DISCLAIMER: due to the ambiguous nature of the issues which have never been officially confirmed by the publisher – Riot Games, all the references herein are just to back the reasoning and assumption, they can not be considered to be unquestionable proofs to trust. Furthermore, also due to the ambiguity, the degree of certainty of the discussion should be judged by the readers themselves.
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When we play defensive-leaning champions like tanks, one of the most important issues for us to consider is AR and MR: how we should build and how much AR and MR we should have for the best effectiveness. Meanwhile when we play very offensive champions like ADC, mid mage, assassin,... we may have to concern how to most effectively damage the opponents, especially the tanks with very high indexes of AR and/or MR.
Very interestingly and in fact, these issues are very closely related, and together very close to health point (HP). Basically, the defensive players want to increase the indexes of their own champions to lose lowest HP possible, while offensive players want to ignore the indexes of the opponents to take highest HP possible in fighting.
At this point, the concepts converge on the central issue: how the defensive indexes of AR and MR reinforce or diminish the index of health point (HP). Understanding this will help us improve the playing of both kinds of defensive- and offensive-leaning champions. Due to the equivalence between the couple of armor and physical damage with the couple of magic resistance and magic damage, we will only mention the former (the later of magic resistance and magic damage will be considered completely the same).
There are two types of index to increase physical damage: armor penetration and armor reduction; for each type, there are two different forms: flat and percent. Finally, all we have are four forms: flat AR reduction, percent AR reduction, flat AR penetration, and percent AR penetration. The sources for these forms include: champions' abilities, items, runes, and masteries; example:
There are two types of index to increase physical damage: armor penetration and armor reduction; for each type, there are two different forms: flat and percent. Finally, all we have are four forms: flat AR reduction, percent AR reduction, flat AR penetration, and percent AR penetration. The sources for these forms include: champions' abilities, items, runes, and masteries; example:
+) Flat AR reduction: Rammus' E-PuncturingTaunt reduces the target's AR by 10/ 15/ 20/ 25/ 30 for 1.25/ 1.5/ 1.75/ 2/ 2.25 seconds
+) Percent AR reduction: The Black Cleaver reduces targets' AR up to 30% for 6 seconds
+) Flat AR penetration: Youmuu's Ghoshblade gives +20 AR penetration
+) Percent AR penetration: Last Whisper gives +30% bonus AR penetration
1. Issues with questionable degree of certainty[1]
+) The order in which the forms are applied in case the attackers have more than one form is[2]
(1) Flat AR reduction
(2) Percentage AR reduction
(3) Flat AR penetration
(4) Percentage AR penetration
+) Example: one tank with 200 AR taken damage from an ADC with 10 AR reduction, 30% AR reduction, 20 AR penetration, and 45% AR penetration (according to the rule):
(1) Firstly, 200 AR will be reduced to 190 AR, by 10 AR reduction
(2) Next, 190 AR will be reduced to 133 AR, by 30% AR reduction
This value of 133 AR will become the AR index of the target as shown on the table of stats instead of the original of 200 AR (always in a short duration of a few seconds). Consequentially, the damage from other team mates on the tank will be treated with the new value of 133 AR instead of 200 AR (within the duration).
(3) Then, 133 AR will be considered as 113 AR for the damage from the ADC, by 20 AR penetration
(4) Finally, 113 AR will be considered as 62.15 AR for the damage from the ADC, by 45% AR penetration
For the particular ADC, the damage dealt on the particular tank will treat with the final value of 62.15 AR, not 133 AR as damage from other team mates nor 200 AR as original.
+) The damage dealt in fighting by attackers always differs from the damage taken by the targets (always gets reduced by defensive indexes of the targets). One of the relations for the damage reduction by AR index is supposed to be:[3]
For the example above, the damage the tank takes from the (damage dealt by the) ADC, according to the relation, is:
This taken damage will be directly subtracted from the total health (HP) of the tank until the tank gets slain. In this case, we can say: "the AR index makes the tank take only 62% damage from the ADC" or "the AR index helps the tank ignore 38% damage from the ADC".
2. Issues with high degree of certainty
No matter how exact the equations are, we can still get something good from the nature of the relations: more AR we have, the HP will be harder to lose; in other words: the AR increases the effectiveness of the HP.
In the example above, if a certain AR index makes the tank reduce 50% the damage from the ADC (we don't need it to be exactly 200 or so for the uncertainty of the equation), this means the ADC will need double damage to take away the same HP from the tank. In other words, the AR index doubles the HP of the tank in fighting against the particular ADC. Here, we have just come to two important conclusions:
(1) AR-HP equivalence: AR and HP are just two equivalent forms of the same index and can be transformed into each other by using some mathematical relations.
(2) Relativity nature: the effectiveness of a certain AR index is different for different attackers due to the different AR reduction and AR penetration indexes the attackers possess. In other words, we are talking about the relativity of AR index in different reference to different attackers.
It's so funny but true to consider these properties just like (1) a kind of the famous relation of mass-energy equivalence and (2) a kind of the relativity concepts by Albert Einstein:
(1) AR-HP equivalence: AR and HP are just two equivalent forms of the same index and can be transformed into each other by using some mathematical relations.
(2) Relativity nature: the effectiveness of a certain AR index is different for different attackers due to the different AR reduction and AR penetration indexes the attackers possess. In other words, we are talking about the relativity of AR index in different reference to different attackers.
It's so funny but true to consider these properties just like (1) a kind of the famous relation of mass-energy equivalence and (2) a kind of the relativity concepts by Albert Einstein:
+) For the nature of armor penetration: physical damage simply ignores the armor on effect, while the armor index of the target is not reduced in reality and still remains as original (as shown on the table of stats). Damage from other team mates will NOT benefit from the armor penetration indexes.
+) Armor reduction, on the contrary, reduces the armor index of the target in reality (as shown on the table of stats, and always in a short duration of a few seconds); damage from other team mates will also benefit from the reduction (increase, within the duration).
In other words: armor reduction on affected targets is applied for damage from all sources (including damage from other team mates), but is limited in time by a short duration: the armor indexes of the affected targets will return as originals off the limited duration; while armor penetration of a champion is perpetual, but is limited to apply only for the damage from the holder champion.
In other words: armor reduction on affected targets is applied for damage from all sources (including damage from other team mates), but is limited in time by a short duration: the armor indexes of the affected targets will return as originals off the limited duration; while armor penetration of a champion is perpetual, but is limited to apply only for the damage from the holder champion.
+) In case the target's armor has been ignored to zero already, flat armor reduction is an exception among the four forms: it can reduce the target's armor further below zero to deal more damage. The three remaining forms (flat and percent armor penetration as well as percent armor reduction) CANNOT ignore target's armor further below the value of zero.
Pragmatically, these characteristics are reasonable: any percentage of zero is zero, so percent penetration and reduction cannot ignore target's armor further below zero; for flat armor penetration, you need something to "penetrate", so nothing to penetrate if the armor gets zero already. In the same way, "penetration" should be considered as "personal characteristics of the attackers", so it should not reduce the armor index of the targets in reality, and damage from other team mates should not benefit from it; while "reduction" should be made to be "general power of the attackers", so it should reduce the armor of the targets in reality and increase damage from other team mates on the affected targets as well.
Conclusion
Due to the equivalent nature of AR and HP, for defensive champions (tanky), we have at least two-plus-one ways to increase the defense capability: increase AR or increase HP, or increase both at the same time. Which and how to increase for the best should depend on the particular games, players, champions, items and plans, etc. For example, Nautilus benefits much more from HP[4] in comparison with AR, so we should build HP-focus for the best of playing Nautilus; Rammus, on the other hand, benefits much more from AR[5] in comparison with HP, and we should build AR-focus for the best of playing Rammus.
In the same way, for offensive champions (ADC, mage, assassin,...), we also have at least two-plus-one ways to increase the damage capability: increase AD index or increase AR reduction and AR penetration, or increase both at the same time (we can also increase critical damage, critical chance, and AS as well of course). Which and how to increase for the most effectiveness, just like the defensive indexes, should depend on the particular games, players, champions, items and plans, etc.
Conclusion
Due to the equivalent nature of AR and HP, for defensive champions (tanky), we have at least two-plus-one ways to increase the defense capability: increase AR or increase HP, or increase both at the same time. Which and how to increase for the best should depend on the particular games, players, champions, items and plans, etc. For example, Nautilus benefits much more from HP[4] in comparison with AR, so we should build HP-focus for the best of playing Nautilus; Rammus, on the other hand, benefits much more from AR[5] in comparison with HP, and we should build AR-focus for the best of playing Rammus.
In the same way, for offensive champions (ADC, mage, assassin,...), we also have at least two-plus-one ways to increase the damage capability: increase AD index or increase AR reduction and AR penetration, or increase both at the same time (we can also increase critical damage, critical chance, and AS as well of course). Which and how to increase for the most effectiveness, just like the defensive indexes, should depend on the particular games, players, champions, items and plans, etc.
This post was completed; there would be just minor adjustments if any on this post
Last update: January 26, 2016
The Silencekeeper
Last update: January 26, 2016
The Silencekeeper
References
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First off, I would remind the DISCLAIMER again: due to the ambiguous nature of the issues which have never been officially confirmed by the publisher – Riot Games, all the references herein are just to back the reasoning and assumption, they can not be considered to be unquestionable proofs to trust.
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[1] [2] [3] According to leagueoflegends.wikia.com, reddit.com, forums.na.leagueoflegends.com:
http://leagueoflegends.wikia.com/wiki/Armor
http://leagueoflegends.wikia.com/wiki/Armor_penetration
http://forums.na.leagueoflegends.com/board/showthread.php?t=2538500&page=3
http://forums.na.leagueoflegends.com/board/showthread.php?t=2929417&page=4#post32707861
https://www.reddit.com/r/summonerschool/comments/424rio/how_do_black_cleaver_and_the_new_last_whisper/
https://www.reddit.com/r/summonerschool/comments/424rio/how_do_black_cleaver_and_the_new_last_whisper/cz7m8oo
http://leagueoflegends.wikia.com/wiki/Magic_resistance
http://leagueoflegends.wikia.com/wiki/Magic_penetration
[4] For more details, look at the following post: Nautling: how to Nautilus? Be the Titan of the Dephs!
[5] For more details, look at the following post: P3 The 'null phase' of a game: bans and picks. How? (Section 3. Some typical examples of my own favorite counter-picks, subsection Strategic counter-picks)
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