Fix Defense in Three moves: Version 2.0
By
Another_Fan,
Posted on: 2008-02-20 18:43 in Player Guides
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Okay, reading comprehension FTW: for some reason, I thought that anti-accuracy would just add with accuracy, instead of multiplying.. Having gone back over the OP more carefully, I can see I was misreading, and that eliminates one of my major objections.
I wonder, however, how this is preferable to simply making all accuracy modifiers multiplicative, and eliminating the distinction between ToHit and Accuracy.
Just pulling numbers out of a hat as an example, suppose I've got Aim (+100% acc), 1 Acc SO (+33% acc) and I'm shooting at a guy running Focused Senses (+50% def) and Agile (+20% def). My base chance to hit is 75%. My actual chance to hit would be
75%*2*1.33*0.5*0.8=80%
Aside from getting the right numbers for proper balance, can anyone explain why it would be preferable to have two kinds each of +accuracy and +defense?
To me, that just adds unnecessary complexity.
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I don't think it is preferable -- it's just what we already have. TBH, I like your suggestion a lot more. Things would be a lot simpler and more understandable if they changed all of the ToHit buffs into Accuracy buffs and all of the Defense buffs into Arcanville's Anti-Accuracy. The thing is though, actually implementing the change would likely not be simpler. To illustrate:
- You'd have to implement Arcana's formula as a first step anyway.
- Arcana's idea can be done piecemeal. Going the extra mile to simplify the ToHit formula would probably need to be done over a very short period of time -- a single patch, really.
- With Arcana's idea, you only need to look at Defensive powers. This idea, you'd have to look at all Defensive powers, all powers that modify ToHit and/or Accuracy, and all Inventions that do too. If that doesn't at least double the number of changes, it doesn't fall far short.
- Since the change would need to be done in one big jump and encompasses so many "little" changes to a whole lot of powers, I doubt it would be reasonable for an issue release -- it may be for a paid-extra-for expansion, but not an issue.
Edit To Add: Of course, there's nothing stopping them from doing Arcana's suggestion first and gradually phasing all Def into Anti-Accuracy and all ToHit into Accuracy. That could probably be done more gradually, but it would also increase the amount of work -- probably not double but still significantly.
yawn
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Aside from getting the right numbers for proper balance, can anyone explain why it would be preferable to have two kinds each of +accuracy and +defense?
To me, that just adds unnecessary complexity.
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Well, first of all, "getting the right numbers for proper balance" is a pretty good reason, and I explain what functionality each type of defense addresses in combination.
Second, the subtractive kind of defense already exists, so there is zero work involved in keeping it around as a game mechanic. Whether the powers designers decide to use it, and what for, is a separate issue from the need for a proper suite of balanced mechanics to be available.
Basically, I'm adding one thing, taking nothing away, and changing nothing about the game that a powers designer himself doesn't actively want to change. No other defense/accuracy/tohit balancing solution makes that claim.
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I don't think it is preferable -- it's just what we already have. TBH, I like your suggestion a lot more. Things would be a lot simpler and more understandable if they changed all of the ToHit buffs into Accuracy buffs and all of the Defense buffs into Arcanville's Anti-Accuracy. The thing is though, actually implementing the change would likely not be simpler.
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I'm not clear on why it is that eliminating the distinction between ToHit and Accuracy (something I've been suggesting occasionally for about the last year) and making defense purely multiplicative (something I've been suggesting for even longer) is inherently more complicated than what Arcanaville is suggesting here, and maybe I'm just missing something.
But it seems to me that both approaches involve a fundamental change to the ChanceToHit equation -- the change you'd have to make to implement this Elusivity business is pretty much identical to what you'd have to do to implement my version. In fact, what I'm suggesting is essentially a special case of Arcanaville's suggestion, with what are currently called "Defense" and "ToHit Buffs" set identically to zero.
The coding therefore should be pretty much the same -- the only difference is in balancing. To be honest, since my version has fewer variables, I feel like it would be easier to balance.
In any case, my sense is that the major barrier to anything being changed is creating new mechanics. If you can get them to admit that a problem is severe enough to write new code, taking the time to do the necessary balance is almost a given. (I could be wrong, of course, but I don't think so.)
In any case, the question at this point is not whether the current to-hit formulation is any good -- I think most mathematically-inclined people would agree that it's pretty lousy -- it's whether or not it's lousy enough to justify a fundamental alteration to game balance. And that's exactly what would be involved in Arcanaville's suggestion, and certainly in mine as well.
To be honest, I don't think any changes are likely at this point, and I'm not particularly convinced that they'd be desirable. So, as far as I'm concerned, this is more about how they should design CoX 2.
But hey, if someone's going to start talking about mathy-sounding stuff, I'll totally jump i with both feet, every time. 
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Well, first of all, "getting the right numbers for proper balance" is a pretty good reason, and I explain what functionality each type of defense addresses in combination.
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I think we have a fundamental disagreement about game design which we've touched on in another thread. Correct me if I'm wrong, but it looks like you feel that diversity of game mechanics is a desirable goal in and of itself.
My preference is to make the mechanics as simple (if I were being snooty, I'd say "as elegant") as possible. The whole point of the to-hit formula is to create a need to make sure that you can hit your targets -- and, conversely, to allow you to mitigate damage by dodging their attacks. You only need two things to do this: a way to make your attacks more likely to hit (either through acc buffs or def debuffs -- I count those as identical, since they are mathematically indistinguishable), and a way to make your enemies' attacks less likely to hit (either through tohit debuffs or def buffs -- again, mathematically identical).
To me, having two qualitatively different ways to alter your chance to hit is just asking for trouble. It's confusing to the playerbase. And it makes the math more difficult for balancing purposes.
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Basically, I'm adding one thing, taking nothing away, and changing nothing about the game that a powers designer himself doesn't actively want to change. No other defense/accuracy/tohit balancing solution makes that claim.
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This is a fair point.
I just question the extent to which "adding one thing" to an already combersome formula is a good idea -- at this point, I think subtraction would be more beneficial than addition.
That would, unfortunately, remove the ability to "phase in" a solution -- you'd have to do it all in one fell swoop.
Also, just to clarify:
Am I correct that the two primary issues that are to be addressed with Defense are (1) the ability of high-magnitude ToHit Buffs effectively to ignore Defense and (2) the ability of small amounts of Defense to add up to massive amounts of mitigation as you get close to the 45% soft cap (e.g., the ability to build perma-Elude SR scrappers, etc.)? Is there something else that I'm missing?
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My preference is to make the mechanics as simple (if I were being snooty, I'd say "as elegant") as possible. The whole point of the to-hit formula is to create a need to make sure that you can hit your targets -- and, conversely, to allow you to mitigate damage by dodging their attacks. You only need two things to do this: a way to make your attacks more likely to hit (either through acc buffs or def debuffs -- I count those as identical, since they are mathematically indistinguishable), and a way to make your enemies' attacks less likely to hit (either through tohit debuffs or def buffs -- again, mathematically identical).
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Technically, the only things you need after that are damage, and the ability to reduce damage. You don't need smashing, lethal, fire, energy, psionic - unless you actually feel making the game more complicated is worth introducing the ability to have different strengths and weaknesses.
Contrawise, if all defense was proportional, the one thing you *couldn't* model is the accuracy/defense-equivalent of partially unresistable damage. And I don't mean literally unresistable. An attack can be coded to do half smashing damage, and half psionic damage. That would affect someone with strong smashing resistances differently from someone with no resistances, in a way that is completely different from the situation where you only had untyped damage, and holistic resistances.
Due to the way defense works, there's no such thing as a "partially defended attack" nor is there such a thing as a "partial bypass of defense." There is an actual attack set - radiation blast - that is conceptually designed to partially bypass defense, but there's no actual way to model it. The only way to actually deliver on that description would be to allow individual attacks to have intrinsic tohit buffs rather than accuracy buffs.
If I was designing the game system from scratch, I might have considered making positional and damage-oriented defense multiplicatively stack with each other (basically, both get to be used separately against all attacks). I could then invent something called the "precision buff" that would act like tohit buffs, and counter positional defense, say, and something else called "penetrator buffs: that would act like tohit buffs, but counter damage-oriented defenses instead. They would be the accuracy-based versions of the concept of "armor-piercing" except one of them would represent the intrinsic ability to compensate for a moving target, and the other would represent the intrinsic ability to negate physical deflection-based protections.
All of that is neither here nor there, except to show that the diversity in game mechanics is not there simply as an abstract benefit, but rather to be able to model actual game complexity. Unfortunately, that's something CoH itself doesn't currently leverage very well (i.e. there aren't strong conceptual game "rules" for what you'd expect to have high smashing defenses vs high lethal defenses vs high energy defenses, and conversely what kinds of things should do well against them).
But on a pragmatic level, there is another reason to keep both types of defenses around. Its a failsafe to prevent external overbuffing from getting out of hand. All other things being equal, it should be a lot easier for player Y to negate (but no more than negate) what player X buys, than it is for player X to buy it. Without that negative reinforcement, protection powers become too powerful in PvP, and in PvE in high-buff teams. This duality of wanting to preserve "intrinsic designed strength" while making it easier to negate "externally buffed strength" is the basis of wanting to keep both types of defenses around. One is good at retaining its proportional strength under all circumstances. One isn't. I want both.
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Am I correct that the two primary issues that are to be addressed with Defense are (1) the ability of high-magnitude ToHit Buffs effectively to ignore Defense and (2) the ability of small amounts of Defense to add up to massive amounts of mitigation as you get close to the 45% soft cap (e.g., the ability to build perma-Elude SR scrappers, etc.)? Is there something else that I'm missing?
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That's a bit of an oversimplification, and the original post outlines the specifics in more detail, but that's not far from the truth. (2), for example, cripples power pool defenses, and makes Force Fields problematic. In fact, FF highlights two simultaneous problems: for the cost of maneuvers, FF can Elude an entire team. Conversely, its own self-protection tends to be low, unless it really stacks power pool defenses for self protection, and then it can be pretty darned high.
As to tohit buffs, there's a dual problem to those. If I get 100% defense, *no* amount of tohit buffs do anything, until you cross the magic 45% net tohit number, and then every point of tohit buff above that has *massive* effect. That's bad for everybody.
Technically, the two problems are stacking mechanics, and extrinsic balance design objectives. But there's a lot of game mechanics buried in those two phrases.
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This is a fair point.
I just question the extent to which "adding one thing" to an already combersome formula is a good idea -- at this point, I think subtraction would be more beneficial than addition.
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Whether it is or isn't is virtually irrelevant. The devs would not pull the mechanics of defense and rebalance every single defensive power and ability for both players and critters around a new version of it in a single giant patch if their very existence as a development house depended on it. Its simply outside of their concept of proper lifecycle support of the game.
And to be honest, even I wouldn't do anything that crazy.
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So basically, this is a supersymmetry theory for "Chance to Hit."
<ul type="square">[*]ToHit = Additive increments in the Chance to Hit. A 20% ToHit Buff on the base Chance to Hit of 50% = 20+50 = 70% Chance to Hit.
[*]Accuracy = Multiplicative scaling in the Chance to Hit. A 20% Accuracy Buff on the base Chance of 50% = 1.2*50 = 60% Chance to Hit.
[*]Defense = Additive increments that are subtracted from the Chance to Hit. A Base Chance to Hit of 50% v. 20% Defense = 50-20 = 30% Chance to Hit.
[*]Anti-Defense (Elusiveness) = Multiplicative scaling reducing the Chance to Hit. A Base Chance to Hit of 50% v. 20% Elusiveness = 50/1.2 = 42% Chance to hit.[/list]
Arcanaville, are there any cases where the Base to Hit is over 100%? Because that would make Accuracy and Elusiveness start to become much bigger buffs than ToHit or Defense.
And are there any cases where the Base to Hit is under 5%? Because that would trivialize the effect of Accuracy and Elusiveness.
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Arcanaville, are there any cases where the Base to Hit is over 100%? Because that would make Accuracy and Elusiveness start to become much bigger buffs than ToHit or Defense.
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Sure: with sufficiently high tohit buffs, you could increase your net tohit before accuracy (and Elusivity) to over 100%.
As a matter of fact, tohit aint capped at all.
However, whether this would be true with the implementation of Elusivity is a complex issue: with Accuracy and no Elusivity currently, Accuracy can (usually) only make tohit larger (I'm aware of powers with intrinsic acc < 1.0), so its not very meaningful most of the time if the 95% ceiling is enforced on intermediate values. That's something that would have to be considered carefully, based on how the powers are going to be designed around it. It could go either way there.
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And are there any cases where the Base to Hit is under 5%? Because that would trivialize the effect of Accuracy and Elusiveness.
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In this case, no, because I'm not tampering with the current tohit algorithm, and the current algorithm places a 5% floor on interim tohit before Accuracy.
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I don't think it is preferable -- it's just what we already have. TBH, I like your suggestion a lot more. Things would be a lot simpler and more understandable if they changed all of the ToHit buffs into Accuracy buffs and all of the Defense buffs into Arcanville's Anti-Accuracy. The thing is though, actually implementing the change would likely not be simpler.
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I'm not clear on why it is that eliminating the distinction between ToHit and Accuracy (something I've been suggesting occasionally for about the last year) and making defense purely multiplicative (something I've been suggesting for even longer) is inherently more complicated than what Arcanaville is suggesting here, and maybe I'm just missing something.
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It wouldn't be if we had a "multiplicative version of Defense" already in the game. We don't have a multiplicative version of defense though. Adding that is essentially what Arcanaville is suggesting with Anti-Accuracy. Once you add in a multiplicative Defense mechanic to the game, you'd then be free to eliminate ToHit buffs and Defense buffs from the ToHit formula, but you have to add that first.
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But it seems to me that both approaches involve a fundamental change to the ChanceToHit equation -- the change you'd have to make to implement this Elusivity business is pretty much identical to what you'd have to do to implement my version. In fact, what I'm suggesting is essentially a special case of Arcanaville's suggestion, with what are currently called "Defense" and "ToHit Buffs" set identically to zero.
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Exactly. The thing I don't know is if you could just plug in the original Defense and ToHit percentages into the Anti-Accuracy and Accuracy variables in Arcana's formula without modifying their magnitude and/or rebalancing the powers by hand. If you can do that in the majority of the cases, then the change could be much simpler than I imagined.
I'd really have to play with the formula and some real powers numbers to see though -- there's too many distractions around me right now to really do that though. (I can tell you now that a majority of the defense set bonuses from inventions would be absolute crap under a multiplicative system.)
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The coding therefore should be pretty much the same -- the only difference is in balancing. To be honest, since my version has fewer variables, I feel like it would be easier to balance.
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It probably would be -- once you're done implementing it -- but doing all that work at once is where the potential pit fall is. In the long run eliminating "Defense" in favor of "Anti-Accuracy" and "ToHit" in favor of "Accuracy" would do more to balance this game than any other change they could make for the man hours -- but they still have to come up with those man hours. I just don't think there's enough in an Issue release cycle. There probably is in an expansion release cycle, but we don't even know for sure that they'll be doing those again. (It's likely, I think, but I haven't seen any guarantees.)
On a side note to go with what you and Arcanaville are discussing: any mechanic that requires as much explanation as the current ToHit mechanic and Arcana's minor modified ToHit mechanic just isn't good game design -- even if it's mathematically sound. Game developers, by and large, are math hacks at best. If a mechanic cannot be intuitively understood, then it's going to be abused and misused. It's even worse when your intuitive understand is often flat out wrong -- and I think ToHit/Defense/Accuracy falls directly into that category.
Even though its complicating things, adding in "Anti-Accuracy" will probably help correct that intuitive (mis)understanding since now you'll be able to compare apples-to-apples. ToHit will compare directly to Defense, like it always has, and Accuracy will finally compare directly to Anti-Accuracy. You won't need to compare accuracy to ToHit or Defense anymore, and that alone will help things quite a bit, I think.
So basically, this proposal would decrease the efficiency of To Hit Buffs? ( I am not very great at maths )
If To Hit Buffs really get lowered i am concerned that i will have a very very hard time when fighting enemies that heavily use To Hit Debuffs. Nerva Spectral Demons and stuff like that are a real pita once you are debuffed. The only char i have who seem to hit them reliably is my SS tanker with Rage on.
I find it really irritating that my scrapper attacks that are slotted with 3 Acc SOs simply cannot overcome To Hit Debuffs while my tanker is nailing them just fine with only Rage and 21% global IO accuracy running.
If To Hit Buffs are to get nerfed then i strongly suggest that To Hit Debuffs potency also be looked at.
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My preference is to make the mechanics as simple (if I were being snooty, I'd say "as elegant") as possible. The whole point of the to-hit formula is to create a need to make sure that you can hit your targets -- and, conversely, to allow you to mitigate damage by dodging their attacks. You only need two things to do this: a way to make your attacks more likely to hit (either through acc buffs or def debuffs -- I count those as identical, since they are mathematically indistinguishable), and a way to make your enemies' attacks less likely to hit (either through tohit debuffs or def buffs -- again, mathematically identical).
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Technically, the only things you need after that are damage, and the ability to reduce damage. You don't need smashing, lethal, fire, energy, psionic - unless you actually feel making the game more complicated is worth introducing the ability to have different strengths and weaknesses.
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The difference here is that there is an obvious conceptual reason for different damage types -- different attacks do different things. Setting someone on fire at someone isn't the same as slicing his face off, and there isn't any reason to think that everyone should be equally vulnerable to both types of damage. (I would in fact argue here that more damage types are desirable -- whay are electricity, radiation and sound all "energy" damage? Sound waves should probably be pure smashing, but electricity needs its own type -- a leaden suit will block radiation but conduct electricity.)
Basically, damage types aren't unnecessary complexity -- getting rid of those would clearly detract from your ability to model realistic superheroics.
The situation is different with chance-to-hit: you aim at your target as best as you can, and try to hit him. He tries to dodge or deflect the blow if he can. That's it.
You might add some other features into this, like a "glancing blow," wherein rolls that are close to the boundary do partial damage. But there's little conceptual reason to make things more complicated than that.
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If I was designing the game system from scratch, I might have considered making positional and damage-oriented defense multiplicatively stack with each other (basically, both get to be used separately against all attacks). I could then invent something called the "precision buff" that would act like tohit buffs, and counter positional defense, say, and something else called "penetrator buffs: that would act like tohit buffs, but counter damage-oriented defenses instead. They would be the accuracy-based versions of the concept of "armor-piercing" except one of them would represent the intrinsic ability to compensate for a moving target, and the other would represent the intrinsic ability to negate physical deflection-based protections.
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Two problems with this: (1) you're basically assuming that positional defense always represents a dodge, and damage-typed defemse always represents a deflection. That's not the case -- look at Heightened Senses, just as an example. (2) More importantly, having any form of accuracy buff that "penetrates" defense additively is prone to imbalance. Essentially, you're leaving the door open for exactly the problems that necessitated the I7 change -- the same amount of defense provides a different proportion of protection depending on the accuracy boost.
In fact I think that's the main reason I'm still objecting to your approach: it still leaves the door open for those additive buffs/debuffs. Those are always a bad idea, for reasons that are not always obvious, so I'd rather remove even the ability to include them.
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But on a pragmatic level, there is another reason to keep both types of defenses around. Its a failsafe to prevent external overbuffing from getting out of hand. All other things being equal, it should be a lot easier for player Y to negate (but no more than negate) what player X buys, than it is for player X to buy it.
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I'm not sure I agree with this at all, simply based on symmetry arguments: you seem to be saying that it should be easier to negate (but no more than negate), say, 30% def than it is to acquire that defense.
Conversely, it should also be easier to negate +30% tohit than it is to acquire 30% to hit.
I have trouble seeing how both can hold true at the same time, short of some kind of diminishing returns system. In any case, I don't see why buying X and buying -X shouldn't have roughly equal costs.
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Whether it is or isn't is virtually irrelevant. The devs would not pull the mechanics of defense and rebalance every single defensive power and ability for both players and critters around a new version of it in a single giant patch if their very existence as a development house depended on it. Its simply outside of their concept of proper lifecycle support of the game.
And to be honest, even I wouldn't do anything that crazy.
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I'm quite sure you're correct, and, to be honest, I doubt that at this stage, anything is going to happen at all -- hence my earlier remark that this discussion is likely more relevant to the question of how they should make CoX 2.
With that said, I don't understand why there's this concept of "rebalancing every defensive power" as some sort of a huge project. It wouldn't be. You simply have to come up with a relationship between current defense and new "anti-accuracy" -- i.e., describe a transformation from current defense to new defense -- which gives the desired behavior -- i.e. comparable to current protection at moderate levels, less broken at the margins -- and then with that formula in hand, you just go through and change the values appropriately. I'd budget two hours, tops, to get the math worked out. Then, obviously, you have to spend some time testing -- say, 10-15 hours. Then I guess there's also the time spend diddling around with the spreadsheets. The whole thing should be done in less than 20 man-hours, plus whatever time you have to spend recoding. (Since we're both talking about roughly equivalent code changes, I figure that the coding time is a wash.) A half a work week to fix and simplify tohit/defense, and to make it impossible to re-break it, seems to me to be a worthwhile investment.
Now, if their approach to balancing is "Hmmm... these numbers look about right. Let's test. Oh, guess not. Let's tweak some... how about now? No? Okay, how about this?" then it would be a huge project. But if you take the time to analyze first, then it's straightforward.
Of course, somehow I don't think Positron or Castle will see it that way.
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Two problems with this: (1) you're basically assuming that positional defense always represents a dodge, and damage-typed defemse always represents a deflection. That's not the case -- look at Heightened Senses, just as an example. (2) More importantly, having any form of accuracy buff that "penetrates" defense additively is prone to imbalance.
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1. If I'm designing the game, *I* say what positional defense means.
2. "Balance" is not a singular objective. When balancing powersets the issue is stability. When balancing things like inspirations the issue is not stability, but counterbalancing.
In more mathematical terms, at least most of the time (short of "Kryptonite") when a powerset offers X mitigation with defense, it should offer that same proportional mitigation in the face of all attackers. But when an inspiration offers Y amounts of incrementally better protection, there has to be a counter inspiration that removes that same level of Y protection, or else PvP breaks down.
Those two requirements cannot trivially be met with a single mode of defensive mechanics. This was discussed in great detail in the original thread.
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With that said, I don't understand why there's this concept of "rebalancing every defensive power" as some sort of a huge project. It wouldn't be. You simply have to come up with a relationship between current defense and new "anti-accuracy" -- i.e., describe a transformation from current defense to new defense -- which gives the desired behavior -- i.e. comparable to current protection at moderate levels, less broken at the margins -- and then with that formula in hand, you just go through and change the values appropriately.
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Nope, and for the very reason you like the math: stacking works differently. Because stacking works differently with the two modes of defense, in a sense there is no "correct" correspondence between dispersion bubble with Defense and dispersion bubble with Elusivity/Anti-Accuracy because there is no value that would make Dispersion Bubble have the same strength relative to the defender and also the same stacked strength on all of his teammates that are bubbled.
So for all cases where defense stacks - FF, Invuln, SR, power pools, etc - a human being actually has to "redecide" what the "correct" strength values are, because +Elusivity cannot exactly replicate +Defense. That's actually the whole point. If DB is calibrated to add the same thing to bubbled teammates than it does now, the defender will end up with more self-protection (that's probably desirable). But if its straight-converted without taking stacking into account, team mates will have less protection than they do now.
A human being rebalancing defense sets one at a time is basically mandatory. If there was a way to do it automagically, I would have suggested it.
Edit: forgot to mention: debuffs, and critter defenses. Right now, its possible to buy your way past Paragon Protector MoG with BU and insights, and that is strictly intentional. Without *both* keeping the current mechanics around, *and* proper rebalancing, PvE changes dramatically, and its all fine and good to say "so what, its better that way anyway" but actual game designers functioning in a live game do not have that luxury. Again: *sometimes* balance means "stability" and sometimes it means "move-countermove" and both are important in different situations.
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1. If I'm designing the game, *I* say what positional defense means.
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Touche. 
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In more mathematical terms, at least most of the time (short of "Kryptonite") when a powerset offers X mitigation with defense, it should offer that same proportional mitigation in the face of all attackers. But when an inspiration offers Y amounts of incrementally better protection, there has to be a counter inspiration that removes that same level of Y protection, or else PvP breaks down.
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I must be missing something here, because I'm not seeing why a purely multiplicative mechanic wouldn't work. Just to be clear, by that I mean that all accuracy and defense powers stack multiplicatively:
p = Pi(Ai)*Pi(1-Di)*p0,
where Pi denotes a product over the index i, the Ai and Di are accuracy and defense adjustments (both buffs and debuffs) p0 is base accuracy, and p is final chance to hit. This formula -- with nothing additive -- is the simplest approach which, I believe, has the necessary balance (in all senses of the word) properties.
Let's say I have a powerset that I want to provide 75% mitigation normally, and I have two powers to do it. With a multiplicative scheme, I can have two powers which each provide 50% mitigation: then my incoming damage is reduced by a factor of 1-0.5*0.5=0.75. So that's the first part okay.
For the second part, I simply need my accuracy and defense inspirations to have a reciprocal relationship:
1+A=1/(1-D), or A=D/(1-D).
Then a 25% defense inspiration is precisely balanced by a 33.3% acc inspiration, etc. So it seems to me that this approach is successful both in the stability and counterbalancing depertments. I realize that the multiplicative stacking is basically what you're asking for with Elusivity. I'm simply claiming that you don't add significant value by including additive stacking as well.
In fact, having both kind of stacking stikes me as likely to muddy the waters, making mathematical balance more difficult to achieve.
(Incidentally, making resistances stack multiplicatively would also have a number of benefits -- for example, as you point out in the context of SR, you could make passives and toggles both stronger individually, while maintaining a consistent level of overall protection. Given the number of complaints about passive resists in Invuln, etc., this strikes me as an eminently good idea. Basically, it just means that now ALL of your mitigation is automatically layered.)
Since it hasn't been addressed yet:
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So basically, this proposal would decrease the efficiency of To Hit Buffs? ( I am not very great at maths )
If To Hit Buffs really get lowered i am concerned that i will have a very very hard time when fighting enemies that heavily use To Hit Debuffs. Nerva Spectral Demons and stuff like that are a real pita once you are debuffed. The only char i have who seem to hit them reliably is my SS tanker with Rage on.
I find it really irritating that my scrapper attacks that are slotted with 3 Acc SOs simply cannot overcome To Hit Debuffs while my tanker is nailing them just fine with only Rage and 21% global IO accuracy running.
If To Hit Buffs are to get nerfed then i strongly suggest that To Hit Debuffs potency also be looked at.
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No, your ability to hit PvE enemies would not be hindered in any way (unless the devs decide to change particular enemies' protection from Defense to Elusivity). It only affects players (again, assuming the devs give players only Elusivity), meaning that it becomes harder for enemies and players to strip away things like SR or Ice Armor with debuffs or toHit buffs.
In essence, it's a PvP buff that happens to buff players in PvE too.
We'll always have Paragon.
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Nope, and for the very reason you like the math: stacking works differently. Because stacking works differently with the two modes of defense, in a sense there is no "correct" correspondence between dispersion bubble with Defense and dispersion bubble with Elusivity/Anti-Accuracy because there is no value that would make Dispersion Bubble have the same strength relative to the defender and also the same stacked strength on all of his teammates that are bubbled.
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But see, with the multiplicative system, it would, for any value, have precisely the same relative effect on the defender as it has on his teammates: 30% defense would block 30% of incoming damage, whether you're a defender with no additional mitigation or an SR who's already dodging 60% of the time. (At least, it works this way until you run into the caps.)
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A human being rebalancing defense sets one at a time is basically mandatory. If there was a way to do it automagically, I would have suggested it.
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I don't disagree with this -- and I realize that I'm not particularly clear on this point based on what I said earlier. (I might have gotten myself mixed up based on which formula I was thinking about at the time, FWIW). Still, I don't think it's a particularly difficult math problem to figure out how much mitigation you want from each set and adjust accordingly. If I thought that anyone would pay attention, I'd go ahead and come up with what the new values "should" be to keep the mitigation levels as they are currently in the absence of inter-set stacking -- this part is honestly quite trivial.
The tricky part then is looking at how they interact through stacking. As you note, they would stack differently than they do now: that's kind of the whole point, isn't it?
To do this, you have a number for overall mitigation from each set. You can find the overall mitigation from combinations by simple multiplication, and you just have to look and make sure these aren't broken. Obviously, then, you have to play test to make sure what you've got on paper ends up working in-game -- but doing the stuff on paper is a pretty simple process, and one which makes an overall defense rebalancing at least plausible.
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The tricky part then is looking at how they interact through stacking. As you note, they would stack differently than they do now: that's kind of the whole point, isn't it?
To do this, you have a number for overall mitigation from each set. You can find the overall mitigation from combinations by simple multiplication, and you just have to look and make sure these aren't broken. Obviously, then, you have to play test to make sure what you've got on paper ends up working in-game -- but doing the stuff on paper is a pretty simple process, and one which makes an overall defense rebalancing at least plausible.
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What I'm trying to say is that this is not a calculation problem, and therefore there's no mathematical way to get the "correct answer."
Picture an FF defender, with maneuvers. The FF defender has a certain level of mitigation X, all by himself, with dispersion. The FF defender provides a certain level of mitigation Y to his allies, with his bubbles. He provides a further level of protection Z, when those allies happen to stand under the dispersion bubble. And when the FF defender turns on maneuvers, everyone's protection changes again.
Its impossible for multiplicatively stacked defenses (Elusivity) to replicate that situation, period. You'll be able to exactly replicate just *one* of those situations, if any. A human being will have to decide which of those they want to preserve as the "right behavior" and then figure out which of the others they want to get *close* to, and which ones they don't mind changing completely, and *then* solve mathematical equations to get the values for all of those powers.
The math is easy. The "who decides which of those is 'working as intended'" is hard. Because you're going to end up screwing with somebody.
And that will kill the idea dead. Mine sidesteps that problem completely.
This was an interesting exercise, the first time I read it, because it took a while for the point of the post to really be recognized. The most difficult part about addressing these issues is not the technical work involved in implementing the solution at all. Its implementing one that everyone can buy into as not causing dramatic problems - and I say "everyone" to include the devs. As hard as it would be to tinker with the tohit algorithms, the political hurdles to making any game mechanical change are ten times higher.
This solution eliminates 90% of the problems associated with attemping any solution, leaving only the remaining 10% of actually doing it, which is itself not a trivial problem. But any solution that focuses on the 10% technical piece, while ignoring the 90% "its never going to happen" piece, is playing a purely hypothetical exercise.
Even as it stands, the odds of making a change to the core tohit algorithms is very close to a "never going to happen" just by fiat. But one that also requires Castle to rebalance all defense powers for players and critters in one single Issue and significantly alters PvE play across the board, and requires retesting of a significant amount of game content prior to release, is literally, 100%, absolutely never going to happen.
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Its impossible for multiplicatively stacked defenses (Elusivity) to replicate that situation, period. You'll be able to exactly replicate just *one* of those situations, if any.
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I had sort of thought that one of the major purposes in changing the tohit equation is to correct the fact that stacked defense becomes too strong unless it's left at values so low as to be meaningless. So the fact that you aren't replicating the levels of protection that you get when you're stacking defense from three different sources isn't a problem to be worked around; rather, it's the motivation for making the change in the first place.
In any case, I'd thought I'd made the first-order balance point clear: the mitigation provided in toto by each set should remain unchanged. The individual components of each set would therefore need to give more protection, while multiply stacked sets would give less than they currently do.
Again, that's not an unintended consequence which I need to work around: it's the entire purpose of changing defense to multiplicative stacking.
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The math is easy. The "who decides which of those is 'working as intended'" is hard. Because you're going to end up screwing with somebody.
And that will kill the idea dead. Mine sidesteps that problem completely.
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I'm not sure that I agree with this argument. You seem to be advocating a wholesale change of the ToHit equation, while touting the fact that it's possible, under this change, to leave things exactly as they are.
If things are okay as they are, there's no need for a change in the first place. If they need to be changed, then rejecting a proposal on the grounds that it forces you to deal with wholesale balance changes is hardly a wise position.
Basically, I agree with you that any change in the ToHit equation at this stage has approximately zero probability, unless they do a wholesale rewrite of the game engine.
My point is simply that if they're going to take the time to rewrite the ToHit equation, they would be utterly foolish not to simultaneously deal with the imbalances that made the changes desirable in the first place.
Additionally, I'm not sure that it's necessarily better to make the changes piecemeal. Given that it will represent a significant change to both PvE and PvP (if it doesn't, why bother with it in the first place?), wouldn't it be better to get it done all in one fell swoop, rather than run into the I4-I6 situation where you have constant major adjustments over the course of most of a year?
In any case, all of my arguments are predicated on the notion that it's easier to balance powers -- you basically need a calculator, pencil and paper, and then a spreadsheet -- than it is to dig through the code (much of which currently seems to be something of a black box even to the developers) and reprogram stuff. If that's not the case, if it's actually fairly easy to mess around with the ToHit equation, then everything I've been saying goes out the window, and I'd have no further objections to your proposal.
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I'm not sure that I agree with this argument. You seem to be advocating a wholesale change of the ToHit equation, while touting the fact that it's possible, under this change, to leave things exactly as they are.
If things are okay as they are, there's no need for a change in the first place. If they need to be changed, then rejecting a proposal on the grounds that it forces you to deal with wholesale balance changes is hardly a wise position.
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I'm not advocating a wholesale change to the tohit algorithm. I'm advocating adding one additional type of effect to it, while leaving the rest completely intact and functioning exactly, precisely as before. And I've given the reason why: so that the day after the change is made to the tohit algorithm the game remains exactly, precisely the same.
Things are not ok, which is why I'm advocating adding a tool that can help fix it. I'm not advocating changing the way all of the existing powers work wholesale because that's not the goal or the responsibility of the game mechanics implementers.
I'm recommending an addition to the existing toolbox of damage mechanics, and while I wear that hat, I have no right to dictate what the game designers do with it. Once its added, I'm free to take up the discussion of the best way to make use of it with the game designers, and as I've articulated in the OP, there are lots of good reasons for using a mixture of both, in a way that preserves certain behaviors that are *better* than any game that only uses one.
Better, at least, in my judgement, and I'm very specific as to why I think its better. All of this is better addressed in the OP.
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*cough*
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It would take too long, and be wholely uninteresting, for me to state all the ways this makes more mathematical sense. So let me put it this way, it makes me happy, and if it makes me happy, I won't complain as much when NCNorCal finally implements this solution. That's worth a lot, actually, especially to NCNorCal
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Ya still need to fix this, m'lady. 
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*cough*
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It would take too long, and be wholely uninteresting, for me to state all the ways this makes more mathematical sense. So let me put it this way, it makes me happy, and if it makes me happy, I won't complain as much when NCNorCal finally implements this solution. That's worth a lot, actually, especially to NCNorCal
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Ya still need to fix this, m'lady.
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Past the editing window. But heck, Cryptic should probably also fix this before I'm in a position to complain about it. 
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I've been a bit slow responding to this, because I've been trying to figure out the best approach to take. I guess I'll first answer a couple points in this post that I particularly want to address; then I'll make a final post where I summarize my objections to the proposal in a more organized form than I have so far. I realize that I'm not likely to convince you of the correctness of my position, since I think some of the disagreement stems from irreconcilable differences in design philosophy. But I still think it's useful to have the opposing viewpoint expressed.
Anyways, here goes:
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I'm not advocating a wholesale change to the tohit algorithm. I'm advocating adding one additional type of effect to it, while leaving the rest completely intact and functioning exactly, precisely as before.
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In some sense, I'll concede that you're correct, in that you wouldn't have to change anything after you'd added your parts. That's not what I'm arguing. I'm arguing that the very fact of getting under the hood and adding terms to the tohit equation constitutes fundamental change -- it doesn't matter much if its and addition or replacement, as far as I'm concerned, in terms of the programming work involved, which, as I've said, strikes me as likely to be the greatest barrier to execution.
Let's be completely clear on this: you are proposing the addition of multiplicatively stacking defense terms to the tohit equation. Whether or not you leave the additively stacking terms in or not, this represents fundamental change. Nothing in the game that I am aware of stacks mltiplicatively. Nothing.
Not that I don't think that multiplicative stacking is a great idea, for reasons that I've already discussed, and for reasons that I'll clarify in my next post. But I have trouble accepting your optimistic appraisal of its ease of implementation. I can't imagine that the programming would be easier than, say, adding Toxic Defense.
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I'm recommending an addition to the existing toolbox of damage mechanics, and while I wear that hat, I have no right to dictate what the game designers do with it. Once its added, I'm free to take up the discussion of the best way to make use of it with the game designers...
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This is not a useful distinction in this context, I don't think, at least as far as I'm concerned.
The only "hat" I'm wearing here is that of an interested, well-informed (I'd like to think) player with some degree of mathematical agility (okay, I'm pretty sure about that one). If I were actually working for NCNC, I might feel more of a need to refrain from allowing design concerns to enter consideration of the mechanics. Since I'm not, I don't particularly see a reason to draw a distinction between the role of a game mechanic implementor and a game designer -- neither one of those is a role I can actually play unless I'm on the payroll.
Also, what I'm suggesting amounts to a mechanical change -- the current mechanics are mathematically pernicious, and adding new mechanics while simultaneously allowing the broken mechanics to survive is not advisable.
If you don't want game design considerations to enter your development of the mechanics, then neither should you rely upon the mathematical acumen of the designers to ensure that the mechanics remain stable: the distinction, if you want to make it, should cut both ways.
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Nothing in the game that I am aware of stacks mltiplicatively. Nothing.
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If there is ever the case that there is more than one Accuracy modifier (not even sure if it would ever happen, but if there were to be more than one Accuracy modifier) then it would stack multiplicatively.
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If you don't want game design considerations to enter your development of the mechanics, then neither should you rely upon the mathematical acumen of the designers to ensure that the mechanics remain stable: the distinction, if you want to make it, should cut both ways.
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The current Chance to Hit mechanic already relies on human developers to manually balance each power. After adding Elusiveness, then the Chance to Hit mechanic will still rely on human developers to manually balance each power, only now, they'll have on more tool to tweak, one that is not as heavy-handed as additive Defense bonuses.
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If there is ever the case that there is more than one Accuracy modifier (not even sure if it would ever happen, but if there were to be more than one Accuracy modifier) then it would stack multiplicatively.
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Maybe so, and that's basically what Arcanaville is talking about adding, but the fact remains that as it now stands, every single attribute that can stack with itself does so additively.
As I've said, I think that additive stacking is mechanically poor, and is conducive to poor design, but that's where we are right now, and I wouldn't make any assumptions about the feasibility of changing it.
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The current Chance to Hit mechanic already relies on human developers to manually balance each power. After adding Elusiveness, then the Chance to Hit mechanic will still rely on human developers to manually balance each power, only now, they'll have on more tool to tweak, one that is not as heavy-handed as additive Defense bonuses.
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I'll discuss this more later, but my complaint isn't with the need for human input into balancing. It's that I don't think that giving them more tools to tweak is a good thing: ToHit is too complicated already. Rather, they should have different tools. Simpler tools. Tools that are less likely to cause things to break.
My point here was simply that a good set of game mechanics is one in which the game designers can do whatever they want (within reason, obviously) without causing pernicious behavior -- i.e., it should be robust. The current system -- and, I would argue, any system which includes additive stacking -- is just the opposite: there's a fairly narrow set of parameters which don't cause bad behavior.
<QR>
Okay, reading comprehension FTW: for some reason, I thought that anti-accuracy would just add with accuracy, instead of multiplying.. Having gone back over the OP more carefully, I can see I was misreading, and that eliminates one of my major objections.
I wonder, however, how this is preferable to simply making all accuracy modifiers multiplicative, and eliminating the distinction between ToHit and Accuracy.
Just pulling numbers out of a hat as an example, suppose I've got Aim (+100% acc), 1 Acc SO (+33% acc) and I'm shooting at a guy running Focused Senses (+50% def) and Agile (+20% def). My base chance to hit is 75%. My actual chance to hit would be
75%*2*1.33*0.5*0.8=80%
Aside from getting the right numbers for proper balance, can anyone explain why it would be preferable to have two kinds each of +accuracy and +defense?
To me, that just adds unnecessary complexity.