Defense and Scaling
By
Aaron123,
Posted on: 2006-01-11 16:47 in Archetypes and Powers General Discussion
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OK i have two theories of how it may work. The two posible formulas in my head are either:
a) (ToHit + buff - debuff) - DEF/50 * (ToHit + buff - debuff)
b) (ToHit - DEF/50 * ToHit) + buff - debuff
I made a small excel sheet with these forumlas so you can see the results with diferent numbers of enemy acc, debufs and buffs.
It is loaded right now with standard PvP numbers, that would be, 50 to hit chance, and +16.5 acc (thats what you get in pvp from one even ACC SO), with no debuffs.
You can find the Excel file here
You will notice it wont mean that you will floor a lt as easily as an AV with this formula, but they do get close with the same number (an AV gets to 7.6 acc with a 45% def)
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A mechanistic change like this wouldn't stop at +5. So either Statesman was being cagey (defense will be just as effective up to +5 ... because it will be so in *all* cases), or the change has to revolve around altering the tohit bonuses due to rank, and the tohit bonuses explicitly granted by the purple patch (although technically, those level bonuses are not really due to the purple patch; I'm pretty sure they predate it).
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Now you fight a +5 boss, who has about 95% base tohit (its really just about that, actually). You flip on CJ. For CJ to be just as effective, it should reduce the chance to hit to 96% of its original value, or about 91%. CJ, in effect, is worth about 5 percentage points of defense against a +5 boss, 2.5 percentage points of defense against a +0 boss, but it always has the same 4 percent mitigation benefit. In effect, CJ "works equally well" against the +0 boss and the +5 boss (currently, CJ's effectiveness drops from about 4% against +0 bosses to about 2.5% against +5 bosses).
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I agree that it will probably be something like this. Similar to how Resist works (100% - Resist value). It may, however, become harder to "bottom out" the ToHit value, but that may be intentional.
For example, right now if an enemy has a 75% chance to hit you, and you have a 30% Defense bonus, their ToHit would be 45%, right? In your version, their ToHit would drop to 70% of 75%, or 52.5%.
Of course, this is all speculation and probably a waste of time. 
Aw crap! I JUST deleted my 29 spine/sr 2 weeks ago! Stupid reverse pod vampire people didn't invade soon enough. 
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Now you fight a +5 boss, who has about 95% base tohit (its really just about that, actually). You flip on CJ. For CJ to be just as effective, it should reduce the chance to hit to 96% of its original value, or about 91%. CJ, in effect, is worth about 5 percentage points of defense against a +5 boss, 2.5 percentage points of defense against a +0 boss, but it always has the same 4 percent mitigation benefit. In effect, CJ "works equally well" against the +0 boss and the +5 boss (currently, CJ's effectiveness drops from about 4% against +0 bosses to about 2.5% against +5 bosses).
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I agree that it will probably be something like this. Similar to how Resist works (100% - Resist value). It may, however, become harder to "bottom out" the ToHit value, but that may be intentional.
For example, right now if an enemy has a 75% chance to hit you, and you have a 30% Defense bonus, their ToHit would be 45%, right? In your version, their ToHit would drop to 70% of 75%, or 52.5%.
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No, in my version (well, its a version, not so much mine) if the foe's *base* tohit chance is 75% (which basically means he's a turret, an AV, or a pet), and you have 30% defense, then your net to hit is still 45%. The only difference is the *level difference*.
Without getting into the sticky math, if the tohit level bonus is some number, like +10% (i.e. +1 minion has base tohit of 55% - 50% * (1.1) ) then whenever you face a +1 minion, your actual defense will also scale up by 10%. So 25% defense becomes 27.5% defense. Basically, we're trying to keep the ratio of Defense/NetToHit constant.
Similarly, instead of looking at Bosses as having +15% tohit, its better to look at it as bosses have 30 percent higher tohit; i.e. 50% * (1.3). In that case, defense will be 30% higher when facing a boss. These two effects are multiplicative, not additive. So when facing a +4 boss, 25% defense will become 30% higher due to facing a boss, and then 40% higher *than that* due to facing a +4. 25% * 1.3 * 1.4 = 45.5%. Does it work?
25% verses even minion is 50% net mitigation (25/50)
45.5% verses +4 boss (91%) is still 50% net mitigation.
Caveat: my level scaling approximation is that +1 villains have 10% higher tohit. That's pretty close, but I believe others have determined that its slightly less than that, and I don't have the precise numbers handy. But the principle is that whatever they are, plug them in and it should work.
How this will "cut off" at +6 is anyone's guess. Potentially, it might be as simple as capping off the defense adjustment at +5. So if you are fighting a +6 boss, your defense will be buffed upward to Defense * 1.3 * 1.5, even though the villains have been scaled up to 1.6 tohit. Hopefully, it isn't a more drastic thing like terminating the scaling altogether.
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Of course, this is all speculation and probably a waste of time.
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Probably. But at least it might prevent people from taking too much or too little away from this announcement. Its a change, and it sounds like the net effect of the change is a good one, but beyond that, it comes down to the numbers, which I hope they share with us, because if I have to watch brawls for thirty seven hours to reverse engineer them just because they want to keep their formulas mysterious, I'm probably going to have an aneurism.
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OK i have two theories of how it may work. The two posible formulas in my head are either:
a) (ToHit + buff - debuff) - DEF/50 * (ToHit + buff - debuff)
b) (ToHit - DEF/50 * ToHit) + buff - debuff
I made a small excel sheet with these forumlas so you can see the results with diferent numbers of enemy acc, debufs and buffs.
It is loaded right now with standard PvP numbers, that would be, 50 to hit chance, and +16.5 acc (thats what you get in pvp from one even ACC SO), with no debuffs.
You can find the Excel file here
You will notice it wont mean that you will floor a lt as easily as an AV with this formula, but they do get close with the same number (an AV gets to 7.6 acc with a 45% def)
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A mechanistic change like this wouldn't stop at +5. So either Statesman was being cagey (defense will be just as effective up to +5 ... because it will be so in *all* cases), or the change has to revolve around altering the tohit bonuses due to rank, and the tohit bonuses explicitly granted by the purple patch (although technically, those level bonuses are not really due to the purple patch; I'm pretty sure they predate it).
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Yes, im asuming there will be a hard coded switch for this formula to not be used if the enemy is over 5 levels higher.
See my previous post for a potentially simpler way to get much more exact defense stability with level and rank.
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In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)
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Aw crap! I JUST deleted my 29 spine/sr 2 weeks ago! Stupid reverse pod vampire people didn't invade soon enough.
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I hear next week they'll be announcing that when you impale a villain you'll be able to bring the body back to a store still on the spine and sell it for salvage.
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In one little corner of the universe, there's nothing more irritating than a misfile...
(Please support the best webcomic about a cosmic universal realignment by impaired angelic interference resulting in identity crisis angst. Or I release the pigmy water thieves.)
Hmm. I wonder if this effects all defense powers. If it works on Parry too, that would be grand.
Heroes
Dysmal
Lumynous
Sam Steele
Pluck
Wile
Slagheap
Pressure Wave
Rhiannon Bel
Verified
Stellaric
Syd Mallorn
Villains
Jotunheim Skald
Saer Maen
Jen Corbae
Illuminance
Venator Arawn
Taiga Dryad
Tarranos
This confuses me...
Mostly because I don't quite get how Defense powers don't already provide the same boost to your defense. It's just that the attacker's base chance to hit is better...
Let's Dance!
will you be looking at the -def from unyeilding? or will vulnerable scrappers and tanks not receive a bonus? while i am posting... will unyeilding actually give scrappers meaningful resistance or will it only be mez protection and lowered defense that invincibility wont negate without several mobs around? as it stands now, for scrappers unyeilding and the passives are not worth slotting if you even take the passives.
anyway, glad sr is getting a much needed bonus, i know a few people that will be very happy. their scrappers, like mine, have been shelved since I5.
YMMV---IMO
Ice Ember
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Some more good news...
Ice Tankers and SR Scrappers have long lamented that Defense doesn't scale with level. Because mobs higher level than a player possess an inherent to hit bonus, Defense isn't as effective over levels as Resistance.
A while ago, peoople have requested something be done. Well, we've done a bunch of work and done this. Defense powers will now work equally well against critters, regardless of their rank or level. For instance, your defense powers will work equally well against a Boss or any critter up to 5 levels higher than you, as it does for an equal level minion. This change has no effect on a player who does not have any Defense.
This change is coming in I7
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Wow, that's going to make Stalkers a whole lot more effective in PvE.
I think what a lot of people seem to think this means is that if you have even 1% defense then everything you fight up to +5 will suddenly have 50% ToHit. More likely what they're doing (and I think this is what Arcanaville is saying) is that whatever amount of defense you have will get the same boost that a mob's ToHit gets.
Meaning if a power provides 10% Defense against an even level minion who has a 50% ToHit, it will provide 13% against an even level Boss who has a 65% ToHit, and 15% against an AV who has 75% ToHit. In all of those cases you are getting hit 80% of the time.
So they're not touching mob ToHit, they're just, well, making defense scale.
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Some more good news...
Ice Tankers and SR Scrappers have long lamented that Defense doesn't scale with level. Because mobs higher level than a player possess an inherent to hit bonus, Defense isn't as effective over levels as Resistance.
A while ago, peoople have requested something be done. Well, we've done a bunch of work and done this. Defense powers will now work equally well against critters, regardless of their rank or level. For instance, your defense powers will work equally well against a Boss or any critter up to 5 levels higher than you, as it does for an equal level minion. This change has no effect on a player who does not have any Defense.
This change is coming in I7
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Under "better late then never": WOOT!
I certainly hope that it slowly devolves after +5 con instead of a +6 con being as hard as it is today with only DEF!
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Wow, that's certainly a nice change!
Is that strictly for +defense powers, or will -accuracy powers be included in this also?
EDIT: Also, under the new system, if you're fighting a +6, will you have the defense value as if you were fighting a +1 today, or is there going to be a steep defense dropoff between +5 and +6 enemies?
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Echosing the two questions in this post.
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Well, we've done a bunch of work and done this. Defense powers will now work equally well against critters, regardless of their rank or level. For instance, your defense powers will work equally well against a Boss or any critter up to 5 levels higher than you, as it does for an equal level minion. This change has no effect on a player who does not have any Defense.
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Good thing you posted this /after/ New Years and far away from any parties I may or may not have been at.
I have been known to kiss the first person I can grab when properly inebriated, and may have inadvertantly tracked you down and planted a wet sloppy one before you realized what happened... Considering my current facial hair growth, you might have suffered some serious beard burn.
Whew! Way to avert a crisis there! Now /that's/ leadership!
Luerim
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See my previous post for a potentially simpler way to get much more exact defense stability with level and rank.
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How can 5 paragraphs be simpler than a simple formula with 4 variables?
If you run my formula you will see that what you explained in 5 paragraphs was covered into the formula already.
Test the excel file with the numbers you just used and you will get exactly the same result you explained with 25% def. Its not more exact, its the same thing, only I gave a formula anyone can use to check any value against diferent enemies.
The only issue is, if your Def goes over 50% you will always get a negative defense, but that may be simply fixed by caping the defense at 50.
Oh and going back to the point of cutting out at +5, honestly, I am not sure if I see a reason for it. I mean, after all, Resistance can have its effect against any enemy, +6s dont suddenly ignore resistances. Why should +6s ignore the new standard defense scheme?
Oh and all in all, i think after this they may coinsider 25% Def on inspirations a bit too powerful, so i would not be amazed to see those getting some big nerf.
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Meaning if a power provides 10% Defense against an even level minion who has a 50% ToHit, it will provide 13% against an even level Boss who has a 65% ToHit, and 15% against an AV who has 75% ToHit. In all of those cases you are getting hit 80% of the time.
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Small correction but its actually a big point:
in all those cases you are getting hit 80% as often as you did before. Truth is you are not getting hit an equal ammount of times under each diferent def number. Even if it scaled proportinatedly, you get that you are bing hit (accounting the 10%):
40% of the time by minnions
52% of the time by bosses
60% of the time by AVs.
It basicaly turns the whole thing multiplicative instead of substractive, by translating the minnion oriented number into a true percentage modifier by dividing it by 50 and then multiplying it against the acc of the enemy and then substracting that result from the acc to get the final chance to be hit.
Simplyfiing my original formula (since i wrote it a bit of in the haste of the exitement)
(ToHit + buff - debuff) * (1-(DEF/50))
This way we dont calculate the enemy final acc twice.
Now that i think about it, i ponder if they may decide to change the minimun 5% chance to hit for a 45% def cap, would be very similar, but maybe a bit more in line with real 90% resist caps.
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Aw crap! I JUST deleted my 29 spine/sr 2 weeks ago! Stupid reverse pod vampire people didn't invade soon enough.
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I hear next week they'll be announcing that when you impale a villain you'll be able to bring the body back to a store still on the spine and sell it for salvage.
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lol thats fine, he was replaced w/ a spine/da...
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See my previous post for a potentially simpler way to get much more exact defense stability with level and rank.
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How can 5 paragraphs be simpler than a simple formula with 4 variables?
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Math intimidates people in a way that grammar never will.
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My major concern with this change is that if it's implemented by changing Def from a flat accuracy reduction into a percentage reduction in accuracy (which would scale with level), Defense sets are actually getting dinged again.
Consider an SR toggle power that right now is 12.5% Def. Against an even con minion, that's actually a 25% reduction in its tohit (37.5/50). Against an even con boss, that's a 17% reduction in its tohit. If the devs simply transfer the current percentages over without adjusting them for such a system, you're taking at worst a 50% reduction in Defense. Under such a system, a minion's tohit would be 43.75 (50 * .875, instead of 50 - 12.5 = 37.5), and that boss would have a tohit of 65.63 (75 * .875, instead of 75 - 12.5 = 62.5). In fact, if the percentages aren't increased, your defense actually will scale *more* poorly as mobs go up in level, unless their base tohit is over 100.
In order to adjust the percentages properly, they'll need to make this change while simultaneously deciding the maximum level of mitigation that Def can provide; I think doubling all Def values would be a good place to start. Obviously, they can't be kept where they are now under this system.
I'm sure they've looked at all this already if the above system is what they're going to use, but if not, perhaps this can serve as a reminder. The devs, no offense, are not immune to the law of unintended consequences -- such as Parry letting you deflect shotgun blasts (Lethal) and Insulation Shield shielding you from some Psionic attacks (Ranged). 
Would this also apply to / help the force fielder? Lord knows that Defender is in a world of hurt all unto themselves...most of it boredom.
~ Jonathan
why can't everyone be happy for the SR scrappers they finally got some true dev lovin (i'm not saying all of you are downing this buff) i'm for one happy with this and am looking foreward to a content issue for once
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sorry i'm just so happy that SR finally got some love that i forgot that this seems to effect all defensive powers
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How can 5 paragraphs be simpler than a simple formula with 4 variables?
If you run my formula you will see that what you explained in 5 paragraphs was covered into the formula already.
Test the excel file with the numbers you just used and you will get exactly the same result you explained with 25% def. Its not more exact, its the same thing, only I gave a formula anyone can use to check any value against diferent enemies.
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Scaling defense buff = Current Defense * RankToHitBuff% * LevelToHitBuff%
One equation, three variables.
Mine and yours diverge under two circumstances. The first is if and when a villain group's even level minions ever have intrinsicly higher base tohit than 50%, separate from any actual tohit buffs. Second, by separating level and rank factors, it points to a possible mechanism for leveling off the defense scaling buff past +5, whereas yours doesn't distinguish between the two.
Someone is probably going to say something about the fact that there aren't any villain groups with minion base tohit anything other than 50%, and even if there were, you could simply look at that as an intrinsic tohit buff. Actually, *assuming* that they did anything remotely close to this, the possibility of having villain groups with intrinsicly higher base tohit in the future jumps dramatically; long time followers of defense and accuracy discussions might guess why, but beyond that I'd rather let that one lie for now.
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This is the biggest change since they added pockets to pants !