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Crumbling Defenses: The Defense Penetration Items

platzapus

platzapus

Mon 1st May 2017 - 1:32pm

Many champions in League of Legends want to build mostly offensively focused items. If you're not playing a tank or one of the fully defensive support champions, such as Janna or Soraka, the issue of flat damage (crit, attack speed, AD, AP) vs. defense piercing (Lethality, armor shred, magic penetration) will be one you'll need to solve in most of your games. By the end of this write-up, I will have covered the defense piercing items, some of the more technical details as to how defensive statistics scale and interact, what to consider in any game when drawing up an item build, and some mid-game damage calculations against different targets with different items.

The Items

Lethality

The mechanic: Every point of Lethality grants your champion 0.6 + (4/180)*(Target's Level) flat armor penetration. In other words, the flat armor penetration granted scales from 0.6*Lethality when your target is level 1 to 1*Lethality when your target is level 18.

Duskblade of Draktharr

65 attack damage

15 Lethality

Unique: +20 movement speed out of combat.

Unique Passive – Nightstalker: After being unseen for at least 1 second, your next basic attack deals 75 + (200% Lethality) bonus true damage on-hit (lasts 4 seconds after being seen by an enemy champion)

Unique Passive - Blackout: When spotted by an enemy ward, causes a blackout for 8 seconds, disabling all nearby enemy wards (90 second cooldown).

Youmuu's Ghostblade

60 attack damage

+10% cooldown reduction

15 Lethality

Unique: +20 movement speed out of combat.

Unique Active: Gain +20% movement speed for 6 seconds (45 second cooldown).

Edge of Night

55 attack damage

35 magic resist

15 Lethality

Unique: +20 movement speed out of combat.

Unique Active: Channels for 1.5 seconds to gain a spell shield that blocks the next enemy ability within the next 5 seconds (45 second cooldown). Damage will interrupt the channel. You can move while channeling. If the channel is interrupted, the item is put on a reduced 5 second cooldown.

As far as the armor penetration goes, these items are all identical. They each give 15 Lethality. For specific reasons to buy one over the other, you'd have to look elsewhere. Duskblade is the biggest damage boost and has a vision control passive. Ghostblade grants you some cooldown reduction and allows you to get around the map even faster. Edge of Night is the magic/spell defense item. Choose what you need. Each is similarly priced (range from 2900 gold for Ghostblade to 3250 gold for Duskblade) and offers similar core stats in attack damage and Lethality. Lethality items are best purchased when targeting low armor targets, as you'll get the largest damage increase for your gold. This will be covered more later when the defensive stat to % damage reduction process is investigated.

Last Whisper Variants

Last Whisper

10 attack damage

Unique - Last Whisper: +45% bonus armor penetration.

Lord Dominik's Regards

50 attack damage

Unique Passive - Giant Slayer: Grants up to 15% bonus physical damage against enemy champions with greater maximum health than you (1.5% damage per 100 health difference, capping at 15% damage).

Unique - Last Whisper: +45% bonus armor penetration.


Mortal Reminder

50 attack damage

Unique Passive - Executioner: Physical damage inflicts Grievous Wounds (reduces all healing effects on target by 40%) on enemy champions for 5 seconds.

Unique - Last Whisper: +45% bonus armor penetration.

Like the Lethality items, the penetrative effects of the Last Whisper items are identical. You upgrade the item for either additional damage against high health targets or the reduced healing effect that applies on all physical damage, not just auto attacks. It is very important to note that the Last Whisper items only cut through bonus armor. This means that the armor penetration provided by these items will have no effect (or little effect if armor is gained through runes or masteries) against targets that have not built any armor items. This detail pushes the Lethality and Last Whisper items even further apart on the armor penetration spectrum.


The Curious Case of Cleaver

The Black Cleaver

400 health

40 attack damage

20% cooldown reduction

Unique Passive: Dealing physical damage to an enemy champion Cleaves them, reducing their armor by 5% for 6 seconds, stacking up to 6 times for a maximum of 30%.

Unique Passive - Rage: Dealing physical damage grants 20 movement speed for 2 seconds. Assists on Cleaved units or kills on any unit grant 60 movement speed for 2 seconds instead. The movement speed bonus is halved for ranged champions.

The Black Cleaver, as we'll also see with Abyssal Scepter later, is an item with a damage amplification or defense shredding effect instead of a piercing effect. This means that a Cleaved target's armor is effectively lowered for all physical damage sources instead of just your own. Because of the ubiquitous nature of AD Carries and the indiscriminate nature of the armor shredding (Cleaves % total armor), there isn't really a bad situation for Black Cleaver like there can be for the Last Whisper or Lethality items. In my opinion, the only things stopping this from being a staple for all attack damage champions are the low attack damage number and the desire to quickly get targets to 6 Cleave stacks, which some champions can't reliably do.

Magic penetration items have rough equivalents to each type of armor penetration in flat magic penetration, % magic penetration, and a unique damage amplification item.

 

Flat Magic Penetration

Liandry's Torment

300 Health

80 ability power

Unique Passive: Eyes of Pain: +15 magic penetration

Unique Passive: Dealing spell damage applies a damage-over-time effect that deals bonus magic damage equal to 2% of the target's current health per second for 3 seconds. This bonus damage is doubled against movement-impaired units.

Sorcerer's Shoes

+15 magic penetration

Unique: Enhanced Movement: +45 movement speed

The options for flat magic penetration aren't terribly extensive, but they also don't compete for item slots in any way. In a situation where you'd want flat magic pen, it'd be very easy to justify getting both. While Liandry's Torment feels like a specialized item because of its unique damage-over-time passive, it is gold efficient even without the passive and becomes incredibly powerful against high health, low magic resist targets.


% Magic Penetration

Void Staff

80 ability power

Unique Passive: 35% magic penetration

The gold efficiency of Void Staff relies very heavily on how much value you're getting out of the % magic penetration. If your target is sitting at the minimum 30 magic resistance, Void Staff is granting you less magic damage amplification than Abyssal Scepter without the upside of the amplification being cast as an aura. The effectiveness can ramp up to more than 3x that value as your target gains magic resist. Void Staff should be a high priority post-core item when the enemy team has a number of high magic resist targets and you're playing a champion who is unable to reliably close to the squishy priority targets. It's important to note that % magic penetration scales multiplicatively.

Abyssal Scepter

60 magic resist

60 ability power

10% cooldown reduction

Unique: Nearby enemy champions take 10% more magic damage.

The Abyssal Scepter aura is unique in that in takes the final product of your damage calculations and increases it by 10% outright. This is worth a varying amount of flat or % magic penetration depending on the target's magic resistance. As such, this would be a great time to transition to.

The Flat Defenses to % Reduction Formula

The formula for determining the fraction of the tooltip damage you'll be doing is as follows:

Damage Multiplication  = (100/( 100 + Defense)) when enemy Defense is 0 or higher.

Damage Multiplication = (2-(100/(100-Defense))) when enemy Defense is a negative value.

Two formulas exist to create a situation mirrored about the Defense = 0 axis, meaning that x and -x Defense will result in a y and -y % damage modifier. For example, the 50 magic resist case and the -50 magic resist case would result in 66% of tooltip damage and 134% of tooltip damage (+/- 34%).

What this means in practice is that each point of armor or magic resist is worth marginally less than the last. For example, the first point of defense is worth roughly 0.99% reduction whereas the second is worth roughly 0.97%. To be completely clear, this is not a linearly decreasing factor.

For quick reference, I'm including a table of some defense values and their corresponding reduction values.

Defense % Reduction
12 10%
30 (Base) 23%
43 30%
66 40%
100 50%
150 60%
233 70%
400 80%

Without masteries, runes, or skipping boots, the highest attainable values for armor and magic resist from items are 405 armor and 325 magic resist. These values also ignore champion abilities. The question that follows is how we get to the final defense values that will be used when calculating damage.


Application Order of Defense Piercing Effects

The defense altering effects are always applied in the same order:

1. Flat Reduction (Wit's End Passive)

2. % Reduction (Black Cleaver)

3. % Penetration (Void Staff, Last Whisper)

4. Flat Penetration (Lethality, Liandry's)

5. Amplification Effects (Abyssal Aura)


Damage Calculation Scenarios

Most games have you decide between more raw damage stats or penetration stats. Below I'll list out the results of calculations concerning what to buy as a third item given a set of preset conditions. I'm working with magic damage instead of physical damage because the majority of armor penetration or reduction items are items that are purchased because "I'm playing X champion" rather than because the enemy team bought enough armor on enough champions. Items like Black Cleaver and the Lethality items are generally bought regardless of the state of the game if they're bought at all.

The conditions are a level 11 Orianna with Sorcerer's Shoes, a Doran's Ring, Morellonomicon and Luden's Echo, a standard core build. She'll be using Command Attack (Q), Command Dissonance (W) and Command Shockwave (R) on targets with 30 magic resist, 90 magic resist (to account for base + 60 from Abyssal), and 160 magic resist (rough assumption for a tankier two item build such as Spirit Visage and Hexdrinker).

The items tested will be Rabadon's Deathcap, Liandry's Torment, and Void Staff, covering pure ability power, flat penetration, and % penetration.

The Vanilla Case

The Stats: 215 Ability Power, 15 Flat Magic Penetration

Target Magic Resist Damage Dealt
30 846.5
90 556.3
160 397.3

Rabadon's Deathcap Case

The Stats: 452.3 Ability Power, 15 Flat Magic Penetration

Target Magic Resist
(Effective Magic Resist)
Damage Dealt Damage Increase
(% Increase)
30 (15) 1238.6 392.1 (46%)
90 (75) 813.9 257.6 (46%)
160 (145) 581.4 184.1 (46%)

Liandry's Torment Case

The Stats: 295 Ability Power, 30 Flat Magic Penetration

Target Magic Resist
(Effective Magic Resist)
Damage Dealt Damage Increase
(% Increase)
30 (0) 1125.5 279 (33%)
90 (60) 703.4 147.1 (26%)
160 (130) 489.3 92 (23%)

Note: Remember that Liandry's is also granting you the DoT passive, which adds 2% or 4% of the target's current health per second for 3 seconds as magic damage. This is nearly impossible to quantify in a test case scenario given how many different values it could reasonably come out to. It was left out of calculations for that reason, but shouldn't be ignored (nor should the 300 health) when considering what to buy.

Void Staff Case

The Stats: 295 Ability Power, 15 Flat Magic Penetration, 35% Magic Penetration

Target Magic Resist
(Effective Magic Resist)
Damage Dealt Damage Increase
(% Increase)
30 (4.5) 1077 230.5 (27%)
90 (43.5) 784.3 228 (41%)
160 (89) 595.5 198.2 (50%)

In summary, the items perform generally as expected for an early-mid game scenario. Deathcap has the best damage output in the 30 MR and 90 MR cases, but is beat by Void Staff against the tankiest target. Liandry's has the second best outcome in the 30 MR case, but the worst in the other two cases before applying the situational damage from its passive.

Something to keep in mind is that this math is being run specifically for Orianna, with one 0.5 AP ratio and two 0.7 AP ratios. A champion with higher AP ratios will benefit more from Deathcap's pure chunk of ability power, while a champion with lower AP ratios would benefit more from one of the penetration items.

The final consideration to make is the gold cost of each item. Liandry's costs 3100 gold, Rabadon's costs 3800 gold, and Void Staff is the budget option at 2650 gold. In other terms, Rabadon's costs about 143% as much as Void Staff and Liandry's costs about 117% as much as Void Staff. For each to be cost efficient compared to Void Staff strictly in terms of damage, they need to at least match 143% and 117% of the damage increase values from Void Staff at the respective MR thresholds.

Item 30 MR  90 MR 160 MR
Rabadon's Deathcap 170% Pass 112% Fail 92% Fail
Liandry's Torment 122% Pass 63% Fail  46% Fail

As could be expected, both items surpass Void Staff against base magic resist targets on a per gold basis. They drop rapidly as the target's magic resistance increases, however. Void staff will be your best bet against any teams where your priority targets get even one major magic resist item. Keep in mind that this deals with a level 11 power spike scenario and is based purely on offensive stats from the examined items. Liandry's is far better than the numbers here show due to the passive and health. Even Rabadon's could be better than it appears to be if a team gets relatively little magic resist as the game progresses and you buy more ability power.

The Conclusion

In the end, we can see that for a sort of middle-of-the-road mage in Orianna, each of the items tested have their times and situations in which to shine. If you're looking purely at damage, you're likely looking at Void Staff or Rabadon's Deathcap for your third item. The big remaining consideration to be made here is how much Liandry's passive is worth for you in any given game on any given champion. I wouldn't even begin to know how to generalize its gold value in any meaningful way.

I didn't give Abyssal Scepter much attention here because, like Black Cleaver and the Lethality items, the scenarios in which you buy it are very obvious. If you feel you need a Negatron Cloak early, you're almost certainly getting an Abyssal Scepter, as that's the only mage item that builds out of Negatron. Put another way, you're buying it because it's the only remaining item with substantial ability power and magic resist values after Athene's Unholy Grail's transition to a support item.

The examples I went through should provide a solid base for determining what other champions may want to buy in a given situation. Thanks for reading and, as always, I appreciate any and all feedback or comments!

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