Combat Ratings at level 85 (Cataclysm) - Page 8

Erdluf · 08/11/08, 4:22 PM

Originally Posted by Prinsesa

I did a comparison of the Savage Saronite set, which looks to be a "starter" set for 80 PvP on the same scale as the renamed HWL reputation sets for 70s:

8 piece Savage Saronite Set:
360 resilience rating (4.39% at level 80)

5/5 Brutal Gladiator Set + Guardian's Plate Belt/Boots/Bracers
192 resilience rating (4.87% at level 70)
What surprised me were how close the resilience percentages were, with a blue 80 set offering nearly as much reduction as the final 70 set of PvP gear. Am I missing something fundamental here regarding scaling?

It strikes me that they may want to get resilience requirements out of the way right off the bat and we'll instead see DPS increases over time instead of resilience.

Is it a case of Paladin Resil catching up with other classes? I've got mostly S1/S2 gear and am at 400 resil.

drumbum · 08/13/08, 2:11 PM

With regard to the recent discussion of "armor penetration rating", without knowing what Blizzard has in mind, I am curious to figure out what other people think the best result would be.

Basically, the current concerns with armor penetration are based on these issues:

1) Armor penetration is nonlinear with respect to itself. Each additional point of armor penetration is superior to the previous point. This potentially creates some undesirable balancing issues as armor penetration is stacked in large quantities. I believe most people agree that this is an undesirable effect and should be fixed.

2) Armor penetration is nonlinear with respect to the target's base armor. The more armor a target has, the weaker armor penetration is compared to alternative stats. This could be viewed either as undesirable or desirable.

My question stems from (2). I've crunched some numbers and it is actually fairly simple to create a formula for armor penetration rating that could EITHER make (1) linear and leave (2) nonlinear -- OR it could make both (1) and (2) linear at the same time.

The question is, which do you think would be a better situation? Would people rather see armor penetration rating effect all armor types equally? (Which, keep in mind, would make armor penetration rating effectively become synonymous with "increases physical damage by X%" with the exception that once a target is brought to zero armor, it would no longer have any effect.) Or would people prefer to leave the current system in tact, which potentially makes PVP somewhat more interesting (i.e., having to decide whether to use EA or not on a given target)? Would this even matter much in PVE where boss armors don't change very drastically?

Personally I think leaving the nonlinear effect of (2) in tact adds a certain element to the game that should be kept, but I'm trying to figure out if there are any good arguments for making (2) linear.

Roywyn · 08/13/08, 3:07 PM

Originally Posted by drumbum

1) Armor penetration is nonlinear with respect to itself. Each additional point of armor penetration is superior to the previous point. This potentially creates some undesirable balancing issues as armor penetration is stacked in large quantities. I believe most people agree that this is an undesirable effect and should be fixed.

2) Armor penetration is nonlinear with respect to the target's base armor. The more armor a target has, the weaker armor penetration is compared to alternative stats. This could be viewed either as undesirable or desirable.

...

Personally I think leaving the nonlinear effect of (2) in tact adds a certain element to the game that should be kept, but I'm trying to figure out if there are any good arguments for making (2) linear.

1) I think 1) being linear would be best, coming from a caster perspective.
Our DPS basically is (c1 + dmg)*(c2 + haste)*(c3 + crit).
If you have high dmg and no haste, you're more encoured to gem haste. If you have a lot of haste, you're more encouraged to gem dmg. If crit wouldn't be so expensive, it would make sense to gem crit if you have little of it.

This model works quite well for casters, and in BT/Hyjal they reach points where sometimes haste is better and sometimes dmg is better to gem.

I'd think that would be a working basis for melee/ARPen as well.

2) I'm leaning towards independence there, but I'm not sure.
What doesn't make sense right now is - the more armour a boss has, the less you want to gear/gem for ARPen.
It's just completetly counerintuitive.
If you make ARPen better the more armour a target has - then your debuffs (Sunder/FF/CoR) become weaker the better your gear is. And people would cry murder in PvP.

I don't really have a problem with that, but still. Easiest thing would be indepence of armour I think.
Simply because ARPen having differrent AP-equivalence values at different bosses/mobs is a bit annoying.

ARPen has a hard cap depending on boss armour, that gives you a limit how far you can stack it per boss, but further worrying shouldn't be needed.
100 ARPen (just a random number) rating increasing my DPS by 3% - regardless whether the boss has high or low armour - sounds like a fair deal. I just have to take note which bossed cap at say 80 ARPen.

• Aldriana · 08/13/08, 3:14 PM

To be honest, I'd be a bit surprised if ArPen rating changes anything in terms of the scaling of the ability; I suspect it primarily exists to prevent Blizzard from having to ridiculously scale opposing armor values to make ArPen devalue as much by 80 as the other stats do. If I had to guess, I suspect we're going to see a straight 1 point of rating = n points of armor reduction conversion, and it will continue to scale positively with itself. And frankly, I think that's fine - it adds richness to the itemization space. I think the only reason it's a concern at all right now is due to the ArPen gem, which makes it rather easier to stack the stat than it currently is - and there's nothing stopping Blizzard from simply removing that gem to fix the problem.

drumbum · 08/14/08, 1:10 AM

Like Roywyn mentioned, I suppose you could also invert the current behavior with respect to target armor value, and make it more potent against high armor targets than against low armor targets. I agree that this makes more sense, and perhaps would be more balanced in PVP. Right now, a fully PVP geared rogue can eat through a priest/lock/mage by taking him down to literally zero armor, and in the same gear feels like you are doing 1/3 as much damage against a heavy plate target. It just seems like it'd be extremely hard to balance melee damage with such a huge difference between armor classes.

This actually could be pretty easy -- for instance, if armor penetration rating simply subtracted the target's armor mitigation percentage by a flat amount.

Erdluf · 08/14/08, 8:54 AM

Originally Posted by drumbum

Like Roywyn mentioned, I suppose you could also invert the current behavior with respect to target armor value, and make it more potent against high armor targets than against low armor targets. I agree that this makes more sense, and perhaps would be more balanced in PVP. Right now, a fully PVP geared rogue can eat through a priest/lock/mage by taking him down to literally zero armor, and in the same gear feels like you are doing 1/3 as much damage against a heavy plate target. It just seems like it'd be extremely hard to balance melee damage with such a huge difference between armor classes.

I think rock/paper/scissors is an intentional part of the game. The intent (if not always the reallity) seems to be

Mage > Sword&Board > Rogue > Mage.

Armor penetration, in its current form, reinforces S&B > Rogue and Rogue > Mage. It goes against Mage > S&B, but not, I think, enough to matter.

Making penetration % based, would weaken S&B>Rogue, which may already be the weakest link in the rock/paper/scissors chain.

Whether or not r/p/s is a good thing is an entirely different debate. I do believe that setting up an equivalence system among 30 diverse specs is not worth the trouble.

drumbum · 08/14/08, 1:02 PM

Yeah, I'm not sure what I was thinking. There's no way an inverted behavior of armor penetration could be a good idea, as it punishes you for increasing your armor value -- something that is supposed to be a benefit. That's why I wanted to get some other people's input on it... I knew I wasn't wrapping my head around it just right.

Anyway, should they choose to make the stat scale in a linear manner, I think the following conversion rate would work as desired:

k = quantity of armor penetration rating
a = target's base armor
z = 10557.5 at level 70, ??? at level 80 (the changing variable in the armor formula)

armor removal = k*(a+z)/(k+a+z-1)

Basically what this does is leaves 1 armor penetration rating where it currently is -- removing exactly 1 armor from the base armor value. Additional armor penetration will simply provide increasing benefit as a multiple of the benefit gained from the first point of armor penetration rating. For example, if you have 4 armor penetration rating, it will remove enough armor to increase your damage by exactly 4 times what 1 armor penetration rating will add. This is actually VERY slightly less than 4 armor removal (at 3k armor at level 70, it's 3.999115), and if this was ever implemented, it would round back to 4 anyway.

However once you obtain larger amounts of armor penetration the difference becomes more significant. For example, with Serrated Blades and S3/S4 gear, I'm sitting around 1200 armor penetration. If I used this formula above, 1200 armor penetration rating would award about 1103 armor removal against a 3k armor target, while at the same time removing about 1134 armor from a 10k armor target. Even this difference is pretty small: the difference between 1200 and 1103 is only about 1% damage increase. So why go to all this trouble?

The real problem comes when you start getting close to reducing a target's armor to zero. For example, let's imagine 1200 armor penetration again, but also stacking with 3075 armor penetration from Improved EA. Let's also assume a 4500 armor target. This scenario is actually very close to what you might see in PVP currently (a 1200 ArP rogue with Imp EA on a priest, for example).

Current system: 4275 armor penetration = 4275 armor removal (5970 times as good as 1 armor removal, 39.6% damage increase)
My system: 4275 armor penetration rating = 3330 armor removal (4275.3 times as good as 1 armor removal, 28.4% damage increase)

Now all of the sudden we're talking about a whopping 11% damage difference. That's huge, and that's where I personally think armor penetration gets out of hand. It scales far too well as you approach bringing a target to zero armor. I personally feel that making this type of a change will help to balance this stat in PVP.

Muphrid · 08/14/08, 1:20 PM

As long as we're talking in a purely hypothetical sense, the easy solution to the armor penetration problem is to use an exponential curve.

That is, you start with the % DPS increase.

$1 + \Delta D / D = b^p$

Where...

$\begin{align} D & = \mbox{DPS} \\ \Delta D & = \mbox{change in DPS} \\ p & = \mbox{armor penetration} \\ b & = \mbox{arbitrary constant} \end{align}$

From here, the value of the exponential base can be tweaked as needed. There is no other way to make armor penetration be equally fair to both a high-armor physical DPS and a low-armor physical DPS.

This is the way it should be with all stats. The effect of a stat should be blind to the amount of stats the player or the target has.

• Aldriana · 08/14/08, 3:11 PM

First, there are plenty of other ways to be ArPen be equally fair to high-armor and low-armor opponents. Second, I don't think your proposal works, or, for that matter, even makes sense. Why should the damage you gain from ArPen scale exponentially with the amount you have? That would basically make armor penetration stacking even more stupidly powerful than it is right now. Exponential scaling is basically always a bad idea, which is why it doesn't currently appear anywhere in the game - hence I see no reason why it should start now, and particularly no reason why it would be considered an "easy solution" in this case.

Additionally, I disagree with your statement that it's desirable that the amount of benefit you gain from a stat should not depend on how much you, or they, have. This isn't true of any of a number of other stats (Hit and Expertise being the obvious examples, but it's fundamentally true of just about all of them), and frankly, I think the game would be really boring if the benefit of all stats was perfectly constant. I mean, if you're going to head in that direction, you might as well only have one stats - plus damage - and all your items would consist of "You do an extra n DPS". The fact that the stats scale differently with each other and are good under different circumstances is precisely what makes itemization so interesting.

Muphrid · 08/14/08, 3:40 PM

There are plenty of other ways to make penetration fair between high and low-armor targets? Fair enough. I ask you to name but one way.

In case you missed the memo, armor penetration as it is on live scales faster than exponential. This is easy to illustrate through the formulas:

$1 + \Delta W / W = \frac{1}{1+\frac{\Delta w}{w + w_0}}$

Where W is damage taken after armor, w the original armor, w_0 the armor constant. If we hold delta w fixed (at a negative value, for penetration) and vary original armor, this number clearly increases as armor decreases. An exponential scaling regime would keep 1+∆W/W fixed at a constant for any constant change in armor ∆w. That is, it would just be b^∆w.

It is desirable to keep the relative values of stats fixed and constant with respect to a metric (i.e. expected DPS) for the purposes of itemization, as this makes item budgeting considerably simpler. It also makes theorycrafting and class balancing simpler; once again, I challenge you to discover any other means to make armor penetration a "fair" stat across classes. Ultimately, the expectation of fairness compels us to ensure that item points themselves be "fair" and not favor any one class over another. How can we do this if the stats themselves are unfair? How can we do this if the relative values of stats varies across classes and across gear levels, meaning we can't predict with any generality how much class A gets from X item points compared to class B?

• Aldriana · 08/14/08, 4:29 PM

First off: you may want to lose the confrontational attitude. The purpose of these forums is discussion, not proving who is right and wrong.

So, lets see here. Ways to make armor penetration fair between high and low armor targets. Well, at the risk of sounding like an ass: having it do absolutely nothing at all would work. It's a *bad* way of achieving that balance, but you didn't assert that yours was the only *good* way - just the only way. And the point is, there are all sorts of funky things you can do to make it scale equally - which is best is a matter of opinion.

So, in terms of actually coming up with something a little more useful with the desired properties: we could set it up so "ArPen" no longer has anything to do with armor - each point of ArPen just gives you a flat .01% damage bonus. You have 600 ArPen? You do 6% more damage. The problem with this - which is also true of your suggestion - is that it doesn't really have anything to do with armor anymore, which strikes me as bad.

Hence, lets look at what the requirement you're imposing is actually saying. If we have a target with A_1 armor, and a target with A_2 armor, we want the percentage damage increase from p armor penetration rating to be the same. So, if p gives p_1 armor penetration at A_1 armor, and p_2 armor penetration at A_2 armor, and setting k = 10557.5 for simplicity, we have:

$\frac{\frac{k}{A_1-p_1+k}}{\frac{k}{A_1+k}}=\frac{\frac{k}{A_2-p_2+k}}{\frac{k}{A_2+k}}$

Simplifying, we have

$\frac{A_1+k}{A_1-p_1+k}=\frac{A_2+k}{A_2-p_2+k}$

And simplifying a bit more, we arrive at

$\frac{p_1}{p_2}=\frac{A_1+k}{A_2+k}$

So if we set $p_i=\frac{A_i+k}{k}p$ , it seems to me that would result in a perfectly flat ArPen rating/benefit curve.

Next up: regarding the current scaling of ArPen. Well, from a PvE perspective, the relevant quantity tends to be the absolute DPS gain, rather than the percentage gain, so lets look at that for a moment. Damage done is raw damage times mitigation; hence, the damage increase from a given amount of armor penetration is given by

$\Delta D = D\left(\frac{k}{k+A-p}-\frac{k}{k+A}\right)=\frac{Dp}{(A+k)(A+k-p)}$ , which scales only barely faster than linearly. And linear scaling is a whole heck of a lot slower than exponential scaling.

And, finally, regarding the overall question of scaling: simple doesn't always mean good. Again, it would be simplest to replace all existing DPS stats with a single stat that says "you do an extra n DPS". It's very simple, and it'd be trivial to balance - but it would also be really, *really*, boring. How to make ArPen a fair stat? Well, I dunno, it seems okay right now. Like, sure, it's bad for mages and warlocks, but from my experience it is a desirable and more-or-less balanced stat for rogues, hunters, DPS warriors, enhancement shaman, ret pallies, and ferals, which isn't too bad a start. And for that matter: why does it possibly matter if a stat is a little better for one class than for another? The classes are different - that's the whole point. Spell damage is terrible for rogues, and that's fine. Agility and hit are better for rogues than fury warriors, while Strength and crit are better for fury warriors than for rogues, and that's fine too. Each class has it's own mechanics, and each prefers different stats - and that's good, because it means we each want different items, rather than all wanting the same thing.

As for the rest: yes, having the value of stats change with gear level does make balance a little harder. Which is why there've been hundreds of hours on these forums discussing that very topic. There are numerous spreadsheets and calculators to track these exact sorts of variation. And yes, it would make our job simpler if all the stats were always perfectly linear in value - but I think it would also be very boring, and not nearly as much fun to play. The fact that different stats are good for different characters, and in different circumstances, and that there are tradeoffs between items that are good now and items that will be good later - is exactly what makes itemization interesting, and I wouldn't want to see that removed, myself.

drumbum · 08/14/08, 5:12 PM

Personally I think the largest issue with armor penetration is a PVP problem -- in that it's too powerful against low armor players. And it's something that I think affects rogues in particular, since they can achieve such absurd amounts of controlled armor penetration in a short amount of time (5cp Improved EA + Serrated Blades + S3/S4 gear can easily put you near 4300 armor penetration as I mentioned earlier, and none of these rely on procs). Warriors can stack pretty high as well, but requires a bit more effort for less overall armor penetration.

Since rogues can achieve such high armor penetration, their base damage has to be scaled down enough so that rogues aren't too overpowered against cloth classes when these effects are active (for example, see the nerf to Sinister Calling in the last patch). By nerfing armor penetration against cloth, you can increase the base damage the class deals without making them overpowered against cloth.

That said, if there are enough gem sockets available in PVE gear such that stacking armor penetration gems will allow players to bring bosses to very low armor values, it would have the exact same problem as I'm describing in PVP. Either way, I think it is in Blizzard's interest to linearize the stat.

Muphrid · 08/14/08, 6:41 PM

Aldriana: I'm not sure how relevant it is to look at p_i as you did. While knowing the effective armor decrease is relevant in comparing to the current system, in the end we're just going to bring it back to DPS anyway.

Furthermore, regarding the scaling of armor penetration, we can consider the ratio of the DPS function to some arbitrary function and look at the trend of this ratio as armor penetration increases (this is the idea behind big O notation, if you're familiar with that). Comparing live's DPS function to an exponential function, the ratio increases and trends toward infinity up until you hit 0 armor (and actually beyond, until A+k-p reaches 0).

We can prove this symbolically using Taylor series.

$\Delta D_{\mbox{live}} = \sum_{n=1}^{\infty} \frac{k}{a+k} \left (\frac{p}{a+k} \right)^n D$

Compare this to an exponential...(for this, I'm using the equivalent change in DPS expression that would result from an exponentially scaling armor penetration).

$D(b^p - 1) = \sum_{n=1}^{\infty} \frac{\left(p \ln{b}\right)^n}{n!}D$

Take the limit of the ratio...

$\lim_{p\rightarrow \infty} \left|\frac{\sum_{n=1}^{\infty} \frac{k}{a+k} \left (\frac{p}{a+k} \right)^n D}{\sum_{n=1}^{\infty} \frac{\left(p \ln{b}\right)^n}{n!}D}\right|$

We'll get something like...

$\lim_{p \rightarrow \infty} \left|\left(\frac{n!}{(a+k) \ln{b}}\right)^n\right|$

And the factorial's gonna win that round, meaning the limit as p goes to infinity is infinity, meaning that armor penetration on live already scales faster than exponential growth.

Now as far as itemization goes, I'm speaking from a very simple standpoint of cost/benefit ratios and the expectation of fairness. We've been talking about the expectation of fairness in this very thread: we don't want +50 armor penetration to advantage a warrior more than a rogue or vice versa. It only stands to reason that, ideally, we wouldn't want +50 itemization points to advantage a warrior more than a rogue, either, and while diversity and fun are good things we should always strive for, I'm of the opinion that balance--guaranteeing that balance can be achieved, at least on paper--must come first. I think balance is fun.

• Aldriana · 08/14/08, 7:02 PM

The problem is that looking at limits to infinity isn't honestly really very productive, as long before you get to the ultra-fast scaling portion of the curve, you hit the ArPen cap and stop going anywhere. So, the scaling as you go to infinity... doesn't really matter. What's relevant is the shape of the curve between 0 and the ArPen cap, and my impression (though this is hard to quantify) is that the current curve has a more smooth, even shape than an exponential, as we're far enough away from the vertical asymptote.

Regarding itemization: again, I think it's perfectly fine if warriors benefit more from armor penetration than rogues, as, again, rogues benefit more from agility than warriors, and both classes benefit a lot less from spell damage or +mp5 than do casters. Every class has it's own set of interesting stats, and that's fine.

Muphrid · 08/14/08, 7:41 PM

I'm not sure I follow what you mean. It's the whole curve (not just in the vicinity of the asymptote) that has faster-than-exponential growth. I mean, it would make sense to say that different areas of the curve have different properties if there were a discontinuity involved, but we're not going beyond that asymptote in practice anyway, and that's not what I was referring to.

Rather, let's build a simple two-stat scaling system. Something like...

$D = \left( \frac{1}{1+\frac{A-p}{k}} \right ) b^x D_0$

I hope you'll forgive me if I skip a little bit; I'll cut to the chase and note that, if we say ∆p penetration gives the same dps increase as ∆x exponential stat, then we're saying...

$\frac{1}{1-\frac{\Delta p}{A-p+k}} - 1 = b^{\Delta x}$

I'm going to solve for ∆x; this will tell us how much +∆p armor penetration is worth in terms of "exponential stat."

$\log_b \left (\frac{1}{1-\frac{\Delta p}{A-p+k}} - 1 \right ) = \Delta x$

Since x doesn't appear in this expression, we can conclude that increasing x, our exponential stat, has no effect on the equivalence. But, if we increase p, the value of ∆x will increase: that is, 1 armor penetration becomes worth more and more "exponential stat" as penetration is stacked.

Edit: of course, if armor penetration rating were to remove a percentage of armor, all these formulas get turned on their heads. Instead of armor favoring the high-armor class, it favors the low-armor class. Aldriana, you said you were comfortable with armor penetration being more beneficial for a warrior than a rogue. How, if at all, would your feelings change if this rating were to work as I've described? Is there an objective way to determine how armor penetration should work or what classes should be favored by a stat? Or is it sufficient to simply have some stats favor certain classes and let itemization drive the balance?