Arcana's Guide to Defense version 1.2

Answering multiple requests, I've updated the Guide to Defense to version 1.2. There appears to have been a couple of minor changes to Defense since the last version of the guide

Here's a list of the major updates:

* Some improvements in the tohit formula explanations
* Specifics of the level scaler
* Specifics of the Streakbreaker
* I7 Defense Scaler
* Purple Patch discrepancies
* More accurate numbers for some things
* Some formatting changes and rearrangements
* Lots of minor fix up and confirmation changes

Of course, additional suggestions always welcome.

Defense in CoH


Defense, and its relationship to the basic tohit equations, is one of the least understood mechanisms in City of Heroes. This guide will try to explain Defense, how it functions, how it relates to tohit probabilities, and how it interacts with the other elements related to Defense in the game.


DEFINITIONS AND THE BASIC TOHIT EQUATIONS

The basic tohit formula

NetToHit = BaseToHit - Defense

where:

NetToHit: the probability that one thing will hit another thing with an attack. If net tohit is 45%, then 45% of the time when A attacks B, A will hit B.

BaseToHit: the probability, associated with the attacker that represents the base probability that attacker has of hitting any target in general, before buffs, debuffs, and defense are taken into acount.

Defense: the ability, or power, to reduce the chances of an attacker from hitting you. Defense is normally expressed in percentage points, and is the number of percentage points that the defensive ability will reduce your chances of being hit by an attacker.


The advanced tohit formula

The advanced tohit formula (my terminology - there isn't really a term for it) takes into account accuracy enhancements, tohit buffs, tohit debuffs, and defense debuffs. It is:

NetToHit = (BaseAcc + AccuBuffs - AccDebuffs) * [ BaseToHit + ToHitBuffs - ToHitDebuffs - (Defense - DefenseDebuffs) ]


Tohit buffs and defense debuffs

One way to improve your tohit chance is to use, or have cast upon you, tohit buffs. Tohit buffs are, according to the devs, additive:

BaseToHit + ToHitBuffs

So if your base tohit is 75%, and you use or receive a 60% tohit buff, your modified tohit becomes:

0.75 + 0.60 = 1.35 = 135%

Note that this is higher than 100%: see tohit floors and tohit ceilings below. Tohit buffs and tohit debuffs are subtractive from each other, as the advanced formula shows.


Defense debuffs are subtractive from defense: if you have 40% defense, and you are hit with a 10% defense debuff, your effective defense becomes: 40% - 10% = 30%.


Base Accuracy and Accuracy enhancements

Both inherent Accuracy bonuses and Accuracy enhancements are Accuracy Buffs. Accuracy Buffs work differently than tohit buffs. As shown in the formula, accuracy buffs take effect after defense, while tohit buffs take effect before defense. The difference is that tohit buffs are much more effective than accuracy enhancements when defense is high. If your tohit on a target is 30%, a 33% accuracy enhancement SO will boost that percentage to 40% (30% * 1.33) regardless of what the defense of the target was (as long as the net effect of base tohit and defense was 30%).

All attacks have what is referred to as "Base Accuracy" or sometimes just "accuracy." As defined by the devs, Base Accuracy is the "inherent accuracy" of an attack power. A "normal" attack has base accuracy of 1.0, or 100%. Attacks that are less accurate than normal have base accuracy values less than 1.0, and attacks that are more accurate than normal have base accuracy values more than 1.0.

Note on accuracy buffs and tohit buffs: it seems that the general rule is that anything that buffs (or debuffs) the accuracy of an individual power is an accuracy buff, while anything that buffs or debuffs the player - and all attacks he or she performs - is a tohit buff (or debuff).

I am currently unaware of anything that is an accuracy debuff (and not a tohit debuff) but I'm told that they theoretically exist in CoH. In practice, the term AccDebuffs is almost always zero.

"Base Accuracy" and "Base ToHit" is very frequently confused. Base ToHit represents the intrinsic accuracy of an attacker: its the chance that he or she will hit a target, in general, assuming all other factors are absent (defense, buffs, debuffs, etc). Base Accuracy represents the intrinsic accuracy of an attack relative to other attacks, and is scaled to 1.0: "normal" attacks have Base Accuracy of 1.0, which means they have no effect on the overall accuracy of the player. Attacks inherently more or less accurate have Base Accuracy values of more or less than 1.0, which increase or lower the overall accuracy of any attacker using them.

The best analogy to distinguish Base Accuracy and Base ToHit is to consider two people shooting firearms. One of those individuals might be inherently a better shot: he will have higher Base ToHit than the other. Separate from that, both of them will have different accuracies when firing snug nose revolvers and sniper rifles: the actual weapons have an intrinsic relative accuracy separate from the shooter, and thus the sniper rifle would have a higher Base Accuracy than the pistol.

(Player) Inherent Accuracy modifiers

Player attacks can have inherent accuracy-related modifiers, which potentially affect Defense sets in PvP.

Certain player attacks have certain inherent accuracy bonuses or deficits. All attacks within an offensive set that require a weapon draw (i.e. katana, assault rifle) are supposed to have an inherent tohit bonus, said to be about 5%. In addition, all snipe attacks also have a tohit bonus, in a similar range. AoE control based attacks have an accuracy penalty, but a recent post by geko stated that normal AoE attacks do not have an inherent accuracy penalty by default. The devs have stated that the archery attacks have an inherent tohit bonus higher than the standard weapon-draw bonus, but the precise bonus has not (to my knowledge) been determined.

At one time, attacks launched while flying had a significant accuracy penalty (said to be about a -50% tohit debuff). This penalty was replaced by travel power suppression when suppression was added to all travel powers.



Floors, ceilings, and caps

There is a maximum net tohit value and a minimum tohit value honored by the CoH game engine. No power or set of powers can drive your net tohit higher than 95% or lower than 5%. In other words, there is always at least a 5% chance of hitting anything, and always at least a 5% chance of missing something.

The 5% minimum chance to hit something is referred to as the tohit floor.
The 5% minimum chance to miss something, or alternatively the 95% maximum chance to hit something, is referred to as the tohit ceiling.

It used to be thought that there was no cap on the amount of defense that a hero could achieve. It turns out there is, but it is very high and not normally applicable to most reasonable combat situations: its in the range of 300% defense at high levels (it scales upward with increasing combat level of your hero).

The *true* tohit formula

Taking into account accuracy, defense, buffs, debuffs, and floors and ceilings, its this:

Bounded[ (BaseAcc + AccuBuffs - AccDebuffs) * Bounded[ (BaseToHit + ToHitBuffs - ToHitDebuffs + Defense - DefenseDebuffs) ] ]

Where Bounded[x] is the result of setting x to be 5% if x is lower than 5%, and 95% if x is higher than 95%. Notice that bounds checking is done twice: first after tohit and defense are combined (cf: the simplified tohit formula) and then again after accuracy buffs and debuffs are factored in.

(In excel terminology, Bounded(x) is MIN( MAX(x,0.05), 0.95) )


Rank and Level scaling, and the I7 Defense Scaling Update

Base tohit of villains

The base tohit of villains is as follows:

minions: 50%
LTs: 57.5%
Bosses, Snipers: 65%
Monsters, Giant Monsters, AVs, Controller Pets: 75%

These numbers are for even level villains: villains equal to your own combat level.

This increase in tohit based on the type of villain is sometimes referred to as the rank bonus or more colloquially "higher ranked villains have better tohit."


Tohit based on level

Villains of higher level than you gain tohit bonuses and become more accurate. Villains of lower level than you become less accurate. The numbers do not follow an exact scale, but have been determined by other players. It is a fairly reasonable estimate to assume that its 9% increase per level (i.e. 50% tohit at +0 becomes 50% * (1.09) = 54.5% at +1).

The actual numbers out to +4 appear to be:

+0 1.00000
+1 1.09400
+2 1.18670
+3 1.26670
+4 1.36000


Base tohit of heroes (players)

The base tohit of heroes in PvE is 75%. In PvP (arena combat and player vs player fights in PvP zones) base player tohit was recently reduced (in I6) to 50%. This improves the performance of defense sets in PvP combat substantially, although tohit buffs (being additive) are still a significant issue. Tohit buffs maybe also have been affected or reduced in I6, but this has not been confirmed. The devs have stated that high tohit buffs severely impacting defense sets is a problem they are working on a solution for.

Question: is this a "nerf?" Answer: no, its a proper balancing of defense sets. Defense sets performance were balanced against even level minions, which have a base 50% chance to hit. Furthermore, it is just as reasonable to view this as a +25% buff to player defense across the board, instead of a base -25% tohit chance.

[Note: as of 11/16/05 a patch note was added which specifically stated this exact thing.]


*** The I7 Defense Scaling Change ***

In I7, the tohit increases that higher rank and higher level villains currently get will be replaced with accuracy increases. This will act to make defense just as effective against higher ranked and higher level foes as even level minions - which is what defense is balanced around. Note: this does not mean higher rank or higher level foes will not hit any more often: they *will* hit more often, but in the same proportional way that they would hit players without any defense more often.

The rank and level accuracy buffs will be scaled in such a way so that the net tohit "works out" in such a way so that a player with no defense sees no change. How can that be done?

Basically (and the basics have been dev-confirmed) rank and level buffs will be converted this way (by example):

AV's currently are +25% tohit (75% instead of 50%) relative to minions. That will be converted to 50% higher tohit (75/50 = 1.5). That will be the new Accuracy Buff for AVs: 50%.

Note that in the simplified case, against no defense AVs used to have 75% tohit, and now they will have (1 + 0.5) * 50% = 75% - the same chance.

Level buffs will be scaled in a similar fashion: +9.4% (at +1) will be scaled to +9.4% accuracy buff instead.

Discussing all of the ramifications of the change is beyond the scope of this guide: there are discussion threads on the forums currently hashing out all of the ramifications. However, there are fundamentally only two real possibilities for how the change actually works.

Possibility #1: Tohit formula basically remains the same, but rank and level buffs get added to the AccBuff term.

Possibility #2: Tohit formula changed to be:

Bounded[ (BaseAcc + AccuBuffs - AccDebuffs) * (RankBuff) * (LevelBuff) * Bounded[ (BaseToHit + ToHitBuffs - ToHitDebuffs + Defense - DefenseDebuffs) ] ]

Note the position of the Rank and Level buffs. Possibility #2 is the tohit formula change that best represents *all* of the properties that the devs have stated for the change, but possibility #1 is numerically similar, and would be difficult to tell the difference in, except for extreme cases.

Note also that Statesman said this would work "up to +5." Its unclear if he was simply picking a number by way of example, or if the change would alter its behavior at +6 and higher. If the defense scaling change does break down at +6, the most likely way that will happen is that starting at +6, villains will begin to receive tohit increases again. It is *extremely unlikely* that at +6, villains will *suddenly* receive the +6 tohit buff; the change is likely to be less abrupt (but I have no information one way or the other).

Its important to note that the defense scaler does not affect tohit buffs in any way (directly). Tohit buffs are just as dangerous for defense sets as before. What the change does is remove the tohit increases from higher rank and higher level foes: anything that nevertheless still possesses high tohit buffs is still a major threat to defense.

Its also important to note that because it changes villain tohit/accuracy, the defense scaler does not affect player's ability to hit critters or other players, in any way.


DEFENSE MECHANICS

Typed Defense and Defense Stacking

Every attack power is classified based on how the attack is delivered, and based on the type of damage it delivers, and every defense power has an associated type or types that represents what types of attacks that defense power is effective against. There are two basic classes of attack types, and many subclasses.

Positional, or attack vector classes

Every attack is classified as either a melee attack, a ranged attack, or an AoE (area of effect) attack. In general, melee attacks are attacks that are limited to melee range (typically 5 to 10 feet maximum). Ranged attacks are attacks that will work to larger ranges. AoE attacks are defined as attacks that affect multiple targets (AoE attacks are typically defined as either cones or (general)AoEs, but that is not generally important to the issue of defense). All attacks in CoH are classified as exactly one of these types: no more and no less (although there is a special case that muddies this a bit: autohitting attacks - see below).

There is a special case issue that comes up with these basic definitions: melee cones and PBAoEs (point-blank area of effect attacks). It seems that in general, melee cones and many PBAoEs are generally considered melee attacks, but other PBAoEs (i.e. PBAoEs of giant monsters) are considered AoE attacks. There is apparently no sure-fire rule guaranteed to predict what a melee-ranged AoE will be classified as, although if its net range is less than 10 feet, it is very likely to be classified as a melee attack for the purposes of defense.

Damage-type classes

Every attack has one or more (usually no more than two) components of damage: each component has a particular type of damage associated with it. The damage types in CoH are:

smashing, lethal, fire, cold, energy, negative energy, toxic, psionic, and untyped

An attack can be all of one type: electric attacks are generally all energy damage. An attack can have multiple damage components: most energy blast attacks have smashing damage and energy damage.

Damage-types are often thought of as coming in pairs: smash/lethal (physical damage), fire/cold (elemental damage), and energy/negative (energy damage), because damage resistances are often organized that way. Toxic and psi are both considered special cases (see the special note on toxic defense below).

*** SPECIAL NOTE ON TOXIC DEFENSE ***

If a power is listed as defense to All but psi, then (as of this writing) that does not include toxic. The explanation is long and historical, but there is no toxic-specific defense in CoH. This does not mean that no power provides such defense, but rather that no such defense can exist due to a complication in how defense was originally designed. If a power is listed as "melee defense" this implicitly works against all melee attacks, even ones with toxic damage, but a power listed as "all damage types" does not include toxic.

Untyped is another special case: there used to be a significant amount of "untyped" damage in City of Heroes, most of which eventually became toxic damage. The main source of untyped damage left in CoH is the damage dealt by Hamidon, and the Hamidon Mitochondria. Its unclear precisely how untyped damage works, and its still heavily debated - the debate is mostly moot given the fact that it now mainly exists only as a singular special case that makes it difficult to generalize. We'll ignore untyped damage in this guide unless specifically mentioned.

Defense types

Just as every attack is classified as melee, ranged, or AoE, and also, smashing, lethal, etc, each defense power is classified based on what type(s) of attacks the defense power is effective against. In City of Heroes, nearly all defense powers are either attack-vector typed (also referred to as positionally typed, or ranged-typed), or damage-typed, but not both. Thus, a particular defense power might be effective against melee, or melee and ranged, but not melee and fire, for example. The one exception appears to be Force Field bubbles, and these were recently changed to provide multiply-typed defense (damage typed and also vector typed).

For more information on the specifics of defense within particular power sets, see the section DEFENSE IN POWER SETS below.

Defense Stacking Rules

If you have multiple defenses running (either your own powers or defense buffs cast on you by other players), certain defenses stack. Defense in CoH stacks additively, which is to say, if you have Defense A, and Defense B, and they stack, your net defense is A+B.

Which defenses stack and which do not is slightly tricky. Fundamentally, the following is true:

* All defenses of exactly the same class stack (melee stacks with melee, fire with fire, etc).
* A single defense that protects against multiple classes of attack functions like multiple defenses, each of which protects against a single one.
* You are only allowed to use the best defense you have against an attack with multiple classes.

For example, if you are attacked with a power bolt (from the energy blast set), that attack is ranged, and has smashing and energy damage associated with it. You are only allowed to use the best of your net ranged defense, your net smashing defense, or your net energy defense.

There was an issue a while ago in which the game engine was considering, say, someone with smashing defense and energy defense to get smash+energy defense against energy attacks with both smashing and energy components. This was considered a bug by the devs and corrected.

Defense enhancements

Each defensive power can be enhanced using defense enhancements. Defense enhancements (along with resistance enhancements) are one of the few enhancements that do not follow the general 8.33%/16.7%/33.3% TO/DO/SO (training, dual origin, single origin) enhancement progression. Defense enhancements are worth 5% for training, 10% for dual origin, and 20% for single origin enhancements.

The way enhancements work in defense powers (and in powers in general) is that the power has a base defensive value. Enhancements increase that value by a percentage amount equal to their value. To be precise: if a defense power's base value is +5% defense, and an (even level) defense SO is slotted into it, the defense power's new enhanced value is 5% * (1 + 0.2) = 6%: the power is increased in value by 20% (and not 20 percentage points, which would be 5% + 20% = 25%).

Defense enhancements themselves vary in strength based on your hero's level relative to the enhancement: enhancements are 10% weaker than their base value for every level lower than your combat level they are, up to three levels lower, where they are 70% of effective strength (they are worthless if you are more than three levels higher). Conversely, they are 5% stronger for each level higher than your level they are, up to 15% stronger when they are three levels higher than you are (enhancements more than three levels higher than your character's level cannot be slotted). For example, a -2 defense SO (normally +20%) is +16% (20% * 0.8) while a +3 defense SO is +23% (20% * 1.15).


Inspirations

Luck inspirations appear to be +Defense to all, and additively stack with any other defense powers you might be running. This has not, to my knowledge, been conclusively tested, but appears to be either explicitly true, or very near true.

Insights, it has been confirmed, work like tohit buffs: they are exactly the opposite of lucks in effect.


***Enhancement Diversification***

New to I6 is a change in how enhancements work called "enhancement diversification." Basically, it works like this for defense SOs: however you slot, and whatever you slot, you get the first 40% benefit (i.e. 2 even level SOs) at full strength, any benefit above 40% and below 60% at 0.85 (85%) of their value, and any benefit above 60% at only 0.15 (15%) of their value.

This is tricky, so an example should help illustrate what's going on. You slot (presume even level SOs) one defense SO. Defense SOs provide 20% benefit, so you get 20% bonus to the defense power you slotted it in. The second SO adds 20%: you now have 40%. The next SO provides benefit above 40% (and below 60%), and so you get 85% of its value. 85% of 20% is 17% (0.85 * 20%). So SO #3 adds 17%, not 20%, and your net benefit is now 57%, not 60%. The fourth SO you slot is providing benefit above 60% (note, this is calculated based on the raw values of the SOs, not the reduced value). So you only get 0.15 (15%) of its value. 15% of 20% is 3%. So you now have 60% total benefit, instead of 80%. The fifth and sixth SOs would similarly provide 15% of the SO strength, so SO #5 brings you to 63%, and #6 brings you to 66%.

Notice the extremely sharp cut off in benefit after enhancement #3. The basic rule on ED is: do not slot more than three SOs *worth* of enhancements. Its based on *benefit* and not on the little round thing you slot. So if you slot three SOs, and then one DO, the DO gets hit by ED. If you slot 3 HOs (Hamidon enhancements) of */*/defense and then an SO of defense, the SO gets hit by ED, even though "I didn't slot more than three of anything."

What matters is *benefit* - you simply aren't going to get much more than 3 SOs *worth* of benefit on anything, no matter what crazy combination of enhancements you try to use to dodge it.

Other enhancements, such as accuracy and damage, follow a different, but proportional scale (i.e. 3 SOs worth is where ED kicks in, even though 3 SOs of damage is about +100%, and not +60%).

I6 introduces something else: you can now tell *exactly* how much benefit your powers are getting from enhancements, by hovering your mouse cursor over the blue bar of the power in the enhancement screen. Also, you can "hover" (without dropping) an enhancement over a slot, and see in a popup window what the net overall change to the attributes will be if you chose to slot there.

One final note on I6 change to enhancements: tohit buff enhancements were originally schedule A enhancements (i.e. one even SO was worth +33% buff). They are now schedule B enhancements (i.e. one even SO is worth +20% buff) just like defense enhancements are.


Resistance to defense debuffs

As of the writing of this guide, supposedly resistance to defense debuffs have been added to hero and villain sets. The powers themselves now state that they include such resistance in the in-game power descriptions. Castle posted that to the best of his knowledge, the debuff resistance is in. However, careful testing has not demonstrated conclusively that they are working properly, and several tests appear to suggest that it isn't working correctly, or is working at a much lower level than originally specified. The thread where the concept of resistance to defense debuffs was originally put forth by Statesman is here. Castle has also stated that the mechanism might not be as simple as we were lead to believe: sometimes the resistance reduces the duration of the debuff, and sometimes the magnitude (but most of the time, the magnitude - see this post for more info. I believe the jury is still out on whether or not this effect is really working properly.


THINGS RELATED TO DEFENSE

What is mez defense?

"Mez defense" is the generic term sometimes used to refer to powers that protect against mez. (Using terminology originally used by geko when explaining mez) there are two types of mez "defense" :mez protection and mez resistance. Neither of these is directly related to Defense in terms of damage mitigation, but its worth reviewing.

The basics of mez are: everyone has a threshold that mez effects must break through in order for the mez effect to take hold. Without any mez defense, everyone has a base mez level of -1. All mez powers have a mez magnitude. When a mez power lands, it adds its magnitude to your mez level. A hero with mez level of -1 that gets hit by a magnitude 3 hold has mez level of 2 (-1 + 3). Any mez level higher than zero means the target is mezzed. Mez protection continuously subtracts its associated defense magnitude from your mez level while the power is running. Someone running a mez defense power with mez protection magnitude 10 has a mez level of -11 (-1 - 10). If hit with a mag 3 hold, mez level increases to -8 (-11 + 3). It would take 3 more such holds for the mez level to reach +1.

Mez effects last for a certain period of time, then expire. Mez resistance allows a target to shake off mez effects faster. So instead of a mez effect lasting ten seconds, it might last eight.

Mez protection and mez resistance are not true Defense or Resistance, but its useful to understand and is often confused with true Defense and Resistance.

All mez protection powers in melee defense sets scale up with level, with tankers getting maximum protection at level 35, and scrappers at level 45.

*** Note: in I6 mez protection powers were reduced from their previous levels. Maximum protection for tanks and scrappers used to be about magnitude 15, which in effect means controllers needed 6 holds to break protection. In I6, this has been tested to happen at 3 or 4 holds, which implies mez protection has been roughly cut in half.



DEFENSE, ACCURACY, AND VILLAINS

Some villains possess tohit buffs (either inherent ones, like those attributed to rank and level, or power-based ones, like Behemoths that use invincibility), and some behave like their attacks are slotted with accuracy enhancements. Rularuu Watchers appear to have significantly higher than normal base tohit (the precise value is unknown to me). Malta gunslingers have an accuracy buff instead of a tohit buff on their pistol's cone attack. Its been approximately measured as about +65% - comparable to two accuracy SOs of accuracy boost.

Also interesting: Paragon Protectors that use MoG have *massively* higher defense than the ones that (apparently) use Elude. Its unclear precisely why the large difference exists.

Villains seem, over time, to be acquiring defense powers and abilities. That could be a large source of people believing that "accuracy" has been reduced, when accuracy is unchanged, but the defensive capabilities of the villains has improved.


DEFENSE IN POWER SETS

Its important to note that the information related to Defense in the printed manuals is, as with all things, both dated and often inaccurate. Again: this guide is not focused on the numbers, but as this information appears to be difficult to find, power set-specific Defense issues (especially what stacks with what) are listed here. Note: just as the manual is out of date, so to this guide might be out of date at the time its read. Force Fields, for example, had positional defense added literally a few weeks before this guide was finalized. For specific details, numbers, and other set information, consult the links provided at the end of this guide.

Super Reflexes defenses (scrapper and stalker) are all positional or ranged-typed. Every SR defense power is effective against one attack vector only: melee (Focused Fighting, Dodge), ranged (Focused Senses, agile), or AoE (lucky, Evasion). The exception is Elude, which is effective against all vectors. Because SR defenses are typed with positional types, SR defenses do not stack with any defense claiming to defend against a particular damage type or types. However, SR defenses do work against attacks that do toxic damage, because positional defenses work against all attacks within their range band, irrespective of damage type. SR defenses also stack with all power pool defenses, because all power pool defenses are melee/ranged (and therefore positional). However, SR defenses do not appear to stack with defense buffs such as fortitude (which appears to be damage-typed), and until recently they did not stack with force field bubbles (FF was recently changed to add positional typing on top of damage-typing to address this).

Ice Defenses are all damage-typed. Ice defense powers are generally typed against two damage types (as is generally true for many damage-typed resistances). Ice Defenses do not stack with power pool defenses, because all power pool defenses are positional, and not damage-typed. However, Ice defenses do work on any attack that has a component of damage within the defensive scope. For example, Frozen Armor provides smashing/lethal defense. Glacial Armor provides energy/negative defense. If attacked with an energy blast attack that does smash/energy, both defenses potentially apply. As with all damage-typed defenses that overlap, Ice tanks will always use the greater of the two - they do not stack together. Ice has one of only two "scalable" defenses in the game: energy absorption is a click power that boosts Ice tanker defenses based on the number of villains it hits with a PBAoE "attack." For more information, consult the links at the bottom of this guide.

Granite Armor has a power that functions differently from the printed manual. Rock Armor provides Defense, not Resistance. Granite Armor has four defense powers. Three are stackable defenses (in the sense that they can be run simultaneously - they do not stack defensively with each other): Rock Armor (smash/lethal), Crystal Armor (energy/negative), and Mineral Armor (psionic). One cannot be used with the others: Granite Armor, which has defense to all but psi (as well as resistance to all but psi). Granite Armors, like Ice Armors, do not stack with power pools (which are melee/ranged).

Force Fields used to be damage-typed. They are now both damage-typed and positional typed. Specifically, Deflection Field provides both smash/lethal defense, and melee defense. Insulation Field provides both fire/cold/energy/negative (energy/elemental) and ranged defense. Dispersion Bubble provides both defense to all damage types except psi (and of course, toxic - toxic-typed specific defense does not exist) and AoE defense. This means Force Fields will stack with anything (specifically, the right bubble will stack with any conceivable defense). It also means - although I have not specifically tested this - that Force Fields now implicitly protect against toxic attacks (since Deflection Field *should* protect against melee-based toxic, Insulation Field should protect against ranged toxic, and Dispersion Bubble should protect against AoE toxic attacks - which are essentially all of them).

Of particular interest to Force Field defenders and controllers is the fact that there are unusal side-effects due to the (new) way the various bubbles' defenses stack. In particular, dispersion bubble stacks with deflection shield by smash/lethal typing only and dispersion bubble stacks with insulation shield by energy/elemental only. This means if the FF defender or controller takes another defense buffing aura power - specifically maneuvers - that stacks positionally, instead of damage-typed, dispersion bubble and maneuvers won't stack with each other, even though each will stack with the smaller bubbles.

The net result is that because dispersion bubble is likely to be stronger than maneuvers, the net effect is for maneuvers to have no effect on team mates within the range of dispersion bubble (except for toxic/psi attacks, since dispersion bubble does not offer either toxic or psi defense specifically by type).

Invulnerability has two defense powers: invincibility and tough hide. It now appears (as of this writing) that invincibility (and tough hide) both provide defense to all (damage types) but psi (and not melee/ranged). At one time invincibility was thought to provide melee/ranged defense (and its possible it did, and that was changed recently). Invincibility is the other scalable defense that exists in CoH (the other being energy absorption). Invincibility, unlike EA, is a PBAoE aura that continuously surrounds the hero while its on, and buffs the defense of the hero using it based on the number of attackers that are in melee range. Its actual internal workings are quite complex and still subject to active discussion. Tough Hide is also defense to all but psi. Interestingly, Invulnerability also has a self defense debuff. Unyielding (the power originally called Unyielding Stance) originally rooted you to the ground when activated. It now has a self defense debuff, of about -5%. This defense debuff appears to be a -DEF to all attacks, but I do not know if this has been carefully tested.


Stalkers

All stalkers have a power called hide. Hide appears to offer defense to melee/ranged/AoE. The defense appears to be about 5% to melee/ranged, and 37.5% to AoE (that's not a misprint: thirty seven point five percent) when hidden, and about 2.5% to melee/ranged/AoE when hide is suppressed (the 5%/2.5% number is one of the numbers I've seen: there have been lots of other numbers quoted, from 5%/2.5% up to 7.5%/3.75%. I cannot say with certainty what the precise value is. The 37.5% AoE defense, however, has been red name confirmed directly). Hide also provides the highest -perception (i.e. stealth) of any power, and while hidden stalker attacks critical (double damage) and assassin's strike powers do six times bonus critical damage.

The Ninjitsu stalker set has positional defenses similar to SR. Ninja Reflexes is similar to Focused Fighting (melee), and Danger Sense is similar to Focused Senses, but it has both ranged and AoE defense.

The Energy Aura stalker set has damage-typed defenses. Supposedly, the energy aura version of hide offers defense to all but psi, instead of the positional hide everyone else has, but I haven't confirmed that yet (if energy aura has the same hide as everyone else does, it wouldn't stack with its own defenses because hide would be positional, and energy's defenses would be damage-typed). Kinetic Shield offers defense to smashing, lethal, and (to a lesser extent) energy. Power Shield offers defense to fire, cold, energy, and negative. Overload offers defense to all damage types except psi (remember, "all but psi" excludes toxic) [note: Overload also has a dull pain component].



*** New for I5/I6 ***
Power Pool defenses are now supposed to offer defense to all, to guarantee that they stack appropriately with any defense that might be possessed by a hero/villain from their primary and secondary sets. This change was made to ensure that power pool defenses did not discriminate for or against any particular defense sets. Originally, most power pool defenses offered melee/ranged defense, and for a short while power pools offered melee/ranged and smash/lethal to try to address some stacking issues. They were changed to defense to all when it became clear that limited typing was not going to fully address the stacking issues, and was going to make stacking highly complex.

Power pool powers with defense components:

Concealment/Stealth
Concealment/Grant Invisibility
Concealment/Invisibility
Fighting/Weave
Flight/Hover
Leadership/Maneuvers
Leadership/Vengeance
Leaping/Combat Jumping



What other powers provide defense?

The following additional powers provide defense:

Devices/Cloaking Device (melee/ranged)
Illusion Control/Superior Invisibility (melee/ranged)
Illusion Control/Group Invisbility (melee/ranged)
Dark Miasma/Shadow Fall (melee/ranged)
Empathy/Fortitude (apparently all damage types)
Storm Summoning/Steamy Mist (melee/ranged)
Dark Armor/Cloak of Darkness (melee/ranged)
Regeneration/MoG (all but psi)
Cold Mastery/Frozen Armor (smash/lethal) [note: this power also has cold resistance]
Force Mastery/Personal Force Field (base defense)
Warshade/Shadow Cloak (melee/ranged ?)
Katana/Divine Avalanche (melee/lethal)
Broadsword/Parry (melee/lethal)

Note: Hasten used to have defense; it was removed in I5


Special Note on Stealth

Stealth powers generally break their concealment component when you either attack or are attacked. When the stealth is broken, most stealth powers that have a defense buff component will have about half their defense also suppressed while the stealth component is broken.

The following stealth powers appear to suppress a portion of their defense when the stealth is broken:

Devices/Cloaking Device
Illusion Control/Superior Invisibility
Illusion Control/Group Invisbility
Ice Control/Arctic Air
Concealment/Stealth
Concealment/Grant Invisibility
Concealment/Invisibility


According to Statesman, stealth powers in "Primary Defensive Sets" do not suppress their stealth when concealment is broken. The following stealth powers appear to not suppress any of their defense even if concealment is broken.

Dark Miasma/Shadow Fall
Storm Summoning/Steamy Mist
Dark Armor/Cloak of Darkness
Warshade/Shadow Cloak


Special Note on Power Boost

The power Power Boost (both the blaster energy manipulation version, and the epic power pool version) boosts defense powers while power boost is active. The boost is equal to the base value of the defense power being boosted. For example, if you have hover running (2.5% defense) and you trigger power boost, hover gains 2.5% additional defense. If hover was 5-slotted with defense SOs (net 5% defense) the boost would still be 2.5% (to 7.5% total defense).


What is the Streak Breaker?

The streak breaker is a bit of code within the tohit calculator that is designed to prevent very long strings of misses. There is a lot of misunderstanding about how the streak breaker works, so I'm going to be very specific in terms of detailing how I know what I know about the streak breaker.

First, the streak breaker only breaks streaks of misses, not hits. Confirmed by my own testing, dev postings, and red name PMs.

Second, the streak breaker affects both heroes and villains. Confirmed by my own testing, dev postings, and red name PMs.

Third, the streak breaker "decides" to break a string of misses when the string of misses exceeds a particular value. That value is dependent on the tohit probability between the attacker and the target. Here is Weirdbeard's specific statements on how the streakbreaker works:

[ QUOTE ]

Final to-hit : misses allowed
>.9 : 1
.8-.9 : 2
.6-.8 : 3
.4-.6 : 4
.3-.4 : 6
.2-.3 : 8
0 -.2 : 100

Auto-hit powers are not included in the system.

Critters get the benefits of the system as well.

The system does not track each power individually; instead it tracks every miss you make in a row, regardless of power (or target). Otherwise you could have nine different powers, each with a 0.95 to-hit, and if you executed them all in a row you could miss each attack (note a caveat at the bottom of the post regarding this).

AE attacks are considered distinct sequential attacks on indivudual targets for the purpose of the system (so if you AEd two targets and had 0.95 to-hit for both, you be guaranteed to hit one of them).

To determine the to-hit used in the table above, you take either the current to-hit, or the worst to-hit in your current miss series, whichever is lower.


[/ QUOTE ]

This basically matches all the testing I've done to measure the streakbreaker, correcting for some errors in my testing methodology that Weirdbeard was able to detect in my discussions with him.


DEFENSE ISSUES

These are some of the issues related to how defense and tohit works in City of Heroes


Autohitting attacks

There are attacks that automatically hit, bypassing the tohit floors and ceilings. Typically, these things are damage auras, such as the aura emitted by Circle of Thorns Death Mages, or patches, such as the damage due to caltrops. No amount of defense reduces the damage of autohitting attacks. Note: some people used to think burn (firey aura) was autohit, but in actual fact it simply has a very high accuracy.

*** Update from version 1.1 ***

It seems that autohitting attacks are being slowly removed from CoH, to address this issue. In fact, it appears that the damage aura from Death Mages is now considered an AoE attack, defendable with AoE defense. This agrees with dev statements that autohitting *damage* (but not necessarily autohitting debuffs) were being toned down or removed from CoH in the long run.


Special Note on defense debuffs

Although defense debuffs were covered earlier, its important to note that the subtractive nature of defense debuffs makes them extremely dangerous. Up to the writing of this guide, defense sets did not have any resistance to defense debuffs (such resistance is currently being added in some form). Their only means of defending against them was defense itself. This creates a problem whereby any defense debuff that manages to land decreases defense and makes the hero both more vulnerable to damage, and more vulnerable to more defense debuffs - a spiralling downward situation.

This is significant because resistance does not work that way. All resistance powers have an inherent resistance to resistance debuffs. When someone with 40% defense is hit with a 10% defense debuff, defense is reduced to 30%. When someone with 40% resistance is hit with a 10% resistance debuff, 40% of the debuff is resisted, and actual damage resistance drops to 34%, not 30%. Furthermore, the resistance to debuffs remains 40%. If hit with another 10% resistance debuff, resistance drops to 28%, not 20% (like defense would be) and not 27.4%, which would be the case if resistance was truely dropped to 34%.

*** Update from version 1.1 ***

There are more specific statements about Defense Debuff Resistance, which are covered in this guide. However, I have yet to be able to construct a test to measure the Defense Debuff Resistance, nor has anyone else posted tests confirming its effect (that I'm aware of). So I think the jury is still out here.


Quartz eminators, quicksand patches

Quicksand patches are autohitting slow and defense debuff patches. These were highly lethal to defense sets, because their defense debuffs couldn't be defended against or otherwise avoided, and once hit, the slow made it difficult to escape (Super Reflexes has a resistance to slow, but it didn't fully mitigate the -fly -jump which could trap a scrapper between villains and friends alike, and it didn't necessarily allow for quick escapes from the patch). Quicksand was also spammed by Earth thorn casters - a CoT minion - in CoT missions from levels 35 to 39. Although this was supposedly fixed (by lessening the frequency of earth thorn casters as well as reducing their propensity to cast quicksand) its still an example of a highly powerful defense-unfriendly power that has few analogs for resistance or regeneration.

Quartz eminators - the eminators dropped by DE LTs - is even more exceptional. Quartz eminators emit a tohit buff to all DE within its buff radius. The tohit buff eminated from quartz eminators is extremely large - by some estimates several hundred percent. To put Quartz eminators into perspective, I3 SR scrappers running perma-elude and the toggles combines were running with more than 150% defense - and still being easily hit by Quartz-eminator buffed DE minions. Once again, there is no analog to the quartz eminator for any other form of damage mitigation, such as resistance and regeneration.


Team scalers and difficulty sliders

Important to note for defense sets: the difficulty slider (also known as the reputation slider) increases the level of villains within your missions, and therefore increases the base tohit of those villains (it doesn't generally increase the ranks of villains, except for the fact that heroic suppresses bosses). The team scaler increases the difficulty of missions based on the number of heroes on the team, and it increases rank and level and numbers of villains. With much lower defenses in I5 than earlier issues of CoH, high level missions can be less than friendly to defense-oriented sets, moreso than other damage mitigation sets.

*** Update from 1.1 ***

In I7, this problem should vanish when tohit increases for both rank *and* level basically go away.


Is Defense really inferior to Resistance?

Not especially. Defense and Resistance both have pros and cons in terms of their inherent effects. Defense's main problems are three-fold:

1. There are sets that rely heavily on Defense, but most other protection sets do not singularly rely on a single mitigation effect.

This is not a critical issue, but it amplifies the others.

2. Defense is - in the opinion of many - scaled too low.

The argument goes that because Defense avoids status effects, Defense has an inherent advantage that more than balances the fact that the damage mitigation of sets that rely on Defense is significantly lower than other sets. Most testing, analysis, and review of a transparent nature (i.e. open to review) suggests this is false. The devs, who do not generally reveal their own analysis, testing, or reviews, disagree.

3. What Defense is most vulnerable to, is plentiful in the CoH environment.

The most common secondary effect in CoH besides DoT (damage over time) is defense debuff. Defense debuffs are more common than resistance debuffs and regeneration debuffs combined. And Defense debuffs are undoubtably more dangerous to Defense sets than resistance debuffs and regeneration debuffs are to resistance and regeneration sets, respectively (regeneration debuffs would be significantly more dangerous to regeneration sets if they prevented things such as reconstruction and dull pain from functioning). Defense is also vulnerable to tohit buffs, and every single villain of higher rank than minion, and every single villain higher in level than even con, has an effective tohit buff.

To say that Defense is inferior to Resistance, given the large environmental disadvantages that Defense faces in CoH, would be comparable to changing all the damage dealth by villains to toxic and psi, and then claiming that Resistance was inferior to Defense.

What's up with tohit buffs?

Good question. Very high tohit buffs are, at least, uncommon in PvE. They are very common in PvP, because high order tohit buffs are extremely common in player power sets.

The two most common tohit buffs are build up and Aim, and both are high order tohit buff (Build Up is a 60% tohit buff, and Aim is a 100% tohit buff). Virtually all blasters, most defenders, almost all scrappers, and most tankers have access to either Build Up or Aim, and many blasters have access to both. Only controllers as a class lack BU or Aim (and pets have a tohit bonus).

If you are relying on defense in the arena, here's the score. If you have SR or Ice, and a couple stacked bubbles, someone who elected to 6-slot Aim with tohit buff enhancements to kill defense sets will hit you no matter what defense level you think you have. Realistically, that one power, and 5 extra enhancement slots, can effectively nullify an entire team's worth of defense buffs (7 stacked bubbles will beat Aim, of course, but all reasonable levels of defense and most unreasonable ones are going to be beat by 6-slot Aim). Without significant buffs, anyone with either build up or Aim will hit you.

It is unclear why Defense was lowered as part of the Global Defense reductions in I5, but tohit buffs were (apparently) not. If they were, this fact was not reported, nor has it shown up yet in anyone's testing.

*** New for I6 ***

One change made to tohit buffs in relation to balancing them with defense is that tohit buff enhancements are now schedule B (like defense: +20% for even SO) instead of schedule A (like damage: +33% for even SO). This at least places tohit buff enhancement and defense enhancement on a relatively even footing, although for high tohit buff powers, the net benefit of even an equal strength SO will be higher than a similar enhancement in a lower numerical strength defense power.


UNANSWERED QUESTIONS ABOUT DEFENSE

(At least, I don't know the answers)

1. When a click defense is triggered, does the defense stack immediately, or only after the activation is completed, or something in-between?

Although I never fully tested this (and now its almost impossible to do so) I (and many other SR scrappers) experienced an alarming sense that we were being hit in mid-backflip while cycling elude more often than chance would suggest, even though the protection of elude should have been fairly continuous. It was conjectured that when elude was cycled, the original cast of elude was momentarily dropped, and the new cast of elude was significantly (by a second or two) delayed. This would have made elude comparable to powers like grant invisibility, which if you refresh it, causes the targetted player to become momentarily visible again.

Whether this is true, and how this affects other defense powers, like parry/DA, is unclear.

2. Just exactly how does invincibility work?

Much more industrious people than me are continuing to investigate invincibility, most recently Stargazer. Invincibility was originally thought to have a base defense, plus an additional amount of melee and ranged defense per villain in melee range. Havok concluded that the original belief that invincibility had a base defense was false, and attempted to correct that mistaken belief. Much more recently, Stargazer seems to have done fairly convincing tests that lead one to believe that invincibility is not offering melee/ranged defense, but rather damage-typed all except psi defense. Whether invincibility was always like this, or changed to be this, is not clear to me, given the complex history of invincibility testing.

Additionally, further testing by others have hinted that invincibility might be offering twice the defense the developers quote for it because (like all auras) it "pulses" to generate its effect, and the pulses might be coming twice as fast as the actual pulse duration, in effect causes invincibility to stack with itself.

Testing of invincibility might be the longest running attempt to define how a power works in CoH by the player community.

3. Are hits and misses "streaky?" Is the random number generator in City of Heroes "broken?"

Its possible the random number generator has some sort of flaw, but in my opinion, whatever flaws it has, they are unlikely to be causing major problems in the game. However, its possible there are other systematic errors in the game related to how random numbers are actually used. There are some instances where it is blatantly obvious that the tohit calculators are doing something weird, but across a wide range of other cases, the randomness of hits and misses appears to be fairly random. Its important to note that "random" does not mean "not streaky." True random numbers are inherently streaky to a degree: the question is whether or not the hits and misses in CoH obey statistical norms of streakiness. This is still an open question, because its such a difficult thing to test for and because few people are able to test it precisely.

(New)4. How do radiation attacks work? How exactly do they "bypass defense?"

The most logical way for radiation attacks to "bypass" defense is for them to have inherent tohit buffs. If that is the case, radiation attacks would be the only exception I am aware of to the rule that *attack specific* accuracy increases are accuracy buffs, not tohit buffs.


THE CANONICAL LIST OF DEFENSE-RELATED COMPLAINTS REGULARLY DISCUSSED ON THE FORUMS

In no particular order (and without commenting on validity):

* SR underperforms other scrapper sets
* SR is a "one trick pony" that has only defense
* Ice tanks uderperform other tanker sets
* Ice tanks performance is too similar to SR scrappers for a tanker
* High defense is too frustrating in the arena
* Low defense is too frustrating in the arena
* There are too many defense debuffs in the game
* Defense debuffs are too strong
* Tohit buffs in the arena are too strong
* Defense requires you to be lucky
* Defense is inferior to Resistance in all respects
* The SR set is too reliant on power pool defenses
* The Force Fields set is insufficiently strong as a buff set
* Resistance buffs are more appreciated than Defense buffs
* The SR (and to a lesser degree Ice) set can be too easily simulated with a few luck inspirations
* Lucky and Evasion are in the wrong order in the SR set
* Invincibility is too powerful a defense power for Invulnerability given that it can outperform the supposedly "defense-oriented sets"
* The -DEF in Unyielding should be removed given the overall reductions to the invuln set
* SR passive defenses are too inefficient to slot
* There are too many autohitting attacks
* There shouldn't exist autohitting defense debuffs
* Quartz eminators
* Defense stacking is too complicated, unfair to some sets, and creates problems in improperly selecting and slotting certain defense powers

Be forewarned: this stuff has been debated to death. Also, while I strongly encourage people to post their ideas, observations, comments, and suggestions on defense-related issues, bear in mind that if you post a message stating, essentially "I have the answer to everything" one of two things is extremely likely to happen: the message will be ignored, or the suggestion in the message will be heavily critiqued. Be prepared for both.


THE PURPLE PATCH

Get asked about this all the time. Here is what happens when you try to attack something much higher than you are, in terms of your powers effectiveness going down, and in terms of your base tohit going down also. Note: this affects players attacking higher leveled foes. Low level villains attacking a higher level player are not affected by the purple patch. These numbers come from a Geko post from the distant past.

[ QUOTE ]

Foes your level have not changed. You have a 75% chance to hit and your powers are 100% effective.
Foes 1 level above you - No Change. You have a 68% chance to hit and your powers are 90% effective.
Foes 2 levels above you - No Change. You have a 61% chance to hit and your powers are 80% effective.
Foes 3 levels above you - You have a 55% chance to hit and your powers are 65% effective.
Foes 4 levels above you - You have a 48% chance to hit and your powers are 48% effective.
Foes 5 levels above you - You have a 41% chance to hit and your powers are 30% effective.
Foes 6 levels above you - You have a 34% chance to hit and your powers are 15% effective.
Foes 7 levels above you - You have a 25% chance to hit and your powers are 8% effective.
Foes 8 levels above you - You have an 11% chance to hit and your powers are 5% effective.
Foes 9 levels above you - You have a 6% chance to hit and your powers are 4% effective.
Foes 10 levels above you - You have a 5% chance to hit and your powers are 3% effective.
Foes 11 levels above you - You have a 5% chance to hit and your powers are 2% effective.
Foes 12+ levels above you - You have a 5% chance to hit and your powers are 1% effective.


[/ QUOTE ]


*** New for version 1.2 ***
Testing seems to indicate that the base tohit of players might not follow this progression precisely. Additional testing seems to show, and the devs seem to have confirmed, that the tohit decrease follows this progression instead:

-4 .95
-3 .90
-2 .85
-1 .80
+0 .75
+1 .65
+2 .56
+3 .48
+4 .39
+5 .30
+6 .20
+7 .08

It is unclear what the source of the discrepancy is.


Things on the horizon

* Statesman has suggested that high tohit buffs are being looked at, but no solution has been put forth by the devs.

* More details about the specifics of the Defense scaler will hopefully allow us to definitively state the modified tohit formula, with all scaling buffs in their appropriate locations.


SOURCES OF ADDITIONAL INFORMATION

I kept the numbers out of this. If you want them, here they are:

Buffy's Scrapper Guide and Tanker Guide is an excellent source of defense (and resistance and regeneration) numbers.

An additional source of numbers, that include power pool values and tohit bases, is The Scrapper Defense Values Site. Note that power pools for tankers are higher than for scrappers (scrappers generally have 75% of the value of tanker numbers).

RedTomax is working on a web-based guide to all of CoH: it contains Defense information including defense types and values in tabular form here.


Use of this Guide

Anyone compiling information for use by players of City of Heroes and City of Villains has permission to reproduce this guide whole or in part, so long as some form of attribution is maintained. But if you make a ton of money off of it, and I find out about it, I'm going to come looking for my cut.

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

Good stuff. Thank you very much.

---

[ QUOTE ]
What other powers provide defense?

The following additional powers provide defense:
Illusion Control/Superior Invisibility (melee/ranged)
Illusion Control/Group Invisbility (melee/ranged)


[/ QUOTE ]

Regarding illusion controls +def powers, it now says its +def (ALL). Does this mean that they now made it damage typed instead of postional vector melee/ranged?

---

[ QUOTE ]
[ QUOTE ]
What other powers provide defense?

The following additional powers provide defense:
Illusion Control/Superior Invisibility (melee/ranged)
Illusion Control/Group Invisbility (melee/ranged)


[/ QUOTE ]

Regarding illusion controls +def powers, it now says its +def (ALL). Does this mean that they now made it damage typed instead of postional vector melee/ranged?

[/ QUOTE ]

More likely, as part of all the stacking changes made, those powers were changed to base defense like the power pools: i.e. literally defense to all.

Defense to all damage types isn't really defense to all: because of how the game engine currently works, defense to all damage types is actually missing toxic defense.

I don't recall when that change was made, though, so I will have to do some checking.

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

The most comprehensive and informative guide on defense I have seen. Thanks so much for your work.

A clarification on Force Fields:

- Because of the strange and situationally suboptimal stacking of the various bubbles as you described in your guide, the devs changed Force Fields so that Insulation Shield includes both Ranged AND AoE Defense. In addition, Dispersion Bubble now provides +Defense(ALL), which includes all damage types (minus toxic, obviously) as well as melee, ranged, and AoE Defense. I just verified the short text for these powers this morning, and they include these changes. You'll also find the implied decision for those changes in Statesman's post here.

And yes, the Illusion invisibility powers also say +Defense(ALL) for the short help texts as well.

Also, I think your toHit formula might have some modifiers in the wrong position. The upcoming change to higher level/rank mobs from getting a toHit bonus (applied BEFORE defense) to getting an accuracy bonus (applied AFTER defense) is supposed to make Defense buffs more useful against those mobs.

The example given by a dev (_Castle_?) was how an even-level AV has 75% final toHit against players currently. The 50% toHit buff will be changed to a 50% accuracy buff, so that defense will have a greater effect.

The formula I've seen posted is:

FinalToHit = {[BaseAcc * (1 + toHitBuff - toHitDebuff) - (DefBuff - DefDebuff)] * (1 + accBuff - accDebuff*)}
* I'm not even sure there are accDebuffs, as it seems all debuffs regarding accuracy are actually toHitDebuffs instead.
Given that formula, the AV gets the same FinalToHit of 75% under both the 50% toHitBuff and the 50% accBuff, as follows:

FinalToHit = {[0.5 * (1 + 0.5 - 0) - (0 - 0)] * (1 + 0 - 0)} = 75%
or
FinalToHit = {[0.5 * (1 + 0 - 0) - (0 - 0)] * (1 + 0.5 - 0)} = 75%

However, Defense becomes much more effective with the impending change (use 25% defense as an example):
FinalToHit = {[0.5 * (1 + 0.5 - 0) - (0.25 - 0)] * (1 + 0 - 0)} = 50%
vs.
FinalToHit = {[0.5 * (1 + 0 - 0) - (0.25 - 0)] * (1 + 0.5 - 0)} = 37.5%

---

Savant
Level 50 Defender - Force Fields/Psychic Blast

As to force fields, I lost track a bit of some of the changes made during the stacking revisions, thus my original omission of the illusion controller changes and some of the FF changes (FF was changed three times). I'll be sure to have that all added for the next version, which will probably be out before I7 is.

As to the tohit formula, lets break it down.

This part: (BaseToHit + ToHitBuffs - ToHitDebuffs - Defense + DefenseDebuffs) has been confirmed a gazillion times, and both geko and castle say that it is checked against the 5% floor and 95% ceiling. That's pretty solid.

This term: (BaseAcc + AccBuffs - AccDebuffs) comes straight from geko. The BaseAcc is the base accuracy of the power you are using, which by default is 1.0. That comes straight from geko. The accbuffs are almost always enhancements. Technically speaking geko didnt mention accuracy debuffs, but if they existed, they would subtract from the accuracy buffs, and castle specifically stated that such debuffs exist, albeit uncommonly. One possible source for them is the accuracy penalty associated with AoE mez attacks.

The relevant quote from Geko (see the Ask Geko thread) regarding accuracy is this one:

[ QUOTE ]

We then do the following:

(Total_To_Hit - Total_Defense)

That value is clamped between 5% and 95%. That is, you can never have more than a 5% chance to hit or miss a target. So if a target's Defense is greater than the attacker's ToHit, the attacker will still have at least a 5% chance to hit.

We then multiply that number by the power's total Accuracy (total Accuracy = Accuracy + the power's Accuracy Enhancements).

We again clamp the values between 5% and 95%.


[/ QUOTE ]

In other threads, he does elaborate on what the term "Accuracy" is in that formula - its the base accuracy of the attack, normally 1.0 (which is the source for a lot of people's confusion between "base to hit" which is normally 75% for players, and "base accuracy" which is normally 1.0 for player attacks.


Then there is this PM from pohsyb which is quoted by another player (in this thread):

[ QUOTE ]

Chance to Hit = MINMAX(.05, .95, (MINMAX(.05,.95, BaseTohit + BuffTohit - Debufftohit - TargetDef)) * (BaseACC + EnhanceACC) )


[/ QUOTE ]


The only question is how the Rank and Level adjustments factor in. Two possibilities:

(BaseAcc + AccBuffs - AccDebuffs + RankBuff + LevelBuff)

(BaseAcc + AccBuffs - AccDebuffs) * (RankBuff) * (LevelBuff)

In the two cases, RankBuff and LevelBuff are calculated in slightly different ways: in the first one, its calculated as a percentage addition (i.e. +50% or 0.5) and in the second as a true scaling factor (i.e. 150% or 1.5).

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

My apologies. I misinterpreted your formula. It is actually mathematically equivalent to the one I posted, but with a different naming scheme and a different reordering of the factors. Your explanation cleared up where I was confused.

---

Savant
Level 50 Defender - Force Fields/Psychic Blast

Wow thats positively got to be the longest post ive ever seen in my life lol. PS. ice control's arctic air does not give defense.

---

Plasmic's Guide to Sonic/Mental

Plasmic's Guide to Regeneration

Plasmic Fire - 50 Fire/Rad Victory Server

[ QUOTE ]
Wow thats positively got to be the longest post ive ever seen in my life lol. PS. ice control's arctic air does not give defense.

[/ QUOTE ]

I don't remember when arctic air lost defense, but you're right, the help text no longer says it offers defense.


And scarily, I'm not sure this is my longest post ever.

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

[ QUOTE ]
My apologies. I misinterpreted your formula. It is actually mathematically equivalent to the one I posted, but with a different naming scheme and a different reordering of the factors. Your explanation cleared up where I was confused.

[/ QUOTE ]

Actually, don't apologize. I've been pursuing something that has been bugging me, even about my own formula. In fact, yours and the one I originally put in the guide *aren't* identical: their different in a subtle, but significant way. And in fact, I now have strong evidence we're *both* wrong.

Stay tuned.

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

[ QUOTE ]
And in fact, I now have strong evidence we're *both* wrong.
Stay tuned.

[/ QUOTE ]

I'm on this bat channel. Gimme a bat time.

---

Be well, people of CoH.

I believe, based on the sum total information out there, and after discussing the subject with pohsyb very carefully, that I know what the I7 "tohit formula" is. Its this:

Bounded[(BaseAcc) * (1 + AccuracyEnhancements) * (AccBuff) * (AccDebuff) * (LevelBuff) * (RankBuff) * Bounded[(BaseToHit + ToHitBuffs - ToHitDebuffs - Defense + DefenseDebuffs)] ]

Where Bounded[x] is 5% if x is less than 5%, 95% if x is greater than 95%, and x if x is between 5% and 95%. The part highlighted in yellow is the main difference between I6 and I7, with the added caveat that in I6, the term "BaseToHit" means a different thing than in I7: its basically 50% in I7, but a looked up value based on rank (i.e. 50%, 57.5%, 65%, 75% for minions to AVs) and then adjusted for level differences.

At least, that is how we *might* express it if it was an equation. It seems clearer to me now that part of the reason for all the various "versions" and discrepancies in how its been described (besides normal human error and typos) is that it *doesn't* exist as an equation *anywhere*. It exists solely as an algorithm implemented in the code for the game engine. There isn't a "tohit formula" there is only a "tohit procedure." We can express it, to varying degrees of fidelity, but the main reason why the devs do not just give us the formula, is that there isn't one.


*IF* the devs were to drop the tohit algorithm onto us, it *might* be something like this:

(disclaimer: this is all me. I'm only quoting it for formatting purposes: absolutely no one gave this to me and you shouldn't infer that anyone gave me anything remotely similar)

[ QUOTE ]

Step One: Look up BaseToHit

If attacker is player, and target is player, then BaseToHit = 0.5
If attacker is player and target is not player, then BaseToHit = 0.75
If attacker is not player, then look up BaseToHit based on type

In I7, BaseToHit = 0.5 by default


Step Two: Calculate NetToHitBuffs

NetToHitBuffs = SumOf(ToHitBuffsOnAttacker)


Step Three: Calculate NetToHitDebuffs

NetToHitDebuffs = SumOf(ToHitDebuffsOnAttacker)


Step Four: Calculate NetDefenseBuffs

NetDefenseBuffs = SumOf(DefensePowersOnTarget) + SumOf(DefenseBuffsOnTarget)


Step Five: Calculate NetDefenseDebuffs

NetDefenseDebuffs = SumOf(DefenseDebuffsOnTarget)


Step Six: Calculate intermediateToHit

intermediateToHit = BaseToHit + NetToHitBuffs - NetToHitDebuffs - NetDefenseBuffs + NetDefenseDebuffs


Step Seven: Check for tohit floor and ceiling boundary

if intermediateToHit < 0.05 then intermediateToHit = 0.05
elseif intermediateToHit > 0.95 then intermediateToHit = 0.95


Step Eight: Look Up BaseAccuracy

BaseAccuracy = BaseAccuracyOf(AttackPower)


Step Nine: Lookup RankScalingBuff

if attacker is minion, RankScalingBuff = 1.0
if attacker is LT, RankScalingBuff = 1.15
if attacker is Boss, RankScalingBuff = 1.3
if attacker is AV, RankScalingBuff = 1.5


Step Ten: Look Up LevelScalingBuffs

if attacker is +1, LevelScalingBuff = 1.0940
if attacker is +2, LevelScalingBuff = 1.1867
if attacker is +3, LevelScalingBuff = 1.2667
if attacker is +4, LevelScalingBuff = 1.3600


Step Eleven: Check for AccuracyBuffs

NetAccuracyBuffs = ProductOf(AccuracyBuffsOnAttacker)


Step Twelve: Check for AccuracyDebuffs

NetAccuracyDebuffs = ProductOf(AccuracyDebuffsOnTarget)


Step Thirteen: Calculate Enhancements, if any

TotalAccuracyEnhancements = SumOf(AccuracyEnhancementsInPower)

AdjustedAccuracyEnhancements = EnhancementDiversificationScaler(TotalAccuracyEnha ncements)

NetEnhancementAccuracy = (1 + AdjustedAccuracyEnhancements)


Step Fourteen: Calculate NetAccuracy

NetAccuracy = BaseAccuracy * RankScalingBuff * LevelScalingBuff * NetAccuracyBuffs * NetAccuracyDebuffs * NetEnhancementAccuracy


Step Fifteen: Calculate final tohit

NetToHit = NetAccuracy * (intermediateToHit)


Step Sixteen: Check for tohit floor and ceiling boundaries

if NetToHit < 0.05 then NetToHit = 0.05
elseif NetToHit > 0.95 then NetToHit = 0.95


Step Seventeen: roll the dice, see what happens


[/ QUOTE ]

Holy Kukamunga.

Now seriously, if they dumped that out there, they would be answering questions about tohit from now until Kingdom Come. As it stands, this is *my* expression of how tohit works, and thus less likely to have ten thousand armchair mathematicians flooding the forums attempting to deconstruct it. But it represents the best expression of how tohit works, based on *all* the information I have available.

(not really: I could have made you all go blind while I added a dozen more steps factoring things like the purple patch, but you get the idea)


Thanks to Castle for answering my initial questions, and special thanks to pohsyb for taking the time to clear up, hopefully once and for all, how this works. I7 was the Rosetta Stone to clarify something once and for all: all accuracy buffs/debuffs are multiplicative, not additive. That means in particular the Rank and Level buffs in I7 will be multiplicative, and will scale properly relative to the current I6 rank and level scaling. Its really the *only* way for them to scale correctly in the presence of other accuracy buffing/debuffing.


What Does This All Mean?

It means the Defense Scaler will work exactly the way Statesman described, and essentially the way that Castle and Geko amplified. The *details* are a bit confused in the forums as to the math, but it *will* work. In particular, it will work the way I've been assuming it will work and have suggested in the forum threads regarding it (with minor math tweaks), so if those make sense to you, the rest of this is really just a lot of math you don't need to know. People like Circeus or Stargazer might need to know for proper quantitative analysis or accuracy testing, but for the rest of us, assuming we trust this version of how tohit works, what we know is this:


1. Defense subtracts from tohit.

2. Tohit buffs and defense debuffs work in basically the same way: by subtracting from defense.

3. Whatever your net chance to hit is, if you have a +60% accuracy buff, you'll hit 60% more often. A similar statement can be made for accuracy debuffs.


These additional rules are mine: they aren't 100% dev confirmed, but they seem to be operative:

4. No matter how its described, if it affects the entire player/attacker, its a tohit buff/debuff

5. No matter how its described, if it affects a single attack power, its an accuracy buff/debuff


If all you know are these five rules, the math is unimportant, unless you want to calculate something exactly. 99.9% of all players are unlikely to ever need to calculate anything related to tohit precisely.

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

That's... this is.... by my complete lack of a god or gods, that's the silliest, frelling thing I've ever seen.

Not that you've figured all this out... that's absolutely amazing... but it is farking insane that they would do it this way.

And you still have to layer the purple patch on that? And does it continue to work that way beyond +5s, or does something else occur against +6s and higher?

EDIT: On the flip side, maybe this explains the lag.

---

Be well, people of CoH.

[ QUOTE ]
That's... this is.... by my complete lack of a god or gods, that's the silliest, frelling thing I've ever seen.

Not that you've figured all this out... that's absolutely amazing... but it is farking insane that they would do it this way.

And you still have to layer the purple patch on that? And does it continue to work that way beyond +5s, or does something else occur against +6s and higher?

EDIT: On the flip side, maybe this explains the lag.

[/ QUOTE ]

Actually, it isn't especially crazy to me: this is actually the first formula I've been moderately comfortable with. Even the previous iteration with additive accuracy buffs has bugged me for a while now, although I accepted it because it came straight from geko's mouth, *and then* was apparently confirmed by pohsyb. But pohsyb explicitly told me that if he previously stated that accuracy buffs were additive, that was a small error on his part.

I'm not saying its the best of all possible formulas, but - and it takes some experience dealing with this sort of thing - its the first one that seems to have the "ring of truth" to it, that I can imagine the tohit formula evolved into, starting from scratch, till now. It hasn't always been this way: the formula/algorithm seems to have evolved (slightly) from release to now. At least two definite revisions: Step Seven Intermediate Checks after the arenas were released (according to Castle) and the I7 changes (tohit increases for accuracy buffs, adding terms to the left side of the equation).

Its been suggested to me, and I tend to agree, that its easy to get caught up in the details of this. In fact, I *could have* made the above algorithm simpler, but I wanted to show it "naked" as it might be really implemented, which is detailed. And the game is sufficiently detailed that the tohit calculator almost certainly has to deal with a lot of special cases, and a lot of detail checking (just the fact that there are many different types of relevant buffs creates a lot of the detail: acc enhs, tohit buffs, defense debuffs, etc).

Its detail for people who want detail. I'm not sure this should be thrust into the face of players who shouldn't care. I'm arrogantly hoping that people who should care might check in this thread periodically. But at least when someone asks, I'll know definitively how the I7 change will affect, or not affect, accuracy. As will my loyal readers

As to +6 and higher: I try not to bug the devs more than I have to (I try, but I usually fail), and now that I know the formula in a more authoritative fashion, the subject of what happens at +6 and higher should probably really be a general forum discussion question that hopefully Statesman or another red name can answer for everyone.


The search for the tohit formula feels like the search for the Grail in the Da Vinci code, with me playing the role of Sophie Neveu, and various people playing the role of Robert Langdon. You know, several times in the book Langdon turns to Neveu and essentially says "I don't want to tell you now, even though your life is in danger and we might be killed at any time, it'll spoil the surprise." By the middle of the book I would have shoved his head into the aircraft toilet. Not that anyone has specifically done that to me in this case, but there are analogies.

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

Actually as far as i can remember arctic air never gave defense. Doesnt say it anywhere, even in planners, and you could never slot it for defense, are you confusing it with steamy mist for storm secondary?

---

Plasmic's Guide to Sonic/Mental

Plasmic's Guide to Regeneration

Plasmic Fire - 50 Fire/Rad Victory Server

[ QUOTE ]
Actually as far as i can remember arctic air never gave defense. Doesnt say it anywhere, even in planners, and you could never slot it for defense, are you confusing it with steamy mist for storm secondary?

[/ QUOTE ]

From the manual:

Arctic Air (TOGGLE)

HIdes your team. It does not make you and your allies Invisible, but it makes them much harder to see as long as you don't get too close or don't attack. Even if discovered, Arctic Air grants a bonus to Defense. Arctic Air reduces your movement speed (but not your teammates')


Clearly, its been changed a couple times since then.

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

MMM no im more willing to bet the MANUAL was wrong and mixed the name up with steamy mist. As i cant recall the power ever being changed since i started playing so the change would have had to occured sometime before i1. Which i also dont recall in the patch notes. But it *is* possible.

The description is EXACTLY steamy mist though, and doesnt even mention the slow and confuse portion of it. Again that *could* have been the change, but ive had incorrect manuals before, and actually read the manual when my friend had it, didnt pay attention to actic air, but i definitely noticed a lot of faults that it had.

---

Plasmic's Guide to Sonic/Mental

Plasmic's Guide to Regeneration

Plasmic Fire - 50 Fire/Rad Victory Server

Actually AA used to be exaclty like steamy mist. Geko didn't like how similair powers were with certain combos ie. ice/storm controllers. I think in I2 (possibly 1) it was changed. The game manual is correct, but with every new issue the game changes; Back when COH first came out, Gravity controls did not have the singularity and wormhole was team-teleport

---

Hmm.

---

Odd :P, well i guess any reference to the manual is still out of the question then :P

---

Plasmic's Guide to Sonic/Mental

Plasmic's Guide to Regeneration

Plasmic Fire - 50 Fire/Rad Victory Server

[ QUOTE ]
Certain player attacks have certain inherent accuracy bonuses or deficits. All attacks within an offensive set that require a weapon draw (i.e. katana, assault rifle) are supposed to have an inherent tohit bonus, said to be about 5%. In addition, all snipe attacks also have a tohit bonus, in a similar range. AoE control based attacks have an accuracy penalty, but a recent post by geko stated that normal AoE attacks do not have an inherent accuracy penalty by default. The devs have stated that the archery attacks have an inherent tohit bonus higher than the standard weapon-draw bonus, but the precise bonus has not (to my knowledge) been determined.

[/ QUOTE ]

The parts I have bolded, shouldn't they be "accuracy?"

Concerning radiation attacks, perhaps they simply have a chance to bypass (as the description says) defense altogther, meaning defense simply isn't factored into the NetToHit? And perhaps Hamidon and his Mitos have this ability with a 100% chance in their attacks, otherwise their untyped attacks should still be subject to positional defense and not hit 100% of the time if you scarf down a tray full of purples.

Also, is it true that player base tohit is lower against higher ranked mobs, and not just higher level mobs?

---

[ QUOTE ]
[ QUOTE ]
Certain player attacks have certain inherent accuracy bonuses or deficits. All attacks within an offensive set that require a weapon draw (i.e. katana, assault rifle) are supposed to have an inherent tohit bonus, said to be about 5%. In addition, all snipe attacks also have a tohit bonus, in a similar range. AoE control based attacks have an accuracy penalty, but a recent post by geko stated that normal AoE attacks do not have an inherent accuracy penalty by default. The devs have stated that the archery attacks have an inherent tohit bonus higher than the standard weapon-draw bonus, but the precise bonus has not (to my knowledge) been determined.

[/ QUOTE ]

The parts I have bolded, shouldn't they be "accuracy?"


[/ QUOTE ]

Yep, I didn't catch all of those when I added the part about weapon draw being accuracy. Fixed for 1.3.


[ QUOTE ]

Concerning radiation attacks, perhaps they simply have a chance to bypass (as the description says) defense altogther, meaning defense simply isn't factored into the NetToHit? And perhaps Hamidon and his Mitos have this ability with a 100% chance in their attacks, otherwise their untyped attacks should still be subject to positional defense and not hit 100% of the time if you scarf down a tray full of purples.


[/ QUOTE ]

I asked about radiation attacks specifically, and it seems they have an inherent accuracy buff, and a defense debuff, and no other weird effects - at least that is the direct information currently given to me.


[ QUOTE ]

Also, is it true that player base tohit is lower against higher ranked mobs, and not just higher level mobs?

[/ QUOTE ]

No, just higher level. Player base tohit is 75% against all villains of even level to the player, before target defense, and target and player buffs and debuffs are taken into account. Except in PvP: its 50% there. It sometimes seems like player base tohit is lower against bosses mainly because bosses are more likely, on average, to have defensive buffs of some kind. Also, they tend to stay alive long enough for you to notice actually missing: short of things like bubbled drones, you don't usually get a chance to miss often against an even level minion.

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)

You wrote "Ice Defenses do not stack with power pool defenses". I tried to figure this out from first principles if this is still true, but I could not. So I will just ask the question:

Do Ice Defenses do stack with power pool defenses now?

In other words, is there any benefit from getting say, weave?

Thank you very much. (I just started playing an ice-tank, so I have a keen interest in the answer. )

---

I'm guessing that's an error. All power pool defense powers now give defense to everything, so they stack with every other defense power in the game.

---

[ QUOTE ]
You wrote "Ice Defenses do not stack with power pool defenses". I tried to figure this out from first principles if this is still true, but I could not. So I will just ask the question:

Do Ice Defenses do stack with power pool defenses now?

In other words, is there any benefit from getting say, weave?

Thank you very much. (I just started playing an ice-tank, so I have a keen interest in the answer. )

[/ QUOTE ]

They didn't used to; I'm still sweeping the AT-specific descriptions for instances of that stuff and trying to get a 1.3 version that corrects them all (I forgot how many places that stuff was mentioned).

Galactiman is correct: power pool defenses now appear to offer defense to melee/ranged/aoe/smash/lethal/fire/cold/energy/negative/psi (i.e. all types) and therefore stack with any defense.

They also stack with force fields, based on the bubble being stacked, and as far as I know, there aren't any cases of an entire set of defenses no longer stacking with Ice defenses (which are damaged typed). Short answer is that as an Ice tank, you should benefit from any power pool defense you can buy, any power pool defense aura (i.e. maneuvers), and if a defense buffer is on your team, you should get some benefit from defense buffs as well (although that is a tiny bit more complicated because of which buffs stack with which defenses).

---

[Guide to Defense] [Scrapper Secondaries Comparison] [Archetype Popularity Analysis]

In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)