How *Should* Defense and Resistance Formulas Work?
By
Arcanaville,
Posted on: 2011-05-05 04:26 in CoH and CoV General Discussions
I think defense should be similar to an attack. If your defense fails maybe 90% normal damage for high defense toons, on a standard miss half damage with critical misses causing no damage, to make it more desirable.
I like the system we have now. I'd prefer if the cap on certain things (such as max HP) was raised considerably for melee archtypes, and would like to see force fields, fortitude, etc., give bonuses to max HP. This way they'd help even softcapped characters, and would help make them feel "tougher", and make defense less "Amazing, then dead". Oh, and scrappers would get a slight boost to their resist cap.
TW/Elec Optimization
Mathematically, the easiest thing to do is 1% resist = 1% decrease from current damage taken. So, if you start from 100%, then 1 resist = 99% damage. Then 2 resist = 99% damage reduced by 1% = 98.01% damage. .99 ^ resist value.
When adding one percent it's not much difference, but 50 resist is still taking 60% damage instead of the 50 it takes now, and 90% is still taking 40% damage. It means you can have meaningful values available for everyone and stacking another X points of resist has the exact same effect for everyone.
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... So you want to replace one of the two most common calculations the server has to perform from a simple multiplication to an exponential function and you call it "mathematically easy"?
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Originally Posted by rsclark
Mathematically, the easiest thing to do is 1% resist = 1% decrease from current damage taken. So, if you start from 100%, then 1 resist = 99% damage. Then 2 resist = 99% damage reduced by 1% = 98.01% damage. .99 ^ resist value.
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Originally Posted by kusanagi
... So you want to replace one of the two most common calculations the server has to perform from a simple multiplication to an exponential function and you call it "mathematically easy"?
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Well, the current "simple multiplication" is broken as heck.
His/her system actually is a lot more reasonable. If it were applied to defense, you wouldn't have to worry that giving a player +5% defense from a power means doubling survivability due to stacking, or that it will do nothing at all because they are over the cap. Its basically a series of dimishing returns. I'm trying to think through a system of "competitive values" where your target defense numbers mostly have meaning in relation to the enemy you are trying to dodge, but I haven't gotten there yet.
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Exponential functions are actually pretty easy for computers, a consequence of being base 2. And actually almost all math is determined through a derivative of exponential functions with computers.|
Originally Posted by kusanagi
... So you want to replace one of the two most common calculations the server has to perform from a simple multiplication to an exponential function and you call it "mathematically easy"?
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While I feel the explanation is clumsy, I do say that a slope of defense effectiveness can be useful, other games do it as well, but they'll label the state as a defense rating or score, and then derive a percentage from that to show the player. The consequence of that is it's harder for squishy characters to stop being squishy.
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I agree with Rsclark.
With current system, your ability to take attacks do not increase linear (as damage buffs do) or exponential (as Rsclark suggest), but asymptotic, an extreme form of faster than exponential growth. You reach an infinite value (division by zero) upon reaching a finite parameter (50%). When soft-cap kicks in, you're 10 times stronger (+900%) in terms of receiving attacks.
Let's compare the effects of defense buffs to damage buffs. If you add 1% to 44% defense, you will take 16.667 percent (1/6) less damage in the long run. If you want to achieve that 16.667 percent by increasing your DPS, you need 20 percent higher (6/5) DPS. In addition, damage buffs from IO set bonuses do not multiply with damage buffs from enhancements. If you have +90% damage from enhancements, you need a whooping +38% damage from IO sets to raise your DPS by 20 percent. At that point, one unit of defense buff is worth 38 units of damage buff.
It's of course correct that defense buffs should yield more than damage buffs in terms of survival, but maybe not 38 times more...
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To a large extent, the non-linearity of defence and resistance comes from how we calculate "mitigation." The formula for damage resistance itself is pretty simple:
FinalDamage = Damage*(1 - Resistance)
This a perfectly linear function, at least for a static amount of damage. The problem comes when you start comparing the damage you would have taken without resistance to the damage you took with it, which looks something like this:
Mitigation = Damage/FinalDamage = Damage/(Damage*(1 - Resistance)) = 1/(1 - Resistance)
This is no longer a linear function. I'm not sure what that one's called in English (fractional or rational, I think), but it is both discontinuous and infinite in at least one place. For Resistance values of 99.99999..., "Mitigation" approaches infinitely large numbers. However, for values of 100.00000...001, "Mitigation" approaches infinitely large NEGATIVE numbers (negative infinity). And here's the clincher - this is independent of the formula for calculating our final resistance numbers from our final stats.
What I'm saying is that no matter what you do to player stats, mitigation will always look like this at the end of the day. The only way to "straighten the curve," as it were, is to give players a diminishing return on their actual resistance from whatever fake "resistance ratings" you supply them with, and all THAT does is clue savvy players in on the fact that a resistance rating past a certain point is pointless because the returns are too poor. In essence, you're trying to suggest Defence/Resistence Diversification by wrapping it up in a mathematical discussion.
Resistance decreases damage taken my a percentage from that damage. Unless you mess with this fundamental mechanic, you will always end up with a fractional function that's discontinuous around 1.0 (100%) and tends towards positive infinity near that mark. Messing with this mechanic, furthermore, is really not something I'd want to try my hand at. The only other even remotely logical mechanic you can apply is a straight damage point nullification, where if you have a 150 resistance rating, it means you resist 150 points from every attack, but this is even more dangerous in that it creates far more situations of complete immunity and far more situations of useless resistance. At least when you resist 50% of every physical attack, you have the same degree of mitigation against both weak and strong attacks, and so the developers don't have to be as skittish about varying enemy damage levels.
P.S. I chosen to speak about defence as the explanations are more complicated but the formulas aren't much more complex.
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Originally Posted by Arcanaville
Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.
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I, personally, find it odd that 45% def is twice as effective as 40%. I find it even weirder that 45% def means that a mob will hit only 5% of the time.
Also ... the defence caps for the individual ATs are so high as to be completely meaningless. With I7, the devs should've taken a page from resistance and instituted meaningful def caps along the lines of: 50% tankers / 50% brutes; 42.5% scrappers / stalkers; 37.5% everyone else.
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For a computer? Yes. In fact, it's pretty common for board and tabletop RPGs, too. Any time you roll X dice and succeed if you get a 6, you're using a similar probability calculation.
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Originally Posted by kusanagi
... So you want to replace one of the two most common calculations the server has to perform from a simple multiplication to an exponential function and you call it "mathematically easy"?
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See, that part I disagree with, and that's the reason I put up my version. With my version, 10 resist would always decrease incoming damage by around 9.6%. It could be the first 10 defense or it could be you going from 1000 to 1010, but in both cases, your incoming damage is reduced by an identical percentage. |
Originally Posted by Samuel_Tow
What I'm saying is that no matter what you do to player stats, mitigation will always look like this at the end of the day. The only way to "straighten the curve," as it were, is to give players a diminishing return on their actual resistance from whatever fake "resistance ratings" you supply them with, and all THAT does is clue savvy players in on the fact that a resistance rating past a certain point is pointless because the returns are too poor.
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It's a diminishing return, but since the damage you are taking also decreases as you go along, it has to be diminishing in order for the ratios to remain constant.
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Base enemy to-hit chance is 50%, and defence is subtracted linearly from this. Because you can never be allowed to reduce enemy chance to hit you down to 0% (which would equate to effective immortality), enemy to-hit is never allowed to drop below 5%, so the most you can subtract from their 50% base is 45%.|
Originally Posted by BurningChick
I, personally, find it odd that 45% def is twice as effective as 40%. I find it even weirder that 45% def means that a mob will hit only 5% of the time.
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The reason 45% defence is twice as good as 40% defence is because at 40% defence, your enemies have a 50-40=10% chance to hit you, while at 45% defence, they have a 50-45=5% chance to hit you. Half the chance to hit, twice the chance to miss, twice the mitigation.
Neither of those is specifically programmed into the system, in that no-one sat down and said "We want defence to soft-cap at 45% and it we want it to be half as strong at 40%." This is just how the numbers work out when you run them through what are, frankly, pretty basic formulas, even with enhancement accuracy, native power accuracy and enemy level and class modifiers. It's lots of numbers, but at the end of the day, the numbers they spit our still behave the same.
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Originally Posted by Arcanaville
Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.
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The other advantage of incremental multiplication over summation is that the values of given powers actually mean something relatively intuitive, even if the calculation is more complex. If total chance to hit is calculated using the formula:
0.5 * (1 - D1) * (1 - D2) * (1 - D3)...
and total damage admittance is calculated with:
1 * (1 - R1) * (1 - R2) * (1 - R3)...
then it's easy to say what a power that grants 5% defense or resistance does: it reduces your incoming damage by 5%. On the other hand, when the formula for tohit is
0.5 * (1 - (D1 + D2 + D3...))
and admittance is
1 - (R1 + R2 + R3...)
then the amount of mitigation provided by a given power depends heavily on your existing situation, as explained above, and defense and resistance no longer translate 1 to 1 as reductions of incoming damage. (Admittedly, there is a slight surprise to be found in this methodology: increasing the amount of defense or resistance from a single buff or debuff has nonlinear returns. Avoiding this requires calculus, though.)
Also, to address kusanagi's point in particular: you don't have to recalculate final mitigation values for every individual event, just when a buff or debuff is added to / removed from the stack. Furthermore, a change can be applied directly to the existing value; there's no need to remultiply the whole stack. To remove an effect, just multiply by the multiplicative inverse. (You'd want to do a full stack multiply every once in a while to clear out rounding errors, of course). Yes, this would be a horrible calculation for humans because it would produce lots of ugly decimal values, but for a computer one's as good as another.
Bear in mind that many of our current mechanics basically come from a human-powered game that uses simple math because humans are bad at arithmetic - there's no technical or design reason to do so. Better hard math and intuitive results than easy math and confusing results.
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Only it doesn't. If you have two powers providing 5% damage resistance resisting a 100 point attack, then under your proposed system they would reduce that to 90.25, or will constitute not the 10% resistance one would expect, but instead a 9.75% resistance. This is because you're not reducing incoming damage by the sum of your resistance powers, but rather by how much they resist each other. In other words, you're dropping it down to 95% of 95%, rather than by 90%.|
Originally Posted by SpittingTrashcan
1 * (1 - R1) * (1 - R2) * (1 - R3)...
then it's easy to say what a power that grants 5% defense or resistance does: it reduces your incoming damage by 5%. |
Not only is this LESS intuitive (at least to me) and much more difficult to figure out without sitting down to crunch the numbers, it's also segregates single large resistance buffs from multiple small ones. Let me explain.
Two cases:
Case 1 - you're opposing a 100 point attack and you have a single 50% resistance power. You drop the attacks damage by 50% and only suffer 50 points of damage.
Case 2 - you're opposing the same 100 point attack, but you have five powers, each providing 10% damage resistance. You then get:
100*(1-0.1)*(1-0.1)*(1-0.1)*(1-0.1)*(1-0.1) = 100*(1-0.1)^5 = 100*0.9^5 = 100*0.59049 = 59.049
You get 5 times 10% damage resistance, but you don't resist the 50% a person would infer. Instead, you resist just shy over 40%. That's unexpected, and it's much LESS than the above-mentioned single power.
This isn't even diminishing returns. This is diminishing returns based on number of buffs. Such a system would be hideously complicated for a player to predict even with full knowledge of the system, and such systems are generally not revealed to the player anyway, so you have an instance where people take resistance powers with specific resistance values, but when the player looks at the damage they're taking, this damage doesn't correspond to anything the player would expect to see.
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Originally Posted by SpittingTrashcan
Bear in mind that many of our current mechanics basically come from a human-powered game that uses simple math because humans are bad at arithmetic - there's no technical or design reason to do so. Better hard math and intuitive results than easy math and confusing results.
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Let's examine 85% resistance vs. 85%+5% resistance vs. 90% resistance vs. 80+10% resistance vs. 45%+45% resistance, all against a 100 point attack. By your formula, those would admit 15 points, 14.25 points, 10 points, 18 points 30.25 points, respectively. If we compare all of those to the basic 85% resistance, we get the following ratios:
85 vs. 85+5: ~1.053, which is close to a 5% increase in mitigation, but not quite. OK, inaccurate and rough, but it is within a percent of 5%.
85 vs. 90: 1.5, or a 50% increase in mitigation. This must be what we're so afraid people won't understand or be able to predict.
85 vs. 80+10: ~0.833, or a DROP of shy under 17%. Wait, what? Wasn't increasing my resistance supposed to, you know, increase my resistance? Surely 80+10 should yield more than 85... Right? It may sound obtuse coming from me, but this is a legitimate question for a new player to ask.
85 vs 45+45: ~0.496. "The hell? I went from 80% resistance to 90% resistance but my mitigation dropped BY HALF? What gives?" Yes, that's an over 50% DECREASE of mitigation.
Yes, a 5% increase in damage resistance does yield "just about" 5% increase in mitigation, but only under very specific circumstances when one has to decide whether an extra 5% from a new power is worth it. However, if one is moving slotting around or deciding if he can't swap, say, Manoeuvres for Weave, or indeed if he can turn off his toggles when running Unstoppable, then the numbers become not just far more complicated, but badly misleading, as well.
And the last one, by the way, is a question I've asked myself before. If I run Unstoppable on an Invulnerability Scrapper, can I turn off Temporary Invulnerability? If I'm running Elude on a SR Scrapper, can I turn off my other toggles?
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The more complex the connection between the numbers you pick and the results they yield, the more you will frustrate your player.
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Originally Posted by Arcanaville
Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.
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Here's an interesting thought experiment, let's say regarding defence. Right now, we have a linear stat curve fro 0% to 45% (rather, from -45% to 45%), and a concave slope curve for the resulting mitigation. So why don't we flip that around. Why don't we examine the results as a linear set and deduce a back formula for calculating how much defence that equates to? Why not introduce "defence ratings?" Well, for a few reasons, but let's look at how one such system might work.
Let's define a basic pattern example. You have 1000 hit points and you get hit with 1 attack per second for 100 points of damage each until you die. Your "Defence Rating" is the time it takes for you to die in this situation, ignoring resistance and regeneration and assuming a predictable repeating sequence of hits and misses. First, the proper formula. How do we calculate how long a character will survive? To do that, we need to find the number of attacks a character will need to sustain, counting both hits and misses, before the damage taken equals the character's health. This goes something like this:
Attacks*100*(1 - BaseTohit - Defence) = HP or
Attacks = HP/(100*(1 - BaseTohit - Defence)) or
Attacks = 1000/(100*(1 - BaseTohit - Defence)) or
Attacks = 10/(1 - BaseTohit - Defence)
What this means that a character without any defence, fighting an even-level minion, will survive for 10(1 - 0.5 - 0) = 20 seconds, or he will have a "Defence Rating" of 20.
How about the reverse? Suppose I already know how long a character is supposed to survive and I need to know how much defence would ensure this happens? I need to deduce Defence from Attacks.
Attacks*100*(1 - BaseTohit - Defence) = 1000 or
Attacks*(1 - BaseTohit) - Attacks*Defence = 10 or
Attacks*Defence = Attacks*(1 - BaseTohit) - 10 or
Defence = (Attacks*(1 - BaseTohit) - 10)/Attacks
So let's go back and ensure I didn't screw up. I want to have a Defence Rating of 20. How much defence would that equate to?
(20*(1 - 0.5) - 10)/20 = (20*0.5 - 10)/20 = (10 - 10)/20 = 0
OK, so in order to achieve a Defence Rating of 20, we need to have 0% defence. So it works, at least for the base case scenario. Let's get some more mileage out of it. Completely out of a hat, I say a player has a Defence Rating of 100 (the player survives the example for 100 seconds on the nose). What actual defence would the player need to have? Well...
(100*(1 - 0.5) - 10)/100 = (100*0.5 -10)/100 = (50 - 10)/100 = 40/100 = 40%
What, seriously, is it? Well, yeah. I was kind of cheeky saying "out of a hat," since 40% defence in this example is something I know from memory. But let's be even more adventurous. Let's go 1000 Defence Rating. What then? Well, let's see.
(1000*(1 - 0.5) - 10)/1000 = (1000*0.5 -10)/1000 = (500 - 10)/1000 = 490/1000 = 49%
OK, so that's a little outside the realm of the defence softcap (that actually caps at a "Defence Rating" of 200) but it gave us a meaningful answer. In fact, I can give the calculation as large a number as you want and it will still work. An attack rating of, say, 10 000 000 comes up to 49.9999%.
Clearly, a Defence Rating system would work, and it would give you a linear increase in survivability for a linear increase in rating, and with a few more tweaks, it could probably give you a direct tug of war between defence and resistance. And as long as the rating isn't given a concrete explanation in terms of what fictional example it uses or how it's calculated, and indeed what it equates in terms of defence, people will probably not notice the HIDEOUS diminishing returns it represents.
What diminishing returns? Well, for ever point of Defence Rating, the player gains one more second of life in the specific example, and that can be correlated to one more "unit" of life all told. However, the defence that each unit equates to drops SIGNIFICANTLY as the numbers grow higher. Let's have a simple example comparison.
Let's say we go from a Defence Rating of 20 to a Rating of 25 and compare that to going from a Defence Rating of 195 to a rating of 200. I'll save you the calculations and give you the results straight away:
20 = 0% defence
25 = 10% defence
195 = ~44.87% defence
200 = 45% defence
See the difference? Gaining 5 points of Defence Rating when you're at the base ups your effective defence by a full 10%, whereas going 5 points up from 195 to 200 ups your defence by less than 0.2%. That's a decrease of 50 times. I really don't see such a severe case of diminishing returns as being very fare.
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As far as my version of "Defence Rating" goes, yes, that's specifically only against even con minions and it disregards accuracy, but that's mostly because I didn't exactly put much work into it. It's also based on starting point of 20 and an end point of 200, but that's easily changed by varying the attack damage and the level of hit points, as well as translating the final numbers down. For instance, if you have an attack that still deals 100 points of damage but the example character has 10 000 hit points and every defence rating is calculated at 200 points over what it says on the interface, you will have a defence rating window of 0 to 1800 to dole out as you please.
I'm still not a fan of this suggestion, even though I'm the one making it. I just figured I may as well contribute something to the thread other than shooting down other people's ideas.
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Originally Posted by Arcanaville
Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.
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Well, it's sort of weird how it works out. It turns out a big part of the reason 45% is often twice as good as 40% is actually that enemy ToHit rarely varies. The hitroll in this game is actually more or less the same as in a d20 game (where normally a 1 always misses and a 20 always hits). The difference in those games is that you pretty much never know much much ToHit the enemy will have, so more defense is always better.| I, personally, find it odd that 45% def is twice as effective as 40%. I find it even weirder that 45% def means that a mob will hit only 5% of the time. |
My suggestion for the raids in the current version of CoH was that instead of boosting enemy ToHit across the board, that they stagger the accuracy of individual powers so that very heavy hitting powers are easier to dodge and light hitting ones are much more difficult. That would essentially "smooth out" the soft cap. The real issue right now is that either just about everything hits you, or nothing does.
There are also other ways to make some really interesting results. If we found that Super Reflexes wasn't living up to par, for example, we could throw in a special ability that lets them automatically reroll one hit attack that hit them every 10 seconds.
I also very strongly favor a "Multi Opponent Combat" rating for characters as I mentioned in the thread about what we would want in COH2. This rating essentially determines how much your defense and resistance suffers when more than a certain number of enemies aggro on you. Having a rating like this allows you to still have Brutes and Scrappers and perhaps even some Stalkers who are almost equivalent to Tanker survivability against small groups, but allows the Tanker to shine in more extreme circumstances.
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Not quite. Enemy BASE to-hit is 50%, but only even con minions ever actually have JUST that. Enemies gain accuracy boosts to all of their powers (think of it as accuracy slotting) based on their rank and on their con to the player. A lot of enemies also have high-accuracy attacks, and some have to-hit buffs on top of that.|
Originally Posted by Oedipus_Tex
Well, it's sort of weird how it works out. It turns out a big part of the reason 45% is often twice as good as 40% is actually that enemy ToHit rarely varies. The hitroll in this game is actually more or less the same as in a d20 game (where normally a 1 always misses and a 20 always hits). The difference in those games is that you pretty much never know much much ToHit the enemy will have, so more defense is always better.
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Now, of course, if you manage to "soft-cap" your defence against enemies of sufficiently high rank and level, then yes, everything lower/smaller than that will still have its to-hit as floored as its accuracy bonuses will allow (you can't floor an enemy down to 5% if he has ANY accuracy), but those with to-hit buffs will still present a problem as those counteract defence rather very directly.
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Originally Posted by Arcanaville
Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.
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Yes, most people would infer that. Those exact same people would infer that "reduces incoming damage by 5%" would reduce 100 damage to 95, when in reality it could reduce it to 99 or it could reduce it to 50 depending on how much mitigation you have from other sources and the original base damage.|
Originally Posted by Samuel_Tow
You get 5 times 10% damage resistance, but you don't resist the 50% a person would infer.
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People are going to infer two mathematically incompatible things - one of them must necessarily be wrong. There is no way to design a system that your average person will not infer something incorrect from, because as a general rule, people suck at math.
Resistance sets generally have a heal power included, while defense sets generally do not, right? I want to say universally but that would require me to look it up...but anyways, doesn't that have to be taken into account when scheming to change how these powers work?
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When you start talking about powers, yes, when you're talking in general, no. This is more specifically discussing the balancing of the weighting of the various attributes at a meta level.|
Originally Posted by LVConvert
Resistance sets generally have a heal power included, while defense sets generally do not, right? I want to say universally but that would require me to look it up...but anyways, doesn't that have to be taken into account when scheming to change how these powers work?
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Also, there does exist areas where it's just a flat +res, or flat +def [IO Set Bonuses come to mind, as well as Inspirations].
Let's Dance!
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Not universally, no. For one, you can't divide all sets into resistance/defence. Where would Willpower fall? What about Regeneration?|
Originally Posted by LVConvert
Resistance sets generally have a heal power included, while defense sets generally do not, right? I want to say universally but that would require me to look it up...but anyways, doesn't that have to be taken into account when scheming to change how these powers work?
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Secondly, Ninjutsu is a defence-based set and that has a heal - Kuji-In Something. Additionally, Electrical Armour is a resistance-based set, kind of, but that doesn't have a full heal, or at the very least didn't use to. Also, Stone Armour is a primarily defence-based set. Rock Armour, Crystal Armour and Minerals are defence toggles. Yet that has a heal in Earth's Embrace. Also, if we count Electric Melee's energise, then we have to count Energy Aura's Energy Drain, which has a heal component to it, yet Energy Aura is a defence set, pretty much.
Finally, no, heals and other aspects don't have to be taken into account when devising formulas, because these concern the mechanics of receiving and resisting damage, as well as the mechanics of dodging and blocking attacks. Regeneration and heals are not relevant to those, at least to the extent that they're not and should not be members of each other's formulas and methods of operation. You don't resist less damage if you regenerate more, for instance.
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Originally Posted by Arcanaville
Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.
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It's only diminishing returns if you look at it in terms of actual defence numbers (which would mean bugger all under this system). It's not really diminishing returns, because each point of Defence Rating would be as valuable as the previous one, and as the next one. In other words, since you're not collecting IO bonuses with +3.75% S/L Defence but rather IO bonuses with +5 S/L D.Rating, there is no loss (or gain) of value as you stack each point. Except perhaps compared to getting increased resistance or something. I think layering protections would be unusually powerful under a system like this one.
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Originally Posted by Samuel_Tow
Let's say we go from a Defence Rating of 20 to a Rating of 25 and compare that to going from a Defence Rating of 195 to a rating of 200. I'll save you the calculations and give you the results straight away:
20 = 0% defence 25 = 10% defence 195 = ~44.87% defence 200 = 45% defence See the difference? Gaining 5 points of Defence Rating when you're at the base ups your effective defence by a full 10%, whereas going 5 points up from 195 to 200 ups your defence by less than 0.2%. That's a decrease of 50 times. I really don't see such a severe case of diminishing returns as being very fare. |
There is a fairly simple way to implement "defense" formulas, which is to do them as multiplicative rather than additive.
Say what?
Okay, right now, say you have a 50% chance to hit. You attack someone with 25% defense. Okay, 50% - 25% = 25%. You now have a 25% chance to hit. That's additive/subtractive.
What if, instead, it were multiplicative? In the same scenario, attack someone who reduces your chance to hit by 25% of itself. So, 50% - (50% * 25%) = 37.5%. (An easy way to understand this is to call 25% defense a 75% hit chance multiplier).
Now, what this does is... The more of them you have, the less the additional ones matter.
Say you have two 25% defense abilities up. Under the normal system, that gives you a 0% chance to hit, which is then saturated at 5%. Under the multiplicative system, you have 50% * 75% * 75%, which ends up being 9/32, or a little over 25%.
Obviously, this would imply a MASSIVE rebalancing of all sorts of stuff. But! It would give you a system under which there aren't "caps" for defense, and where buffers are always useful. As is, another layer of +defense is totally wasted once everyone's soft capped, which they tend to be.
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Defence is a bad example because it's hard to "visualise." But the system works just as well for Resistance (for half the final "Resistance Rating" values), but the result from such would be largely the same. I don't want to get mired into even more unnecessary calculations, so let's use some imaginary numbers.|
Originally Posted by SlyGuyMcFly
It's only diminishing returns if you look at it in terms of actual defence numbers (which would mean bugger all under this system). It's not really diminishing returns, because each point of Defence Rating would be as valuable as the previous one, and as the next one. In other words, since you're not collecting IO bonuses with +3.75% S/L Defence but rather IO bonuses with +5 S/L D.Rating, there is no loss (or gain) of value as you stack each point. Except perhaps compared to getting increased resistance or something. I think layering protections would be unusually powerful under a system like this one.
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You turn on a toggle that takes you from 10 to 20 Resistance Rating and notice that an enemy who previously hit you for 100 now hits you for 90. Now imagine you have around 900 Resistance Rating already. An attack that deals 100 damage normally only hits you for 15. You run a toggle which gives you another 10 Resistance Rating and notice that this attack now hits you for 14.95. My first question would be: "The hell?" While I may be theoretically aware of what that minute percentage does for my overall mitigation, the fact remains that I see almost no change in the damage I'm taking.
This creates a system that makes the player wonder "What's the point of going for more Rating if all it'll do is drop the damage I'm taking by half a point?" And I would not blame a player for asking that. Of course, once I plot the defence curve on a flat, I'll see that that half a point actually equals a ton of mitigation because it's on the steep end of the slope, but you try telling that to a player who spent a considerable investment to see almost nothing change on his end.
And, yes, if need be I can run the numbers and present a real example, but unlike Arcana, I'm lazy and incompetent.
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I can already hear people asking "So? Right now a player will scoff if offered 1.75% defence and ask what the hell that'll do, unaware that this percentage can count for a lot if you have a lot of defence before it." That's true, I agree, but here's the kicker - I don't feel that "softcapping" defence or even resistance should be part of the regular game as it is now. OF COURSE the last few percent before the defence softcap matter a lot. That's how the numbers work out, but as far as I'm concerned, this shouldn't be coming up. The fact of the matter is that the slope doesn't get really very steep until around 35-40% defence, and players shouldn't be hitting their own caps by themselves.
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Originally Posted by Arcanaville
Samuel_Tow is the only poster that makes me want to punch him in the head more often when I'm agreeing with him than when I'm disagreeing with him.
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This is related to the discussion about things you would change in CoH2. I didn't want to tie up that thread with this discussion, so I started a new one.
[Note: This is not a discussion about actual changes to be made to the existing game. It is only a theoretical discussion about what the formulas could look like in the future.]
Most of us know that the current implementation of Resistance and Defense increases survivability multiplictavely as you approach the cap. For example, going from 40% defense (1/10 chance of being hit) to 45% defense (1/20 chance of being hit) doubles your survivability.
My question is, what should these formulas look like if they are kept in future versions of City of Heroes? Should Defense still be all-or-nothing? What does the formula for defense buffs look like in the future? Can you still stack 10 force fields on top of each other? Is Resistance a competitive value that is determined only after looking at the power of the attacker? Does the purple patch still apply?