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### Why No One Should Ever Buy Crit DMG

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EnderA

Senior Member

Quote:
Hellpyre:
I read this a while ago, and you know what? It's really helped. Looking at the math help make more sense out of why I did X much damage with Y choice, even though choice Z was considered better. Also, it's nice to have an easy to figure proportion for how this works. Thank you for the excellent thread.

You're welcome! I'm glad it was helpful.

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kayman37

Junior Member

Quote:
EnderA:
Believe me, I've checked them. You can follow my calculations yourself, and plug the numbers in.

The problem is that Crit Damage deceives you. You think "I'll do 40% more damage on my crit!" but no, that's 40% more of your base damage, not your crit damage. So you only get an overall increase of 20% (and that's best-case.) Armor penetration, however, applies to both the base damage and the crit bonus. So a 25% increase from armor penetration makes an overall increase of... 25%.

Riot has (massively) failed at balancing crit damage and armor penetration runes (the crit damage nerf was... ******ed.) Perhaps they will soon release a patch that restores that balance.

first off endrA may i say that i greatly respect what you're trying to accomplish here. education and utilization of rescources to help people not waste their time is very honorable.

actually what koss smith was trying to tell you is that the formula for final damage is not 100/(100+armor)*crit damage*base damage (which for our purposes you used 100 base damage which we'll keep because it's easy) it is total armor/(100+ total armor)*crit damage*base damage as stated in the champion statistics (http://www.leagueoflegends.com/learn/champion_statistics). I can' t seem to find a patch where they say that they converted it to your formula, if you can find it can you please link it?

so under the "correct" formula:

with 33.45% Crit Damage: 100 * 2.3345 * (100/200) = 116.725 damage
With 29.37 Armor Pen: 100 * 2 * (70.63/170.63) = 82.7873 damage

so crit damage is 29% beter on a crit... so you still need a high crit rate to make it plausible, but either are still decent runes to go with, depending on your char. (sure makes the crit damage rune nerf in v1.0.0.74 (http://www.leagueoflegends.com/board/showthread.php?t=58247) make a lot more sense..

edit: added the "correct" formula so peeps dont have to goto the page and look it up

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EnderA

Senior Member

Quote:
kayman37:
first off endrA may i say that i greatly respect what you're trying to accomplish here. education and utilization of rescources to help people not waste their time is very honorable.

actually what koss smith was trying to tell you is that the formula for final damage is not 100/(100+armor)*crit damage*base damage (which for our purposes you used 100 base damage which we'll keep because it's easy) it is total armor/(100+ total armor)*crit damage*base damage as stated in the champion statistics (http://www.leagueoflegends.com/learn/champion_statistics). I can' t seem to find a patch where they say that they converted it to your formula, if you can find it can you please link it?

so under the "correct" formula:

with 33.45% Crit Damage: 100 * 2.3345 * (100/200) = 116.725 damage
With 29.37 Armor Pen: 100 * 2 * (70.63/170.63) = 82.7873 damage

so crit damage is 29% beter on a crit... so you still need a high crit rate to make it plausible, but either are still decent runes to go with, depending on your char. (sure makes the crit damage rune nerf in v1.0.0.74 (http://www.leagueoflegends.com/board/showthread.php?t=58247) make a lot more sense..

edit: added the "correct" formula so peeps dont have to goto the page and look it up

If that formula were true, then armor wouldn't protect, it would amplify damage.

Example:

No armor: 100 * 0/100 = 0
50 armor: 100 * 50/150 = 33.3 damage
100 armor: 100 * 100/200 = 50 damage

Clearly against a target with zero armor you should do damage, and armor should make you take less damage. Hence, that equation is wrong.

EDIT: Correction, it's not wrong, it's just another way of looking at it. That equation calculates the fraction it's reducing the damage.

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Smuggler

Member

One word, Tyrndamere. Critting people at level 1 for 300 damage proves this entire theory wrong, so what if I have to get a Last Whisper as my 2nd or third damage item, Need attack speed anyway.

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Phi Trigger

Senior Member

Quote:
kayman37:
first off endrA may i say that i greatly respect what you're trying to accomplish here. education and utilization of rescources to help people not waste their time is very honorable.

actually what koss smith was trying to tell you is that the formula for final damage is not 100/(100+armor)*crit damage*base damage (which for our purposes you used 100 base damage which we'll keep because it's easy) it is total armor/(100+ total armor)*crit damage*base damage as stated in the champion statistics (http://www.leagueoflegends.com/learn/champion_statistics). I can' t seem to find a patch where they say that they converted it to your formula, if you can find it can you please link it?

so under the "correct" formula:

with 33.45% Crit Damage: 100 * 2.3345 * (100/200) = 116.725 damage
With 29.37 Armor Pen: 100 * 2 * (70.63/170.63) = 82.7873 damage

so crit damage is 29% beter on a crit... so you still need a high crit rate to make it plausible, but either are still decent runes to go with, depending on your char. (sure makes the crit damage rune nerf in v1.0.0.74 (http://www.leagueoflegends.com/board/showthread.php?t=58247) make a lot more sense..

edit: added the "correct" formula so peeps dont have to goto the page and look it up

The formula you found is damage *reduction*, not final damage modifier. So for example, if you have 0 armor, you'd reduce the damage by 0.

While armor penetration is very alluring, there is one item that makes all the mathematics go a bit awry. That item is last whisper. The reason why this item screws with the math is because it has a percentage armor penetration rather than a set number of armor penetrated, which means that it's effectiveness is increased if you do not have armor penetration runes by the order that armor reduction is applied (percentages come last). The combination of critical damage and last whisper is very potent indeed.

The correct formula for total damage is actually:

Total damage = Attack * Crit damage - Attack * Crit damage * armor/(100 + armor)

Which simplifies to:

Total damage = Attack * Crit damage * (1 - Armor / 100 + armor)
= Attack * Crit damage * ( (100 + armor - armor)/(100 + armor) )
= Attack * Crit damage * 100/(100 + armor)

Which we can see is the formula ender gave....except.....one thing about armor penetration - I am not quite so sure that it modifies as a direct negative from armor in the way that is listed. I don't see any help files relating to the way armor penetration effects, but it seems to me that armor reduction effects would not be the same as armor penetration effects, which would be the case by the equations used in this thread.

My guess, without proof, would be armor penetration value is the maximum number of damage that is delt without any armor reduction. So for example, someone with 100 damage with 20 armor penetration attacking a player with 100 armor would deal 60 damage instead of 50 if that armor penetration were 0. This would make it a distinct statistic from armor reduction.

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kayman37

Junior Member

agreed the formula i gave doesn't deal well with a person having 0 armor or even less as we can all agree reduction can take you below. for these purposes i believe riot merely makes the equation if x=<0 then *(-1)+1. aka they add one so that now it becomes a multiplier instead of a wierd undefinable negative (-.2 would become 1.2). i'm sorry i'm not grasping this, you're trying to be very specific, but i'm really not following your simplifications phi trigger, the math seems to be wierd since in the second line you just subtract armor from armor but don't keep the equation balanced, what am i missing? are you meaning ArP?

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EnderA

Senior Member

Quote:
Smuggler:
One word, Tyrndamere. Critting people at level 1 for 300 damage proves this entire theory wrong, so what if I have to get a Last Whisper as my 2nd or third damage item, Need attack speed anyway.

Tryndamere should definitely not be getting crit damage. He already has a crit damage skill (making armor pen/crit chance more appealing,) would love some more crit chance for his abilities, and does more damage with armor penetration. Last whisper's % pen applies before flat pen, making armor pen more appealing. So either crit chance or armor pen. Not crit damage.

But feel free to completely ignore everything said in the thread.

Quote:
Phi Trigger:
The formula you found is damage *reduction*, not final damage modifier. So for example, if you have 0 armor, you'd reduce the damage by 0.

While armor penetration is very alluring, there is one item that makes all the mathematics go a bit awry. That item is last whisper. The reason why this item screws with the math is because it has a percentage armor penetration rather than a set number of armor penetrated, which means that it's effectiveness is increased if you do not have armor penetration runes by the order that armor reduction is applied (percentages come last). The combination of critical damage and last whisper is very potent indeed.

Actually, Last Whisper's % penetration is applied *before* flat armor penetration, meaning it makes flat armor penetration *more* effective.

The order is:
-Armor Reduction
-% Armor Pen
-Flat Armor Pen

Quote:
Phi Trigger:
The correct formula for total damage is actually:

Total damage = Attack * Crit damage - Attack * Crit damage * armor/(100 + armor)

Which simplifies to:

Total damage = Attack * Crit damage * (1 - Armor / 100 + armor)
= Attack * Crit damage * ( (100 + armor - armor)/(100 + armor) )
= Attack * Crit damage * 100/(100 + armor)

Which we can see is the formula ender gave....except.....one thing about armor penetration - I am not quite so sure that it modifies as a direct negative from armor in the way that is listed. I don't see any help files relating to the way armor penetration effects, but it seems to me that armor reduction effects would not be the same as armor penetration effects, which would be the case by the equations used in this thread.

My guess, without proof, would be armor penetration value is the maximum number of damage that is delt without any armor reduction. So for example, someone with 100 damage with 20 armor penetration attacking a player with 100 armor would deal 60 damage instead of 50 if that armor penetration were 0. This would make it a distinct statistic from armor reduction.

Nice, you correctly derived the damage equation from the listed equation in champion statistics.

I am certain Armor Penetration works as I described. The three differences between armor reduction and armor penetration are: 1) It's applied before armor penetration, meaning it stacks very poorly with % penetration. 2) Armor reduction affects the actual statistic, making it increase all damage dealt to the target. Meaning with a black cleaver, you're increasing everyone's damage versus that target, and you'll see their armor drop by that amount every hit. Armor penetration just makes your attack do damage as though they had that much less armor. 3) It can reduce their armor below 0. (Armor penetration's effect is capped at 0 armor.)

If you reduce their armor to below 0, then the new damage calculation is:

Total damage = Attack Damage (* Crit Damage if it's a crit) * (100 + |Armor|) / 100, since Armor is negative.

If they didn't change that equation, you'd end up with infinite damage at -100 armor.

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Phi Trigger

Senior Member

Quote:
EnderA:
Actually, Last Whisper's % penetration is applied *before* flat armor penetration, meaning it makes flat armor penetration *more* effective.

The order is:
-Armor Reduction
-% Armor Pen
-Flat Armor Pen

Nice, you correctly derived the damage equation from the listed equation in champion statistics.

I am certain Armor Penetration works as I described. The three differences between armor reduction and armor penetration are: 1) It's applied before armor penetration, meaning it stacks very poorly with % penetration. 2) Armor reduction affects the actual statistic, making it increase all damage dealt to the target. Meaning with a black cleaver, you're increasing everyone's damage versus that target, and you'll see their armor drop by that amount every hit. Armor penetration just makes your attack do damage as though they had that much less armor. 3) It can reduce their armor below 0. (Armor penetration's effect is capped at 0 armor.)

If you reduce their armor to below 0, then the new damage calculation is:

Total damage = Attack Damage (* Crit Damage if it's a crit) * (100 + |Armor|) / 100, since Armor is negative.

If they didn't change that equation, you'd end up with infinite damage at -100 armor.

I remember the order of armor related effects differently, but I am not saying by any means you are incorrect. Do you by any chance have a link so we can verify the order, or do you know simply from testing? Same with armor penetration - is your knowledge based on empyrical evidence or hard evidence?

Assuming you are correct, that certainly means that last whisper and armor penetration are in fact imbalanced together in combination and worth trying out. I do play poppy though, so neither crit, crit damage, nor armor penetration really matter to me...

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EnderA

Senior Member

Quote:
Phi Trigger:
I remember the order of armor related effects differently, but I am not saying by any means you are incorrect. Do you by any chance have a link so we can verify the order, or do you know simply from testing? Same with armor penetration - is your knowledge based on empyrical evidence or hard evidence?

Assuming you are correct, that certainly means that last whisper and armor penetration are in fact imbalanced together in combination and worth trying out. I do play poppy though, so neither crit, crit damage, nor armor penetration really matter to me...

Heh, sure, look at the guides & strategy sticky: http://www.leagueoflegends.com/board/showthread.php?t=3287

Also: http://www.leagueoflegends.com/board/showthread.php?t=2220&highlight=@zileas&page=4

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Phi Trigger

Senior Member

Quote:
kayman37:
agreed the formula i gave doesn't deal well with a person having 0 armor or even less as we can all agree reduction can take you below. for these purposes i believe riot merely makes the equation if x=<0 then *(-1)+1. aka they add one so that now it becomes a multiplier instead of a wierd undefinable negative (-.2 would become 1.2). i'm sorry i'm not grasping this, you're trying to be very specific, but i'm really not following your simplifications phi trigger, the math seems to be wierd since in the second line you just subtract armor from armor but don't keep the equation balanced, what am i missing? are you meaning ArP?

The second line where armor is subtracted from armor is in fact just derived from the first line. 1 can be rewritten as (100+ armor) / (100+armor) with the assumption that armor can't be -100. Then the two have a common denominator and can be combined, which is the point that line 2 adds 100 + armor and -armor, which negates the armor and leaves 100 after the dust settles.