four, then three, then two...). Erasing two minions on average is actually like making three or four of them disappear in average combat. Just from those bonuses. Slotted health can make another five or six go away. The combination can make a whole even level Boss vanish when operating under soft cap conditions (assuming you're fighting more than one, and if you're driving a soft-capped scrapper, I'm guessing you are).

Basically, the OP seems to be arguing against a position no one takes. That fact is just hidden among some strange math.


** On the other hand, we are in a position to trade about 9% defense for 400% regen starting from 33%. That's basically the trade that Ninjitsu makes and it does fairly well with that trade. Fully slotted, reconstruction (Kuji-in Sha) is equivalent to about +400% regen, which compensates for a lot of defense. And you can still soft-cap Ninjitsu if you try hard enough.

I said that already Though you did say it with a tad more detail.

I read all this and can honestly say, this whole thing( the whole thread) made my head hurt. Honestly? WAY too much thought/maths involved in playing a game. But kudos anyway, it did give me some insight on defenses in the game. Now I'm gonna go take several shots of Jack until all the numbers swimming in my head go away :P

Well this has been a good thread to read. Great example of using technically sound math to describe an invalid real-world scenario.

Speaking of theoretical arguments, is defense always better than resistance? Is it true that 45% defense is better than as 90% resistance?

Given a finite number of HP, is it better to dodge 100% of incoming damage 95% of the time or is it better to take 10% of the damage 50% of the time?

My initial inclination is that 10% of "a lot" over a short period of time can still kill a player pretty fast. Faster than the RNG, anyway. I would think that the RNG would be even more punishing for a resistance user, especially when bosses come into play. Though this argument quickly sinks back into a theoretical debate over given enemies who deal arbitrary amounts of DPS and buffs/debuffs enemies may be affected by.

It's time for another "you're wrong" statement, so here it is for Arcanaville.

Quote:

But I would take +5% defense over just +50% regen, because the former doubles my survivability while the latter increases it by only 50% (or less, if I start with slotted Health). The break even point, if you have slotted health, is about +180% regen.

Wrong. Again, why people should not use %s like this. Which is also what this whole thread is about. Comparing on %s leads to bad maths.

+50% regen does not always equal +50% survivability.

Proof 1:

Case a.

DPS Faced: 300
Defence: 0%
Resistance: 0%
HP: 2000
Base Regen: 20

Damage Received: 130/second (300*0.5-20)

Time until Defeat: 15.38s

Case b.

DPS Faced: 300
Defence: 0%
Resistance: 0%
HP: 2000
Base Regen: 30 (20+50%)

Damage Received: 120/second (300*0.5-30)

Time until Defeat: 16.66s

% increase to survival = 16.66/15.38 = 8.32% increase for a 50% increase in regen.

Proof 2.

Case a.

DPS Faced: 300
Defence: 35%
Resistance: 0%
HP: 2000
Base Regen: 20

Damage Received: 25/second (300*0.15-20)

Time until Defeat: 80s

Case b.

DPS Faced: 300
Defence: 35%
Resistance: 0%
HP: 2000
Base Regen: 30 (20+50%)

Damage Received: 15/second (300*0.15-30)

Time until Defeat: 133.33s

% increase to survival = 133.33/80 = 66.66% increase for a 50% increase in regen.

If you up the starting Defence to 40%, you'll find that +50% regeneration in fact makes you invincible. That's surely more than a 50% boost to survivability.

However Arcanaville would tell us that it's a 50% (or less, if there's existing % increases to regeneration, such as health) boost. But, she is wrong. There is not a singular answer, only a range of possibilities. Like almost everyone that has posted in this thread, %'s are misunderstood and incorrectly applied. A % increase is a nice way to express a benefit of something, but it is almost entirely useless when making decisions between mutually exclusive options.

If you want to know how to compare between mutually exclusive choices, give up on %'s. Right now. You will NOT answer it correctly this way. You need to calculate how much mitigation it provides and choose the better. That answer will depend on what amount of damage you face.

As for other things:

Quote:

So as you stack defense on top of defense, each time you do the value of that defense increases, but the value of regeneration you're comparing to also increases in value in direct proportion, so they stay equal.

Try expanding out the formula for how long you survive. That is:

HP / (Damage - Mitigation) = t

You'll have an expression something like:

HP/((1-x)D - y) = t

Where x = mitigation through resistance/miss/defence, D is the maximum DPS, y = regeneration rate, t= time (survival). Clearly there is no x term next to y, or a D term... or anything else. It is trivial to say that overall survival improves when regen and defence improves, but regeneration itself is not being multiplied by defence. Also, try multiplying y by 1.5 and it should be immediately obvious that t is not going to automatically grow by 50% either (the original error above).

I think I might call it a day here. The fact that Arcanaville thinks +50% regen = +50% survival highlights to me what the first post is about. If you disagree, then so be it (but you're also wrong). When considering your options think in terms of actual changes in mitigation, not % increases to the various factors, else you will flat out get it wrong. Anyway, I won't be reading or responding any further, but do feel free to run amok if you want

Wow. Just wow.

I eagerly await a response to that.

Edit: I'll toss in my own.

Quote:

Originally Posted by BunnyAnomaly It is trivial to say that overall survival improves when regen and defence improves, but regeneration itself is not being multiplied by defence.

No one said it is. What was said is that the survival benefit of a given amount of regen is multiplied by (the mitigation of) defense.

Gaining defense (or DR) that reduces incoming DPS by a factor X has a mathematically identical impact on your time to defeat of having your HP and HP recovery rate multiplied rate by 1/X.

BunnyAnomaly, if absolutely everyone in the entire thread tells you you're misinterpreting what they're saying, don't you think it might be wise to consider even for a moment that they might be right? Because, once again, you've taken a explanation of the disagreement with your approach and interpreted it in a manner completely contrary to the intent.

For the bleeding-edge performance oriented characters here, they generally aren't going up against some static level of DPS and simply computing their survivability against it. That's just not the point. The question isn't "how long can I last against a certain level of DPS?" as you assumed in your last post, it's "what is the highest level of DPS I can survive long-term?" The players making use of these metrics are in the business of finding the absolute toughest things they can take on while still winning. If a character who can survive at most 300 DPS improves his survivability by adding more defense or regen, he's going to go out and *increase the DPS he faces* until he once again hits the limit of what he can survive. It's in *this sense* that adding 50% additional regen is a 50% boost in survivability, because it increases the maximum sustainable incoming DPS by 50% (assuming you are currently at base regen, as Arcanaville noted). Let me present a few numbers to explain this:

Base scrapper HP at level 50: 1338.6
Base scrapper regen:5.578 hp/s

The damage received will then be equal to (base incoming damage)*(.5 - defense). Assume that the scrapper will seek out the toughest enemies he can survive, so average long term damage taken is equal to regen. In that case, the maximum sustainable base incoming damage will be equal to (regen)/(0.5 - defense).

Assume 40% defense and base regen. In this case, the maximum sustainable average damage intake will be 5.578 / (0.5 - 0.4) = 55.78 dps. Any more, and the scrapper will eventually die as damage taken outpaces regen.

Imagine the scrapper increases his defense to 45%. Now, the maximum sustainable average damage intake will be 5.578 / (0.5 - 0.45) = 111.56 dps.

Now imagine the scrapper instead adds 50% bonus regen, for a regen rate of 8.367 hp/s. The maximum sustainable average damage intake will be 8.367 / (0.5 - 0.4) = 83.67 dps.

Initial maximum sustainable damage intake was 55.78 dps. Adding 5% extra defense increases this to 111.56, an increase of 100% over the initial value. Adding 50% regen instead of 5% defense changed this to 83.67, an improvement of 50% over the inital value. *This* is the sense in which adding 5% defense doubles your survivability and 50% regen increases it by 50% - adding 5% defense allows you to take twice as much incoming damage without dying, while adding 50% regen only allows you to take an extra 50% incoming damage.

The critical point you're missing is that, in general, nobody is interested in seeing what the effects are of incrementally improving your mitigation/regen against static amounts of DPS. You can calculate this all you like, mind, the problem is it's simply not relevant. A performance-oriented scrapper is almost always going to attempt to fight the most difficult enemies he can survive. If he can survive at most X DPS long-term and he then improves he survivability, he's not going to keep fighting things which do X dps. He's going to seek out tougher targets until he once again hits the limit of his survivability. If at 40% defense he can survive X DPS, going from 40% defense to 45% defense allows him to fight things which deal 2*X DPS, and that's what he's going to do. If he instead adds 50% regen to his 40% defense, he can now fight things which deal 1.5*X DPS, and *that's* what he will go do. Adding 5% defense allows him to fight things which are twice as nasty, while adding 50% regen only allows him to fight things which are 1.5 times as nasty.

*This* is why we say that the last 5% defense is a 100% boost in survivability, while 50% regen is only a 50% boost in survivability. To us, 'survivability' is 'what are the most dangerous possible things we can survive?' What you are doing is taking calculations that are based on *THIS* definition of survivability, changing the definition, and then claiming the calculations are wrong. They're not wrong, you are simply approaching the issue from a different set of assumptions. You can do that all you like, but it doesn't make what you are doing any more relevant to the issues we're actually talking about. Again, the problem is is *NOT* that Arcanaville, of all people, doesn't know what she's talking about, but that you are applying a different set of definitions and assumptions to the problem than everyone else is. You're arguing against a position that *nobody is actually taking*.

I applaud the time and effort you have obviously put into this, it raises some intresting questions.

:: Gets popcorn while awaiting for Arcana's return ::

You guys are still feeding the math troll?

2% sucks..... I like whole better

Epic troll thread. A+, would read again.