(Relative) Damage Reduction from Armor, explained. - Page 2

Mijae · 05/22/08, 12:27 PM

Originally Posted by TheSorcerer

No seriously, I believe you a stretching the discussion a bit. This Graph and Oaken's calrifications pritty much is what Mr Random GlassJoe wants to know. If you increase your armor by X you will live Y seconds longer, regardless of your current armor value. That's good. That's nice. That's it.

I believe discussion about frames of view or if relative returns or absolute returns are the numbers to look at, may be exciting for all the people involved, but honestly, will not provide is any further information.

The problem is you just interpreted the graph wrong. It does not tell you "increase your armor by X you will live Y seconds longer", it tells you "increase your armor by X you will live %Y seconds longer". Obviously, it's less clear than you thought. What you're looking for is actually the absolute difference, not the relative.

Changing your armor by 1K at a higher level is a lesser relative armor increase, so you expect the relative TTL to be smaller also. What I'd be interested to see graphed is relative TTL change / relative armor change.

Muphrid · 05/22/08, 3:33 PM

Originally Posted by TheSorcerer

I like armor.

No seriously, I believe you a stretching the discussion a bit. This Graph and Oaken's calrifications pritty much is what Mr Random GlassJoe wants to know. If you increase your armor by X you will live Y seconds longer, regardless of your current armor value. That's good. That's nice. That's it.

I believe discussion about frames of view or if relative returns or absolute returns are the numbers to look at, may be exciting for all the people involved, but honestly, will not provide is any further information.
And if it really is so unclear what a tank really wants to optimize for, then you should stop discussing how good armor is and start a topic on "Tanking: Optimizing for less damage, softer damage or getting cock gibbed?"

Living through to the next heal is all what it's about. That's what I needed to explain to my tanks aswell. As long as they can be healed through they actually don't want to take less damage - tanks want to get smacked and smacked hard for the sake of threat. Just not so hard, that healers cannot heal it anymore. That's all about it. I mean healer's will get bored if you go "dodge, parry, dodge, miss, dodge, parry" - but they will go "oh f*ck noeeeee!!11" if you then het "hit crush hit".

Which, btw, is another point for armor and against other evasion stats: armor softens the amount of damage you take, while evasion has a chance to remove damage completely which may decrease the amount of healing needed more than armor would, but will increase the chance of instagibs relative to armor - oh my, there's that bad word again...

I understand what you're talking about. As I've said, it depends heavily on the metric you're using, or what you're really trying to optimize as you gear. That said, it is my opinion that absolute/relative diminishing returns under a given metric mean very specific things that are not open to interpretation.

The problem is you just interpreted the graph wrong. It does not tell you "increase your armor by X you will live Y seconds longer", it tells you "increase your armor by X you will live %Y seconds longer". Obviously, it's less clear than you thought. What you're looking for is actually the absolute difference, not the relative.

Changing your armor by 1K at a higher level is a lesser relative armor increase, so you expect the relative TTL to be smaller also. What I'd be interested to see graphed is relative TTL change / relative armor change.

Yes, the graph tells you something that has meaning regardless of the incoming DPS against you. How many seconds longer you would actually live is very dependent on that (but not, in turn, dependent on armor).

Anyway, here's a graph that shows the relative increase when you increase one's armor by a percentage.

The curve is clearly increasing, showing increasing returns. It is for this reason I've argued against changing armor penetration to removing a percentage of armor. The percentages simply have a much more significant effect for higher armor values. Increasing armor by a percentage favors high armor, but decreasing armor by a percentage naturally favors cloth.

Mijae · 05/22/08, 4:12 PM

While this graph is also useful. I was thinking more like, at 10k armor a 1K increase is a 10% relative armor gain, but at 20k armor it is a 5% relative increase. So, how does this relative increase compare to the relative increase in TTL (using a constant armor change).

Not able to do all the math right now, but:

1K : 1K increase -> X% relative TTL / 100% relative armor
10K : 1K increase -> X% relative TTL / 10% relative armor
20K : 1k increase -> X% relative TTL / 5% relative armor

If the relative TTL at 20K armor is 50% less than at 10K armor, then the graph would be flat. Wouldn't this be a better metric for the relative value of a change in armor?

Muphrid · 05/22/08, 4:48 PM

Originally Posted by Mijae

While this graph is also useful. I was thinking more like, at 10k armor a 1K increase is a 10% relative armor gain, but at 20k armor it is a 5% relative increase. So, how does this relative increase compare to the relative increase in TTL (using a constant armor change).

Not able to do all the math right now, but:

1K : 1K increase -> X% relative TTL / 100% relative armor
10K : 1K increase -> X% relative TTL / 10% relative armor
20K : 1k increase -> X% relative TTL / 5% relative armor

If the relative TTL at 20K armor is 50% less than at 10K armor, then the graph would be flat. Wouldn't this be a better metric for the relative value of a change in armor?

You want to see relative TTL increase divided by relative armor increase for +1k armor?

Edit: I can do the calculation, but I don't think the metric makes sense or has meaning as long as 0 is a valid value for armor, even if it is an unlikely value.

Allev · 05/22/08, 5:07 PM

So, here's my problem with TTL calculations:

In reality, dodge, while not increasing the TTL in a worst-case, reduces the number of bad-cases. For instance, if worst-case is 2 consecutive hits, a 50% dodge tank gets a .5^2 chance of that happening, or 25% of the time, while a 40% dodge tank has worst-case occurring .6^2 or 36% of the time.

The real question when tanking Brutallus for instance is not whether your TTL or avoidance is high enough. TTL really doesn't reflect your chance of dying, which is the sum of (chance of dying to bad-case sequence * likelihood of bad-case sequence happening). TTL measures the chance of dying to a generic constant-damage-no-healing sequence.

The point of armor is that it gives both a mitigation benefit and a "TTL" benefit but doesn't affect the third dimension, which is chance-of-bad-case. Which can underrate avoidance and expertise (if applicable), and is at the heart of eliminating crits (and crushes), which is the first tank guideline

Edit: The relevance to this discussion is that while you can claim armor affects both TTL and overall mitigation, you can cite dodge's overall mitigation but don't get a feel for how much it affects the chances you'll need to rely on your TTL.

Muphrid · 05/22/08, 5:25 PM

It's sufficient to consider time-to-live as a probability distribution, and not as a single number. It has a mean--the average or expected TTL. It has a variance--variance that is based on how much of your average TTL is derived from avoidance, for instance. The as overall avoidance approaches 50%, variance increases. As it increases or decreases from 50%, variance decreases.

In visual terms, you can imagine a graph with a peak at your expected TTL that may be wide or narrow. Below some TTL, the tank dies. Avoidance both increases the average TTL (thus making deaths less likely) but, below 50% avoidance, it also widens the graph (making deaths slightly more likely--the net effect is still positive, it's just mitigated somewhat). Armor and stamina simply shift the graph by increasing TTL by a flat amount of time.

Muphrid · 05/22/08, 9:24 PM

As a note, increasing armor by a factor of 1+k increases TTL/eff. HP by a factor of $\frac{k}{1+\frac{v}{w}}$ , while Mijae's measure, if I read him correctly, generates the function $\frac{1}{1+\frac{v}{w}}$ .

Thus, they really say the same thing; the two measures are just proportional to one another, and both show increasing relative returns.

Iluminati · 05/22/08, 9:47 PM

tanks want to get smacked and smacked hard for the sake of threat.

Wrong. If you need rage turn around, don't gimp your gear. There is so much good threat gear (hit/expertise) out there that you should never, never, ever say "well I'm not getting hit enough so I better take off some dodge/parry/etc."

Mijae · 05/22/08, 10:06 PM

Originally Posted by Muphrid

You want to see relative TTL increase divided by relative armor increase for +1k armor?

Edit: I can do the calculation, but I don't think the metric makes sense or has meaning as long as 0 is a valid value for armor, even if it is an unlikely value.

I tried out some numbers and it turns out ∆ TTL % / ∆ A % = M ... I didn't try actually solving the function, but plugged some numbers in at different values. It just takes us in a big worthless circle. So yeah, nevermind.