I will lead off this post by reproducing an article I wrote for a group of my friends who recognized the weakness of Defense in certain situations but had only a sketchy understanding of why. These friends all had mathematical training, but no real numerical intuition, so the article is unfortunately not targeted at those completely unschooled in statistics. It was also hastily converted from HTML using a 'sed' script. But I simply don't have the time to rewrite it. Anyway...
Damage Mitigation Strategies in City of Heroes
The Stress Test
There are four types of damage mitigation in City of Heroes: Resistence, Defense, Recovery, and Preemption.
Resistence is the ability to shrug off damage, it simply reduces the effects of being hit. Defense is the ability to avoid being hit. Recovery is the ability to heal or negate the adverse effects of a power (such as escaping from immobilization), and Preemption is the ability to keep an opponent from attacking at all. (NOTE: Because the term 'defense' has a very specific meaning in the game I will use it in that manner. Defense in more general terms will be termed 'damage mitigation'. With 'damage' meant to include being held, put to sleep, and other similar effects.)
The three basic tests of a damage mitigation strategy are how well it works on average, how well it works at its best (in case you feel like gambling), and most importantly, how well it works when things go wrong.
This last test is what I'm calling the "Stress Test". It is the ability of the damage mitigation strategy to bend without breaking. A failure here is basically a stress fracture of your armor, and may result in very bad things.
The course of events in City of Heroes can turn ugly for a number of reasons. Surprise is one reason things can go wrong. Drawing aggro from a second group by mistake, having a patrol wander into a fight, overlooking a particularly nasty member of the opposition, blundering into a group, or simply encountering an opponent that you know nothing about can lead to a real test of your damage mitigation abilities. All of the damage mitigation strategies except Preemption handle situations such as these fairly well. Recovery can shine here, while Resistence does its usual steady job (especially strong is the ability to resist holds and the like). Preemption isn't likely to happen here (exceptions are Preemptive toggles such as Ice Armor's Chilling Embrace, Dark Armor's Cloak of Fear, Radiation Emission's Choking Cloud, or perhaps Gravity
Control's Singularity.) Lastly, Defense can reduce a surprise situation to one of being lucky or unlucky. An example of getting lucky would be having an Aberrent Rector miss your Super Reflexes Scrapper, allowing her to put up Practiced Brawler instead of being put to sleep and having all her defensive toggles get turned off.
Simple luck is the most common reason that your damage mitigation ability will be stress tested. This plays a big role in the value of all types of damage mitigation except Resistence. A run of lucky hits can overwhelm a hero relying on Defense, or knock someone relying on Recovery down to the point where only the ultimate Recovery powers will work. And anyone who has fought Malta Sappers knows how bad things can get when your preemptive strike fails.
Expected Damage Taken and Its Variance
T Number of time periods considered
n Number of times attacked per period
p Probability of each attack hitting
d Damage each attack does
r Resistence to each attack
H Maximum healing rate
D Expected damage taken
Tnpd(1-r)
h Estimated effective healing rate
H(1-(1-p)^n)
i Estimated injury rate
Tnpd(1-r) - H(1-(1-p)^n)
sn Variance of hits taken Tnp(1-p)
dD Mean deviation of damage taken
sqrt(Tnp(1-p)/(Tnp)^2)
sqrt((1/p-1)/Tn)
cn Critical hit number; the number of hits that is
three standard deviations more than expected
Tnp + 3*sqrt(Tnp(1-p))
cD Critical damage amount; the amount of damage
one by cn hits
d(1-r)(Tnp + 3*sqrt(Tnp(1-p)))
ci Critical injury amount; the amount of injury
sustained by cn hits over time T
d(1-r)(Tnp + 3*sqrt(Tnp(1-p))) - HT(1-(1-p)^n)
Notes:
(1) All attacks are assumed to have the same chance of hitting.
(2) All attacks are assumed to do the same amount of damage.
(3) The resistence to all attacks is assumed to be the same.
(4) The damage rate is assumed to be higher than the healing rate.
All of these simplifying assumptions are generally untrue. This means that the variance of damage taken is really quite a bit higher in practice than is estimated here.
The Downfall of Defense
Defense is great, up to a point. Being able to avoid damage altogether is better than being able to absorb it. The problem arises when you simply can't avoid getting hit often enough any more. And this inevitably
happens in City of Heroes. No matter how good your defense is you will, at some point, find yourself up against opponents who are either so numerous or so skilled that they will hit you. For a Scrapper you can usually avoid drawing too much attention to yourself and supplement your Defense with Recovery (often through inspirations) or Preemption to handle this. But if you are a Tanker you will have problems dealing
with the ever increasing likelihood of being hit as you move up in level.
Looking at the equations for mean deviation of damage (dD) given above, you can see that as the chance of being hit (p) goes down, the mean deviation goes up. Hence, increasing Defense garners diminished returns in avoiding critical failure. Relying on good luck too much tends to lead to trouble in the end, no matter how lucky you are.
In short, Defense yields dimishing returns as the villains you fight go up in level and class (Lieutenants, Bosses, and Archvillains.) And there are some powers that hit you no matter how high your Defense is (e.g. Devoured Earth Swarms effectively ignore the defenses of an Ice Tanker and can do a surprising amount of damage as a result). Also, the best defenses (e.g. Phase Shift, Personal Force Field, Hibernate) render you unable to attack or do anything else but use whatever Recovery skills you have.
If you are going to rely on Defense as your primary formof damage mitigation you will either have to aggro fewer bad guys, villains who do less damage or are less likely to hit (i.e. are lower level), or heavily supplment your Defense with other forms of damage mitigation. Just try fighting Devoured Earth Guardians, The Envoy of Shadows, or the Devilfish with an Ice Tanker and you can quickly see the shortcomings of
Defense as a damage mitigation strategy. If you rely entirely on Defense, then you will often run an unacceptably high risk of a critical failure of your armor as you move up past level 30.
Bouncing Back (or Dead Men Eat No Insps)
Recovery takes many forms. The Regeneration Secondary for Scrappers and Empathy for Defenders are the best
Recovery sets. The biggest problem with Recovery for damage mitigation is that it can be overwhelmed by a
simple increase in the number of bad guys or their strength. As a primary damage mitigation strategy Recovery either needs some supplementation from other strategies or a degree of caution.
Some strategies aren't immediately recognizable as Recovery damage mitigation. One of these has been employed by every hero - run away and rest. A less extreme version is running to buy time to allow you to eat an inspiration, get healed by a teammate, or simply to allow your own healing abilities to bring you back to a safe level (the "Bouncing Baby Regen Scrapper" tactic.)
The ultimate Recovery powers are the self-ressurects. These include Rise of the Phoenix (available to Fire Tankers at level 32, and to Blasters with the Fire Mastery Epic Pool at level 47), Revive (Regeneration Scrappers can get this at level 35), and Soul Transfer (Dark Armor Scrappers have this available at level 38). But since these Recovers don't return the lost experience points to you (they should return at least 50%, in my opinion) they are poorly thought of by most heroes under level 50. In addition, Revive is hard to use if there are bad guys still around since you come back with no endurance, 50% health and no active damage mitigation running. Unless you have Moment of Glory ready to go Revive isn't much better than an Awaken.
Never Give a Sucker an Even Break
All Archetypes may Preempt an opponent. In fact Blasters have few other ways to mitigate damage until level 41. The best defense is to keep your opponent from being able to use an offensive power. However some Archetypes offer very few powers whose primary value is Preemption (Ice Armor's Chilling Embrace and Energy Absorption and Fiery Aura's Rise of the Phoenix are it for Tanker Primary pools).
Like a reliance on Defense, a reliance on Preemption is putting your trust in luck. Preemption works very well at its best, is pretty good on average, and can be disastrous when it fails.
All archetypes should use Preemption whenever they can, but it is most important for those not possessing any other form of damage mitigation. Even for those with good damage mitigation it offers a solid supplement, even if it does no more than buy time to use Recovery powers. For a Tanker, Preemption is just icing on the cake, or perhaps an Ice Patch at her feet.
Resistence is King
Resistence is the steady performer, always working as
advertised. There are no "armor piercing" attacks in the game. There probably should be, but there aren't. As is the only time Resistence fails the "Stress Test" is when a group of villains hit you with multiple holds or the like and overwhelm your "Mes Res". (NOTE: A form of "Armor Piercing" may be used in the Arena for Player-vs-Player, allowing a percentage of Blaster damage and Scrapper Critical Hits to bypass Resistence.)
The only way to beat a Resistence Tanker is to go around their Resistence (can you say "Psi Clocks"?) or to grind them down. And the latter takes time, which gives the Tanker a chance to supplement their Resistence with Recovery (Dull Pain, Healing Flames, Earth's Embrace) or Preemption defense (Hand Clap, Ice Patch, Clobber, or the like - or just plain dealing out damage and reducing the number of foes doing the grinding).
Resistence removes luck from the equation and buys time for a Tanker to use other damage mitigation strategies. In addition, it is usually the only way to avoid a true disaster such as being held.
One way of looking at Resistence is to consider it to be an increase in a hero's health and the amount of any heals he receives. If you have 50% Resistence to the attacks you are facing you effectively have not only twice as many hit points, but since you only took half as much damage, each heal is twice as good to you. An Invulnerability Tanker with the usual 95% Resistence effectively has 20 times as many hit points as a same level Ice Tanker. And in addition, his Dull Pain repairs the damage done by 20 times as many hits as
does the Ice Tanker's Hoarfrost. Yes, it truly is good to be King.
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The last point, that heals help Resistence tankers more than Defense tankers, is one commonly overlooked. And until I5, most buffs didn't help a tanker with near maximum Defense much either. So Resistence tankers benefitted more from Bubbles and the like as well (for example, and Icer might go from being hit 10% to just 5% while a Fire tank could go from being hit 30% to the same 5% with a Bubbler around).
What the high varience in the performance of Defense means is that for it to work as well in large teams at higher levels as other Tanker damage mitigation strategies do, it would have to be scaled up as the tanker levels. Otherwise it would be over-powered at lower levels where such things as DE Guardians, Crey Radiologist, DE Swarms, and Archvillains don't exist. The obvious way to do this is to move more of the damage mitigation ability to later powers.
Personally, I'd prefer to see Endurance Draining a foe actually mean something. That would make EA much better. As it is now, I recently drained a pair of Freak Tanks (conning orange) and they didn't suffer a single missed attack or lose a single defense. And in I5 a pair of orange conning bosses are quite dangerous. I suggest two changes:
1) EA should prevent END recovery for a short period of time as Short Circuit does.
2) Mobs who have no END should suffer a penalty to their damage mitigation. Since they are not getting their protection from toggles, I'd suggest a simple Defense debuff when they are out of END and having their resistence to Mez removed.
Next, to deal with autohit attacks, I'd make Slow effects reduce the tick rate (or if implementing that is too difficult, simply reduce the damage) of Auras in use by effected foes. This should include the damage done by foes such as DE Swarms.
Lastly, I'd make Permafrost worth having. The Slow Resist isn't enough to make this power even marginally worthwhile. Since Ice Tankers biggest problem is handling big hits I would make Permafrost give a permanent 10% HP boost. Perhaps even an enhanceable boost.
As for my I5 experiences with Ice Armor; much improved, but still more scrappy than tank-like. I did a L35 Invincible mission against Nemmies. Mobs were 37 and 38, conning orange to purple. I was able to collect several groups together and do OK against them. I had to use Hibernate too often. It's a nice power now, but taking a time out during a fight isn't likely to endear one to the team. IMO, at least Chilling Embrace (and it's punch-voke) should continue while Hibernate is on.
Once again, the testing has led me to conclude that many powers are simply not worth having any more in I5. Powers such as Icicles should be improved. I'd increase the aggro generation of damage auras.
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Kosmos
