Commander
Join Date: Jun 2012
Posts: 461
Diminishing Returns, Damage, and Damage Resistance
or,
Why power creep so heavily favors offense on ground.

Note: I'm posting this in the PVE forums because this affects all of us, PVEers and PVPers alike. The examples I use here are framed in the format of PvP. However, bear in mind: if you boost the offensive potential of the players, you have to boost the difficulty of PVE to compensate, or the game becomes too easy. So even if you have never shot at another player and never intend to, this affects YOU.
Here is how so called "diminishing returns" in damage resistance works in most games. STO's is slightly different, but close enough to describe with the same model, at least for small damage resistance numbers. It works like this: your numerical damage resistance value, times a scale factor, plus one, multiplied by your health, is the effective amount of damage somebody has to do to kill you. (STO actually follows a considerably less elegant equation, but to the first order approximation, this description holds. I will plot the difference between this approximation and STO's actual formula at the end of this post.)
Let's go over that again, as an equation.

  • Damage to Kill = K
  • Numerical Resistance (the sum of resistance granted by powers, armor, passives, etc) = R
  • Scale factor = s
  • Health = H

    So,
  • K = H(1+sR)


In STO, s approximates to 1/100, so the formula comes out to:
K = H(1+R/100)
Now, let's look at some numbers. Let's say you have 500 points of health and your enemy can do 500 points of damage.
  • If your resistance is 0, K = 500(1+0/100) = 500, so your enemy can kill you in one hit.
  • If your resistance is 100, K = 500(1+100/100) = 500(2) = 1000, so your enemy takes two hits to kill you. (Example: the kinetic resistance of high-level pollyalloy armor.)
  • If your resistance is 200, K = 500(1+200/100) = 500(3) = 1500, so your enemy takes three hits to kill you. (Example: the energy resistance of a character in full Omega armor using the Distortion Field mk12 and Engineering Proficiency.)
  • If your resistance is 300, K = 500(1+300/100) = 500(4) = 2000, so your enemy takes four hits to kill you. (Example: the energy resistance of a fully tanking Medic in full Omega armor using the Distortion Field mk12 and Engineering Proficiency).

Et cetera. Linearly increasing your damage resistance linearly increases the quantity of damage your enemy has to do to kill you. (At least in this first order approximation. More details on the difference between this approximation and the and reality are below.)

"But wait," you say, "on my character sheet, my percentile damage resistance increases by less and less as I increase my numerical resistance."

Let's look at those numbers again, but as percents.
  • If your resistance is 0, your enemy's 500 damage attack destroys your 500 health in one hit, killing you: 0%
  • If your resistance is 100, your enemy's 500 damage attack takes 2 hits to destroy your 500 health, which means your resistance is blocking 250 damage each shot. 250/500 = 50%
  • If your resistance is 200, your enemy's 500 damage attack takes 3 hits to destroy your 500 health, which means your resistance is blocking 333 damage per shot. 333/500 = 67%

So the first time you increased your resistance by 100, your percentile resistance went up by 50%, but the second time you increased it by 100 (from 100 to 200) it only went up 17%. (The actual numbers are close to this first-order approximation, but somewhat less, about 49% and 61% respectively at 100 and 200 damage resistance. See graphs below.)

If it increased by the same amount both times, then when you were at 200 numerical damage resistance, your percentile resistance would be 100%, and you would be completely indestructible: it would take an infinite number of hits to kill you.
SIDEBAR: This is observable on the ground engineer's shield tanking, where there are no diminishing returns and 100% resistance is achievable for a short time (although bleedthrough damage can still kill you even if your shields stay up, and the duration of the 100% resistance is relatively short - 3 seconds without Tactical Initiative, or about 21 seconds with a well-specced Tactical Initiative).
This, however, brings us to a problem. Let's suppose that Cryptic takes a piece of armor with 100 damage resistance, and a gun with 100 damage, and makes super versions of both of them. The armor will have 200 damage resistance, and the gun will have 200 damage. Sounds fair, right?

Wrong.

Before, each attack from the gun dealt 50 damage, because 100 damage resistance means 50% and 100*(1-50%) = 50. Now, each each attack from the new 200 damage gun does 66 damage, because 200 damage resistance means 67% and 200*(1-67%) = 66.

Or, considered as a number of hits to a kill: if you started out with an attack that could do 500 damage, and an enemy that could obtain 100 damage resistance, it took 2 hits to get the kill. But now, your weapon does 1000 damage and the enemy has 200 damage resistance, and it only takes 1.5 hits to kill them.

Does this sound problematic, yet?

It gets worse.

Suppose we have two different kits (for example: Fire Team and Medic). Suppose that one kit can increase your damage by 100%, the other can increase your resistance by 100. If we start out at 0 resistance, these are perfectly even: the first kit doubles the damage, the second kit halves the damage, and the total damage comes out the same. It doesn't matter how much we increase or decrease the weapon damage, the two kits will take the exact same number of hits to kill each other.

But now let's look at our weapons that do 100 and 200 damage, and our armors with 100 and 200 resistance. With the first set of weapons and armor, the two kits come out with 200 damage and 200 resistance, meaning that each hit from the attacker does 67 points of damage instead of the 50 points of damage that it would have done if neither character were using a kit.

But with the second set of weapons and armor, the attacker has 400 damage and the defender has 300 resistance. Now 100 points of damage come through. 100/67 = 150%. In this hypothetical scenario, by increasing armor and damage "equally", Cryptic has made the damage potential of the offensive kit 50% stronger than the damage mitigation potential of the defensive kit.

(In actual fact, it's more like 100% stronger, with 132 damage coming through, not 100. My approximation considerably overestimates percentile damage resistance at high resistance values. See the graphs below.)


This exact scenario is already happening, albeit not so blatantly as in this post. New weapons are coming out with more and better modifiers, and new passives and set bonuses grant additional bonuses to weapon damage, critical hit chance, and crit severity. Melee attacks (including Lunge) have recently received a major boost to both nominal and effective dps. At the same time, defensive abilities and items are improved... but the improvements are inevitably degraded by the constant march of diminishing returns. This is even further compounded by the fact that knockback severity scales with damage, meaning that boosting damage provides an unintentional buff to the knockback chance of high-damage classes and powers.

So what is the solution? Asking Cryptic to avoid power creep is a lost cause. Many players are interested in working towards the next best thing, and as they achieve it Cryptic needs to add a new next best thing to keep them interested, playing, and paying. And asking Cryptic to systematically buff defensive kits every time they add a new, more powerful item or passive, is a logistical and balance nightmare.

The fact of the matter is, I don't know what a true lasting solution is. I do know what one fantastic stopgap solution would be, however.

Going from Cryptic's current formula to the approximation I used would actually go a long way in the right direction. It would also reduce the processor load required to calculate the damage dealt, by going from Cryptic's second-power formula
y = 3(1/4 - (75/(150+x))^2)

to my first-power formula
y = 1-100/(100+x)

My formula and Cryptic's produce identical results at small values of resistance, and do not begin to diverge significantly until around 100 resistance, which is roughly the maximum resistance attainable through armor, skills, and passives, before adding powers into the mix. However, this would only slow the problem down, not solve it. Eventually, after enough power creep, we would be right back where we started, as the above examples show.

So what do you think? Would going to my formula help? What could we do for a lasting solution to this problem?

Please look at the following graphs. They will greatly help to get a mental picture of the math behind this post.
percentile resist vs numerical resist

number of hits needed to do face value attack damage


tl;dr: power creep, combined with the mechanics of diminishing returns on resistance, is slowly killing defensive kits and classes in favor of offensive kits and classes that scale with the attack power of the character's guns.

Last edited by guriphu; 01-17-2013 at 03:38 PM.
Captain
Join Date: Jun 2012
Posts: 993
# 2
01-17-2013, 04:01 PM
Reported for being awesome.

Seriously now, im seeing more and more buffs to the tactical officer and nothing for the other classes, is there a master evil plan to make the tactical the only playable class?
Division Hispana
www.divisionhispana.com
Captain
Join Date: Jul 2012
Posts: 2,248
# 3
01-17-2013, 06:24 PM
Two details you forgot about that actually make it worse.

1) Critical Hit Chance and Severity continue to increase
2) +% damage all multiply (in space at least) while +resist stack linearly. By that I mean if you activate power A that gives +50% damage and power B that gives +50% damage the base damage is not increased by 100%, instead by 125%. This applies to space abilities such as attack pattern alpha, omega, Epower to Weapon boost etc. I do not know if or how it applies on the ground.

But yes I have long complained about the needless complexity of how the resistance formula in this game works.
Commander
Join Date: Jun 2012
Posts: 461
# 4
01-17-2013, 07:24 PM
It's mixed on ground. Most powers boost damage multiplicatively, but at least one (Target Optics) stacks by addition. Note that resistance (at least on ground) actually stacks sublinearly for large resistance values, as my second graph illustrates.
Lt. Commander
Join Date: Jun 2012
Posts: 120
# 5
01-17-2013, 08:02 PM
Yeah, This is a MAJOR issue! I have mentioned it to a few people before. The base damage increase is linear but the same increase in resistance has to suffer under diminishing returns.

A good example is the Squad Leader kit. It use to be a vital kit, but with the high resistance values on armor, its boosts to resistance is dramatically reduced. His kit use to be responsible for massive percentage increases on your resistance. It no longer does the same percentage shifts. On the other end the general move from Mk XI to Mk XII has increased the base damage of the general weapons out there. With new modifiers, items, passives we are seeing an increase in the average damage, which is scaled by the base.
Captain
Join Date: Aug 2012
Posts: 3,553
# 6
01-17-2013, 09:31 PM
Can we have a tl:dr for those who don't feel like doing math outside of class?
It is said the best weapon is one that is never fired. I disagree. The best weapon is one you only have to fire... once.
Tired of Wasting EC and Time trying to get Superior Romulan Operative BOffs? Here's a cheap and easy way to get them, with an almost 100% chance of success.
Why the Devs can't make PvE content harder.
Commander
Join Date: Jun 2012
Posts: 461
# 7
01-17-2013, 10:01 PM
There is a tl;dr at the bottom of my opening post, just for you. I put it there before you asked for it because I'm a psychic.
Captain
Join Date: Aug 2012
Posts: 3,553
# 8
01-17-2013, 11:45 PM
Quote:
Originally Posted by guriphu View Post
There is a tl;dr at the bottom of my opening post, just for you. I put it there before you asked for it because I'm a psychic.
Aaaah, ok ty. And yes, you are correct with that assessment.
It is said the best weapon is one that is never fired. I disagree. The best weapon is one you only have to fire... once.
Tired of Wasting EC and Time trying to get Superior Romulan Operative BOffs? Here's a cheap and easy way to get them, with an almost 100% chance of success.
Why the Devs can't make PvE content harder.
Captain
Join Date: Aug 2012
Posts: 1,820
# 9
01-18-2013, 12:26 AM
I dont really understand all the OPs math its probably right on

What i do know is our fleet ground team now has finished the reputation system we all have from it what we want and we flat Faceroll the elite STFs now.

Getting the Opp is no problem with a noob/boob on the team

Elite STfs are easy and regulars a joke
Jellico....Engineer.....Stargazer KDF Tac
Saphire.. Science.....Ko'el Rom Kdf Tac
Leva........Tactical.....Mailu KDF Sci

JJ-Verse will never be Canon or considered Lore...It will always be JJ-Verse
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