Ignoring Defense
[i]Ignoring defense is a crucial part of gameplay, especially with higher end bosses. Defense [b]must[/b] be taken account for when funding a character. Even at lower levels, cheap sources of ignoring defense can be helpful.[/i]
Find defense rates by searching each individual monster in the search bar.
[url=http://maplevault.com/index.php]Search defense rates here.[/url]
[url=http://docs.google.com/spreadsheet/ccc?key=0AoVZazJObtFxdHpkQkpmVUFLTWlVWS1sSkl3eEUwZlE#gid=0]My multiplicative PDR Calculator![/url]
In the "Sources" column, just put how much defense each source ignores.
Defense rates range from -10% on Snails to -300% on Chaos Vellum!
[*]There are two systems when it comes to ignoring defense. Any time before the Unleashed Patch, the "additive" system was used. Any time after the Unleashed patch, the "multiplicative" system was used, which is subject to change. Generally, for players, the additive system is better because it is easier to ignore more defense. The multiplicative system hinders success when attempting higher end bosses.
[*]When people see something with defense rates [b]over[/b] one hundred percent, people become very confused. One example of this is Chaos Vellum with an defense rate of -300%. With no experience pertaining to the math behind calculating defense ignore, the idea of a defense rate can be intimidating. Once the math is applied consistently, you can begin to understand why in this situation, there is a [i]threshold ignore rate[/i]. If you ignore less defense than this number, you will hit ones (1's). If you hit more than this number, you will hit more than one.
[b]Ignoring Defense Additively[/b]
[*]Add all of your sources off "ignore DEF". This number will be a percent. If this percent is over the value of 1 (100%), you ignore [b]ALL[/b] defense. If you ignore less than 100% of defense of a monster, continue reading. [i](10% + 30% + 30% = 70%)[/i]
[*]Subtract this [b]new[/b] number from 1. This will be the percent of defense that you [b]do not[/b] ignore. [i](1 - 70% = 30%)[/i]
[*]Multiply this [b]new[/b] number by the defense rate of the monster. This will be the damage reduction that will take effect. [i](30% x -50% = -15%)[/i]
For skills like the Paladin's threaten, take the percent of the defense off the monster's defense. Then do the math.
Ignoring defense additively is much more effective than ignoring it multiplicatively. In this system, it is possible to ignore [b]ALL[/b] defense by simply attaining 100% or more of the stat "ignore DEF". It is not possible to ignore all defense of a monster with the multiplicative system but this does have few exceptions.
[b]Ignoring Defense Multiplicatively[/b]
The idea behind multiplicative PDR is that a fraction of the defense of the monster is taken off one at a time corresponding to the sources of "ignore DEF" you have. To find out how much defense you ignore multiplicatively, you can use this formula if you ignore defenses [i]a[/i], [i]b[/i], [i]c[/i], [i]d[/i], [i]e[/i], etc, where these variables are percents. For example, one source of ignore DEF, [i]a[/i], can be 30% from the Leafre Set in the Codex.
[b]1 - [1 - a][1 - b][1 - c][1 - d][1 - e][ 1 - ...][/b]
[i]Yes[/i], PEMDAS is used. Do what is in the brackets first. Then multiply everything. Then subtract.
Although giving a formula is sufficient, why multiplicative PDR can be generalized into one equation can be explained.
For skills like the Paladin's threaten, it is counted as once source of ignore defense. That is why a Paladin is needed in every high end expedition. It cuts the monster's defense in half with the hyper skill. The way that ignoring defense multiplicatively ends up working out is: the higher sources of PDR you have, the better. Optimizing this is getting extremely high sources of ignore defense, such as one line of ignore 30% defense instead of two lines of ignore 15% defense.
Note that when you ignore a [i]certain amount of defense[/i], if you subtract [i]it[/i] from 100% (or 1), you get the defense that is not ignored. When the source that ignores [i]a[/i] defense is looked at, [1 - a] is the defense [b]not[/b] ignored. This same principal applies for the other sources of ignore defense. Defense not ignored is defense taken into effect. The idea behind multiplicative PDR is that each source of defense ignore is taken into account separately, one at a time. When everything is multiplied out, you get the amount of defense that [b]is not[/b] ignored. When subtracting this from 1 (or 100%), you get the percent of defense that [b]is[/b] ignored.
[i]Working With Some Variables[/i]
Horntail has a defense rate of -50%. You ignore defenses from several sources: 30% from Leafre Set, 10% from level 100 ambition, 30% from a skill, 15% from a potential line on a weapon, 15% from a nebulite on that [b]same[/b] weapon. [b]Note that the weapon is two sources of ignore defense. The weapon is accounted for as two different lines of 15% ignore defense.[/b]
[*]First, the 30% from the Leafre Set takes effect. You ignore 30%. You must not ignore 70%. Multiply this 70% with the 50% to find what defense still remains.
[70%][50%] = 35%
[*]Second, the 10% from ambition takes effect. You ignore 10%. You must not ignore 90%. Multiply this 90% with the number found in step 1.
[90%][35%] = 31.5%
[*]Third, the 30% from the skill takes effect. You ignore 30%. You must not ignore 70%. Multiply this 70% with the number found in step 2.
[70%][31.5%] = 22.05%
[*]Fourth, the two 15% from the weapon takes effect. You ignore [i]1 - [.85][.85], which is 27.75%[/i] You must not ignore 72.25%. Multiply this 27.75% with the number found in step 3.
[i]The product that yields from this multiplication is the percent of the damage that Horntail takes off.[/i]
[72.25%][22.05%] = 15.931125%
[*]Lastly, if Horntail takes off a certain amount percent of damage, he must not take off a certain amount of damage. Take the number from step 4 and subtract it from 1.
[i]This will be the percent of your damage being done.[/i]
100% - 15.931125% = 84.068875%
[url=http://docs.google.com/spreadsheet/ccc?key=0AoVZazJObtFxdHpkQkpmVUFLTWlVWS1sSkl3eEUwZlE#gid=0]My multiplicative PDR Calculator![/url]
In the "Sources" column, just put how much defense each source ignores.
[b]Ignore Defense Threshold[/b]
There are several bosses with defense rates over -100%.
[*]Chaos Pink Bean statues have -160% damage.
[*]Chaos Pink Bean bodies have -180% damage.
[*]Chaos Vellum has a defense rate of -300% damage.
There is a critical percent of defense you must ignore in order to hit more than "1" damage.
[i]Chaos Pink Bean statues: -160% damage[/i]
To do more than "1" damage, you have to ignore enough defense so that the effect of the defense is less than -100% damage. Therefore, you must ignore 60% out of the 160%. This is a fraction.
60/160 = 37.5%
To do more than "1" damage on a Chaos Pink Bean statue, you must ignore [b]more than[/b] 37.5% defense.
[i]Chaos Pink Bean bodies: -180% damage[/i]
To do more than "1" damage, you have to ignore enough defense so that the effect of the defense is less than -100% damage. Therefore, you must ignore 80% out of the 180%. This is a fraction.
80/180 = 4/9 ~ 44.4%
To do more than "1" damage on Chaos Pink Bean bodies, you must ignore [b]more than[/b] 44.4% defense.
[i]Chaos Vellum body: -300% damage[/i]
To do more than "1" damage, you have to ignore enough defense so that the effect of the defense is less than -100% damage. Therefore, you must ignore 200% out of the 300%. This is a fraction.
200/300 = 2/3 = 66.7%
To do more than "1" damage on Chaos Vellum, you must ignore [b]more than[/b] 66.7% defense.
All of these numbers work with both systems. Both systems only differ in the way you find the amount of defense you ignore.
Notice that this information is to hit over "1". You have to a [b]lot[/b] more to even complete the expedition. Much of the difficulties of these bosses is in the defense and extremely high HP. I believe Chaos Vellum has 63,000,000,000 (63B) HP and you have 20 minutes to kill it. All of Chaos Pink Bean includes statues 15 statues (1+2+3+4+5) and 14 bodies of Chaos Pink Bean.
I believe the tall statues have 4.2b HP and appear 9 times. I believe the birds have 6.3b HP and appear 5 times. I believe Ariel has 8.4b HP and appears once. Chaos Pink Bean has 14 bodies of 4.2b HP each.
All of this HP adds up to 136.5b. There is a 30 minute timer. Even with impossible conditions, 76m damage would be needed per second. Only higher end expeditions can complete something like this.
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[url=http://maplestory.nexon.net/news/updates/update-notes/00HhT/v-148-grand-athenaeum-update-notes]So with this update[/url], your multiplicative PDR now shows properly. (Updated April 16, 2014)
TL; DR: Calculating how much defense you ignore post-Unleashed is poop. Reverting back to the old way ignore defense was calculated is much better.
[url=http://docs.google.com/spreadsheet/ccc?key=0AoVZazJObtFxdHpkQkpmVUFLTWlVWS1sSkl3eEUwZlE#gid=0]My multiplicative PDR Calculator![/url]
In the "Sources" column, just put how much defense each source ignores.
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Feel free to point out any mistakes or ask a question. I will try to answer them. As I learn more, I edit this post. This goes for the [url=http://docs.google.com/spreadsheet/ccc?key=0AoVZazJObtFxdHpkQkpmVUFLTWlVWS1sSkl3eEUwZlE#gid=0]PDR Calculator[/url] also.
45 Comments • Newest first
[quote=David0696]I am actually not sure about this.
[url=http://www.basilmarket.com/MapleStory-Paladin-Skills.html#Blast]Paladin's Blast[/url]
[url=http://www.basilmarket.com/MapleStory-Buccaneer-Skills.html#Typhoon-Crush]Buccaneer's Typhoon Crush[/url]
[url=http://www.basilmarket.com/MapleStory-Mercedes-4-Skills.html#Defense-Break]Mercedes's Defense Break[/url]
Paladin's Blast actually treated as a normal 30% defense ignore. I know the way it is worded suggests something else. I was shocked too when learning about the nature of how the skill really is. Anything else with that phrasing, I am also not sure about.
This is encouraging.
A post about math is intimidating to me too and probably is not worth putting so much effort into. That is why I later on added the [url=http://docs.google.com/spreadsheet/ccc?key=0AoVZazJObtFxdHpkQkpmVUFLTWlVWS1sSkl3eEUwZlE#gid=0]PDR Calculator.[/url]
I am glad it helped. Even if it helped a few, the effort was worth it.[/quote]
technically since we're going to have co on at pretty much all times its really 34% pdr =p
[quote=gamemage3]does this mean mercedes are in a good spot right now since they have a 40% chance to do true damage?[/quote]
I am actually not sure about this.
[url=http://www.basilmarket.com/MapleStory-Paladin-Skills.html#Blast]Paladin's Blast[/url]
[url=http://www.basilmarket.com/MapleStory-Buccaneer-Skills.html#Typhoon-Crush]Buccaneer's Typhoon Crush[/url]
[url=http://www.basilmarket.com/MapleStory-Mercedes-4-Skills.html#Defense-Break]Mercedes's Defense Break[/url]
Paladin's Blast actually treated as a normal 30% defense ignore. I know the way it is worded suggests something else. I was shocked too when learning about the nature of how the skill really is. Anything else with that phrasing, I am also not sure about.
[quote=Darkstar764]I feels smarter[/quote]
This is encouraging.
[quote=LGSlayer]What[/quote]
A post about math is intimidating to me too and probably is not worth putting so much effort into. That is why I later on added the [url=http://docs.google.com/spreadsheet/ccc?key=0AoVZazJObtFxdHpkQkpmVUFLTWlVWS1sSkl3eEUwZlE#gid=0]PDR Calculator.[/url]
[quote=steven7x23]Thanks for this. It helped me a lot for understanding the new and weird multiplicative system that I was so confused from.[/quote]
I am glad it helped. Even if it helped a few, the effort was worth it.
does this mean mercedes are in a good spot right now since they have a 40% chance to do true damage?
This is very useful. Thumbs up!
@David0696
The net damage decreases the more boss% you have...?
shouldnt it be (1 - damage reduction/100) * (1 + bossdmg/100) * 100
something like:
http://docs.google.com/spreadsheet/ccc?key=0AujvRhays54FdHBJaWt6N1JnNFFLZTh5X2pidWVfWFE
You can steal this one if you want, i cleaned up some of the equations and the overall look.
I feels smarter
[quote=SombraManx]@lazershock: lol I've been looking for that link since 2-3 days ago u.u
since i have like 10+ sources of pdr i'm just too lazy to do the calcs manually e.e[/quote]
[url=http://docs.google.com/spreadsheet/ccc?key=0AoVZazJObtFxdHpkQkpmVUFLTWlVWS1sSkl3eEUwZlE#gid=0].[/url]
@David0696: Ooh okay thanks appreciated.
What
@ryuushinou: I updated the thread with my own. I never had the idea until you showed yours. I'll go ahead and delete the one that you own.
@David0696: Ah right. That's fine. If it starts to bother me alot I'll just have to make it non-editable. But you can always make your own copy on your own google docs, it's just asking a tad more effort from the user that's all.
I added a link to a PDR calculator.
Thanks for this. It helped me a lot for understanding the new and weird multiplicative system that I was so confused from.
[quote=ryuushinou]@David0696: Could you under that link say "Please do not touch Row 2 of this spreadsheet" or something along those lines. I noticed that someone fiddled with the formula and it was not working properly.
[Edit] Nvm. I fixed the protection settings.
[2nd Edit] Adding rows will wreck the formula so avoid doing so. Otherwise I'll have to prevent people from entering into the spreadsheet directly.
Also, I've noted people adding sources of 50% and 60%. Equipment potential lines do not stack additively with each other. e.g. if you have 20% and 30% on separate lines, they are two different sources. (I don't think some are understanding your explanation).[/quote]
That was probably me. Hero's skill ignores 50% defense and 60% with Combat Orders from Paladins. I'll try to play around with Google Docs and figure it out. I am guessing it is similar to Microsoft Excel but I have to learn how to control permissions. Thanks for pointing out concerns. Sorry for the inconveniences. Ask me anytime to remove it from the original post.
[Edit]
Also, threaten takes off half of the monster's defense. I check that up sometimes too.
@David0696: Could you under that link say "Please do not touch Row 2 of this spreadsheet" or something along those lines. I noticed that someone fiddled with the formula and it was not working properly.
[Edit] Nvm. I fixed the protection settings.
[2nd Edit] Adding rows will wreck the formula so avoid doing so. Otherwise I'll have to prevent people from entering into the spreadsheet directly.
Also, I've noted people adding sources of 50% and 60%. Equipment potential lines do not stack additively with each other. e.g. if you have 20% and 30% on separate lines, they are two different sources. (I don't think some are understanding your explanation).
@ryuushinou: >.< I will eventually rationalize this to not be my fault.
@bluebomber24: Pft. It's all over my calculator and utility thread. You're just being oblivious!
[quote=ryuushinou]@David0696: No problem. I had to do this for aomethign else. Thought I'd share it here.
@SombraManx: The top number under "Your ignore def" [Row 2] is your product sum (or product of a sequence) of all your "pdr" sources. i.e. What your stat UI should actually read instead of a stupid arithmetic sum.
i.e. After you fill out Row 4 and below > Row 2 = what your 'total' ignore def is. You can use this number instead of having multiple *(1-ignoreDEF%) in your equation.
[i]1-BossPDR*(1-[b]Row2[/b]) = [b]%of damage that gets through[/b][/i][/quote]
You never informed me of this tool. How rude.
@David0696: No problem. I had to do this for something else. Thought I'd share it here.
@SombraManx: The top number under "Your ignore def" [Row 2] is your product sum (or product of a sequence) of all your "pdr" sources. i.e. What your stat UI should actually read instead of a stupid arithmetic sum.
i.e. After you fill out Row 4 and below > Row 2 = what your 'total' ignore def is. You can use this number instead of having multiple *(1-ignoreDEF%) in your equation.
[i]1-BossPDR*(1-[b]Row2[/b]) = [b]%of damage that gets through[/b][/i]
[quote=ryuushinou][url=http://docs.google.com/spreadsheet/ccc?key=0An5-TcCPsuLqdHp2TV9UMjFPN25zOTRvNWVTYUF3WlE#gid=0]For lazy people.[/url][/quote]
hmmmm, mind doing a quick guide on this? you add all pdr sources, then... (?)
Your added pdr is pretty useless; you have to calculate each individual source multiplicative into the equation to find out how much you truly ignore (already stated by the guide).
But yea. who knows why they even bother showing added pdr </3
[quote=ryuushinou][url=http://docs.google.com/spreadsheet/ccc?key=0An5-TcCPsuLqdHp2TV9UMjFPN25zOTRvNWVTYUF3WlE#gid=0]For lazy people.[/url][/quote]
It's not only for lazy people. This saves a lot of time.
I made one for personal use but anyone can use this, which makes it awesome.
Thanks for sharing.
[url=http://docs.google.com/spreadsheet/ccc?key=0An5-TcCPsuLqdHp2TV9UMjFPN25zOTRvNWVTYUF3WlE#gid=0]For lazy people.[/url]
[quote=ytv090]So that luminous link skill that ignores 10% is pretty useless huh?[/quote]
It is not that great, especially with this multiplicative system. If someone is purely concerned about damage, they would put in the work for it. Also, some people get hook ups like GPA (Grandpa) leech, or Zakum leech. At level 120, it is 15%. I plan on getting mine to 15% since I probably have not much better to do.
So that luminous link skill that ignores 10% is pretty useless huh?
[quote=LetThereBeFradd]Doesn't that include freakin' Horntail...[/quote]
Hahaha you made me laugh so hard I fell to the floor
OT: Now I finally understand how all this PDR thing works, thanks for the amazing info!
For people with Root Abyss Set:
Weapon ignores 10%
Top/bottom ignore 5%
Helm ignores 10%
When looked at [b]multiplicatively[/b], those combined ignore 26.8975% defense. Of course, when looked at [b]additively[/b], it is 30%.
@David0696
Ambition doesn't work btw
@lazershock: lol I've been looking for that link since 2-3 days ago u.u
since i have like 10+ sources of pdr i'm just too lazy to do the calcs manually e.e
didnt read, just went straight to the comments
[quote=iluvme]Wait, you're a dark knight, so you should have ignore defense on dark impale and its hyper skill. If you can't get the Leafre set, a decent alternative is the Hoblin set (I think this is the one with 15% ignore defense and +1% all stat, or maybe not). You can also get, I believe, the Luminous link skill for an extra +10% defense ignore.[/quote]
or use sacrifice, 100% ignore def right there.
[quote=SombraManx]ther was a multiplicative PDR calculator somewhere.. Does any1 still have the link?
It would be so usefull for all maplers now[/quote]
I know which one you're talking about =P, let me find it and i'll post a link when I do
(though the new formula isn't too troublesome since its literally 1 - (1- source a) (1 - source b) (1 - source c) and so on)
Edit: can't find this thing for the life of me, maybe someone else knows the link.
To elaborate on my earlier formula by the way incase it was unclear or someone didn't understand
Say for instance I have 50% from gungnir, 30% from sacrifice (I believe the other 10% is counted seperately) and 30% from leafre codex = 110% additively, but
multiplicative it would be 1 - (1-.50) (1-.30) (1-.30) or 0.75, 75% defense ignore. So a boss like C-Vellum would reduce my damage by 75% still (and then physical resist would cut my 25% remaining damage in half, to 12.5% of my original numbers)
[quote=TrillaJays]Tl;dr please[/quote]
Calculating how much defense you ignore post-Unleashed is poop. Reverting back to the old way ignore defense was calculated is much better.
Very informative +1 Like Thanks for the info.
ther was a multiplicative PDR calculator somewhere.. Does any1 still have the link?
It would be so usefull for all maplers now
[quote=LetThereBeFradd]@David0696: Doesn't that include freakin' Horntail...[/quote]
Yes, it does include Horntail. D:
[quote=LetThereBeFradd]@David0696: Yeah, you're a Demon Slayer so it's easy for you to get PDR ignore. I'm saying it's NOT easy for me. Leafre Set? I don't even know what that is, and if I did, then I'd have to scroll it and pot it.[/quote]
Get all of the monster cards from the Leafre area, including PQs. Then open your codex. Use the set effect.
[quote=LetThereBeFradd]Of course it is for you, Demon Slayer.
I have like no ignore defense on any character. How am I supposed to get PDR ignore, boss damage, and all that other crap on my potential.[/quote]
Simple, you don't! once you pass say 90% ignore it becomes very very hard to go higher, you can usually get it from skills, nebulites, lumis link skill, etc
I calculated that post-RED i'll have 205% defense ignore additively, which is 90% multiplicative and due to his physical resist, C-Vellum will STILL reduce my damage by 80% (honestly they either need to STOP giving bosses physical resist, or turn it into a buff that they cast *or just give us more ways to ignore it than the crappy 5% insight gives* because its a little ridiculous when a boss has such INSANE amounts of defense AND physical resist at the same time)
Also the leafre crusader codex set (you get this by getting all of the cards from leafre, hornedtail, dragonoir, and dragon rider included) gives +30% defense ignore
[quote=LetThereBeFradd]Of course it is for you, Demon Slayer.
I have like no ignore defense on any character. How am I supposed to get PDR ignore, boss damage, and all that other crap on my potential.[/quote]
Leafre Set gives 30% ignore defense. Ambition gives 10% ignore defense. Binding Darkness gives 30% ignore defense passively. Demon cry lowers defense of monsters by 15%. Demon impact ignores 30% defense. Anything else I think would need funding, such as cubes and nebulites.
I think its just to show the flat number of pdr...
[quote=iCyan]Wildcannon14 i keep trying it says offline and when i try to add to buddy says char not registered[/quote]
16 not 14
Edit:Send me in 5 or 10 minutes
[quote=Splutter]I wish there was an explanation for characters with [b]over[/b] 100% ignore def. I apparently have 177% ignore defense and I have no idea why, but I don't know what that means for me either.[/quote]
Right now in the User Interface (UI), it [b]adds[/b] up all of your sources of ignore defense. My guess it that the combination of skills and equips, along with other sources add up to 177%. For example, heros have a skill that ignores 50% defense.
@PoepieFTW
http://www.basilmarket.com/MapleStory-Page-Skills.html#Threaten
With the hyper skill, threaten takes off half (50%) of the enemy's defense.
[quote=iCyan]Wow nice info thanks , i will read it later thanks for taking your time redacting this[/quote]
Bro chat on wildcannon16 but fast!
I wish there was an explanation for characters with [b]over[/b] 100% ignore def. I apparently have 177% ignore defense and I have no idea why, but I don't know what that means for me either.
[quote=Quasar]Okay.[/quote]
OMG, so glad you liked it!
Okay.