Penetration: Y u so misunderstood? :: League of Legends (LoL) Forum on MOBAFire

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So here's me, puttering along, reading a lovely Anivia guide (http://www.mobafire.com/league-of-legends/build/anivia-in-depth-mizore-v2-updated-by-castermaster-173059) when I stumble across this: "Greater Mark of Insight - Magic penetration is a nice addition to mages, and works for the entire game, since it will always penetrate magic resistance. However, alone, these are rather bad, so you might want to build a Void Staff, to stack up a bit more magic penetration."

Of course, you're aware the quints are a flat pen boost and the void staff is 40% penetration. I would like to draw your attention to how exactly these two stats interact, which inevitably involves magic resistance too. It's worth noticing that all this applies equally to armor and armor penetration (their formulae are identical) but I'm a mid player mostly so spell pen is just what I'm working with for now.

First things first, the magic resist formula.

Let's assume we're working with positive magic resist targets. Therefore, the damage multiplier applied by a target's magic resist will be 100 divided by 100 + their magic resist. For example, a target with 100 magic resist: 100/(100+100) = 0.5, so any damage dealt to that target is cut in half if you've got zero penetration.

Clearly, you're a smart mage; you don't have zero magic penetration. You've got yourself the 10% spell penetration mastery, perhaps sorc boots, spell pen quints, Void Staff and even an abyssal sceptre. You're also smart enough to notice these all have different types of penetration, because I like to make things complicated.

It's not really all that complicated; all of these modifiers have a standard order to be applied. First, Flat MR Reduction from your abyssal sceptre cuts 20 of their MR off; Flat MR Reduction Goes First. Then, any Percentage MR Reduction is applied; let's say you're Kayle and you've stacked your passive up nicely, so that goes second, 15% MR reduction; Percentage MR Reduction Goes Second. Then, your shoes and marks are applied; 20 Pen from the shoes, 8.55 Pen from the marks; Flat Pen Goes Third. Finally, Void Staff finally gets its turn, and cuts 40% off whatever's left; Percentage Pen Goes Last.

Well. The mathematically minded of you immediately realise that Void Staff is barely doing a damn thing; there's not a lot left to reduce. That original 100 MR we worked with earlier is down to 40 before the Void Staff is even applied! It only removes a feeble 16 MR in the end.

So at least now we're aware the order things occur in, and we're aware Void Staff goes last.

Conclusion One: Void Staff Gets Less Valuable the more Flat Pen, Flat Reduction and Percentage Reduction you have.
So spell pen is less valuable the more you have, right!?

WRONG, sir. The way that formula up there works basically means that (although resistances don't technically have diminishing returns, they always increase your effective health by the same % per point) the less armor or MR there is, the more valuable it is to remove another point or 25.

Example 1: 200 MR target, hit with a spell dealing 300 magic damage after AP ratios and all are applied. They take a pathetic 100 damage. You're a smart player, you've heard the conventional wisdom, so you grab you the cheapest, least out-of-the-way spell pen you can buy; Get me some Sorcerer's Shoes, STAT! Now they've got only 180 MR, haha! But... Your spell now deals 107 damage instead. That's... Not a very big boost. ****.

Example 2: 50 MR target, that squishy opponent in lane. Same 300-damage spell hits 'em for a whole 200 damage! Much better. You don't need no spell pen to hurt THEM! But you're a guide sheep, so you grab your Sorcerer's Shoes because that's next in the build, and your spell only goes up to - 230. Wait, what?

Yeah, that's right, against squishier targets, flat spell pen boosts your damage MORE than against tanky targets.

Conclusion Two: Flat Spell Pen Is More Effective Vs. Squishies than Vs. Tanky Targets

All righty then, now we've got some useful stuff to work with. That jackass who keeps insisting you should rush your sorc boots vs. Galio in mid is wrong, you should be saving for Void Staff first.

But let's see what happens when we REALLY start stacking flat spell pen, because earlier we said that more spell pen makes it worse, right? No, we said more spell pen makes Void Staff worse, because it's a percentage reduction to their MR applied AFTER flat boosts.

Example 1: 50 MR target, 300 damage spell, 200 damage done, we know. Now we apply flat Spell Pen marks (8.55 penetration), Sorcerer's Shoes (20 Penetration), that super-unpopular Haunting Guise (20 Penetration). The target's now got a feeble 1.45 MR; you're practically doing true damage! 295 damage! Take off the Haunting Guise - and suddenly he's taking only 247 damage.

Example 2: 200 MR target, 300 damage spell, 100 damage done, yep yep. Same again: Flat spell pen marks (8.55 penetration), Sorc Shoes (20 Penetration), Haunting Guise (20 Penetration). You're removing the same amount of MR - just under 50 - and the damage goes up to a whole... 120 points. Erm. Take off the Guise like before, and your damage drops only to 110. But you built pen versus a tanky target! Guess you shoulda read my last conclusion, huh?

Conclusion 3: Stacked Flat Penetration Versus a Squishy Target is VERY STRONG, and VERY WEAK Versus A Tanky Target

Let's do one final test.

Example 1: 50 MR Target, 200 Base Damage Spell. Let's say you've got 35 AP or so already, and the spell has a straight-up 1:1 AP:Damage Ratio. You've got your sorc boots and a Doran's Ring and 20 AP from masteries and runes. You've got Flat Pen Marks. You've got a choice when you go back: Either pick up a Needlessly Large Rod, the biggest flat AP boost, or grab the Haunting Guise. You grab the Guise: You've read my stuff from earlier, you now know flat Pen is stronger vs lower-MR targets, you wanna use it. Your AP goes up by 25, you gain 20 Pen and your damage jumps from 196.67 to a whole 256.65! Wow!

Example 2: Same situation. You have that choice again, but this time you decide you want to build for lategame, because you're more conservative and suchlike. So you grab the Rod, and your damage spikes to... 263.93.

Well. Frankly, when I reached this point, I was pretty annoyed. All this maths trying to help out the Guise because I think flat pen is super-strong, and it is. But in the early game, you just don't have enough AP damage output for spell pen to be as valuable as it is later on. What this reveals is simple: Haunting Guise is currently in a HORRIBLE SPOT. It's cheaper than the Rod, of course, so it's in a bit of an unfair position, but realistically if you can get the Guise you're often able to hang around a little longer to get the rod, and in the long term you want to have the rod. Haunting Guise is not as good in the early game, and it doesn't build into anything, so yes, it's underpowered.

Sad times. Now it's late, and I'm tired, so tomorrow I might weigh in further on this; further comparisons between the Void Staff, Haunting Guise and Abyssal Sceptre are needed. Until then...

DISCUSS.

[quote=Daigeil]So here's me, puttering along, reading a lovely Anivia guide (http://www.mobafire.com/league-of-legends/build/anivia-in-depth-mizore-v2-updated-by-castermaster-173059) when I stumble across this: "Greater Mark of Insight - Magic penetration is a nice addition to mages, and works for the entire game, since it will always penetrate magic resistance. However, alone, these are rather bad, so you might want to build a Void Staff, to stack up a bit more magic penetration." Of course, you're aware the quints are a flat pen boost and the void staff is 40% penetration. I would like to draw your attention to how exactly these two stats interact, which inevitably involves magic resistance too. It's worth noticing that all this applies equally to armor and armor penetration (their formulae are identical) but I'm a mid player mostly so spell pen is just what I'm working with for now. First things first, the magic resist formula. [img=http://images.wikia.com/leagueoflegends/images/math/a/d/9/ad9fd95547ddca63b763514308998d6c.png] Let's assume we're working with positive magic resist targets. Therefore, the damage multiplier applied by a target's magic resist will be 100 divided by 100 + their magic resist. For example, a target with 100 magic resist: 100/(100+100) = 0.5, so any damage dealt to that target is cut in half if you've got zero penetration. Clearly, you're a smart mage; you don't have zero magic penetration. You've got yourself the 10% spell penetration mastery, perhaps sorc boots, spell pen quints, Void Staff and even an abyssal sceptre. You're also smart enough to notice these all have different types of penetration, because I like to make things complicated. It's not really all that complicated; all of these modifiers have a standard order to be applied. First, Flat MR Reduction from your abyssal sceptre cuts 20 of their MR off; [b]Flat MR Reduction Goes First.[/b] Then, any Percentage MR Reduction is applied; let's say you're Kayle and you've stacked your passive up nicely, so that goes second, 15% MR reduction; [b]Percentage MR Reduction Goes Second.[/b] Then, your shoes and marks are applied; 20 Pen from the shoes, 8.55 Pen from the marks; [b]Flat Pen Goes Third.[/b] Finally, Void Staff finally gets its turn, and cuts 40% off whatever's left; [b]Percentage Pen Goes Last.[/b] Well. The mathematically minded of you immediately realise that Void Staff is barely doing a damn thing; there's not a lot left to reduce. That original 100 MR we worked with earlier is down to 40 before the Void Staff is even applied! It only removes a feeble 16 MR in the end. So at least now we're aware the order things occur in, and we're aware Void Staff goes last. [b]Conclusion One: Void Staff Gets Less Valuable the more Flat Pen, Flat Reduction and Percentage Reduction you have.[/b] So spell pen is less valuable the more you have, right!? WRONG, sir. The way that formula up there works basically means that (although resistances don't technically have diminishing returns, they always increase your effective health by the same % per point) the less armor or MR there is, the more valuable it is to remove another point or 25. Example 1: 200 MR target, hit with a spell dealing 300 magic damage after AP ratios and all are applied. They take a pathetic 100 damage. You're a smart player, you've heard the conventional wisdom, so you grab you the cheapest, least out-of-the-way spell pen you can buy; Get me some Sorcerer's Shoes, STAT! Now they've got only 180 MR, haha! But... Your spell now deals 107 damage instead. That's... Not a very big boost. Shit. Example 2: 50 MR target, that squishy opponent in lane. Same 300-damage spell hits 'em for a whole 200 damage! Much better. You don't need no spell pen to hurt THEM! But you're a guide sheep, so you grab your Sorcerer's Shoes because that's next in the build, and your spell only goes up to - 230. Wait, what? Yeah, that's right, against squishier targets, flat spell pen boosts your damage MORE than against tanky targets. [b]Conclusion Two: Flat Spell Pen Is More Effective Vs. Squishies than Vs. Tanky Targets[/b] All righty then, now we've got some useful stuff to work with. That jackass who keeps insisting you should rush your sorc boots vs. Galio in mid is wrong, you should be saving for Void Staff first. But let's see what happens when we REALLY start stacking flat spell pen, because earlier we said that more spell pen makes it worse, right? No, we said more spell pen makes Void Staff worse, because it's a percentage reduction to their MR applied AFTER flat boosts. Example 1: 50 MR target, 300 damage spell, 200 damage done, we know. Now we apply flat Spell Pen marks (8.55 penetration), Sorcerer's Shoes (20 Penetration), that super-unpopular Haunting Guise (20 Penetration). The target's now got a feeble 1.45 MR; you're practically doing true damage! 295 damage! Take off the Haunting Guise - and suddenly he's taking only 247 damage. Example 2: 200 MR target, 300 damage spell, 100 damage done, yep yep. Same again: Flat spell pen marks (8.55 penetration), Sorc Shoes (20 Penetration), Haunting Guise (20 Penetration). You're removing the same amount of MR - just under 50 - and the damage goes up to a whole... 120 points. Erm. Take off the Guise like before, and your damage drops only to 110. But you built pen versus a tanky target! Guess you shoulda read my last conclusion, huh? [b]Conclusion 3: Stacked Flat Penetration Versus a Squishy Target is VERY STRONG, and VERY WEAK Versus A Tanky Target[/b] Let's do one final test. Example 1: 50 MR Target, 200 Base Damage Spell. Let's say you've got 35 AP or so already, and the spell has a straight-up 1:1 AP:Damage Ratio. You've got your sorc boots and a Doran's Ring and 20 AP from masteries and runes. You've got Flat Pen Marks. You've got a choice when you go back: Either pick up a Needlessly Large Rod, the biggest flat AP boost, or grab the Haunting Guise. You grab the Guise: You've read my stuff from earlier, you now know flat Pen is stronger vs lower-MR targets, you wanna use it. Your AP goes up by 25, you gain 20 Pen and your damage jumps from 196.67 to a whole 256.65! Wow! Example 2: Same situation. You have that choice again, but this time you decide you want to build for lategame, because you're more conservative and suchlike. So you grab the Rod, and your damage spikes to... 263.93. Well. Frankly, when I reached this point, I was pretty annoyed. All this maths trying to help out the Guise because I think flat pen is super-strong, and it is. But in the early game, you just don't have enough AP damage output for spell pen to be as valuable as it is later on. What this reveals is simple: [b]Haunting Guise is currently in a HORRIBLE SPOT.[/b] It's cheaper than the Rod, of course, so it's in a bit of an unfair position, but realistically if you can get the Guise you're often able to hang around a little longer to get the rod, and in the long term you want to have the rod. Haunting Guise is not as good in the early game, and it doesn't build into anything, so yes, it's underpowered. Sad times. Now it's late, and I'm tired, so tomorrow I might weigh in further on this; further comparisons between the Void Staff, Haunting Guise and Abyssal Sceptre are needed. Until then... [b]DISCUSS.[/b][/quote]

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Hey look, someone who actually understands how flat pen works. If I see one more person recommend rushing Brutalizer vs people stacking armour I swear I'm going to snap.

This is why I like getting Sorc Shoes as early as possible for true damage against anyone without MR runes, and then Abyssal Scepter later in the game for true damage against anyone with MR runes. I figure I'm generally not targeting tanks anyway.

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Haunting Guise needs to be the Black Cleaver of magic pen imo. Abyssal and Sorcs already give 20 pen each and they have other useful bonuses. Guise gives a meager amount of AP, a little health and doesn't build into anything. Would be nice if Guise reduced target's MR by X amount for every spell hit up to 3 hits. Or maybe an item with an active that increases your mpen (and something else like MS if you want) for a few seconds.

Something needs to change about that item for sure.

Thanks to Jovy for the sig!

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Cheers. I've been saying this for eternities. :)

+1

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So very true, but still the early sorc shoes I like for the extra movement not just the magic pen(though it helps)but, yes void staffs are insane at shredding through MR!

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wrote:

So very true, but still the early sorc shoes I like for the extra movement not just the magic pen(though it helps)but, yes void staffs are insane at shredding through MR!

Against Galio or someone who's getting a lot of fast MR, I'd probably just go mercs or mobility boots and get void early. You can still get lvl2 boots even if you aren't building sorcs.

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Im very torn... For you see, even though i like theory crafting and finding the loopholes through theorys and blasting people away with superior knowledge... FML so much MATH!!!!

Hey, if you liked any advice i gave, be sure to +rep me! Oh, and check out my Shaco and Maokail lorecraft in my Blog! I'm a starving artist in need of attention, so please feel free to read, respond, and critique me! Please? Anybody that leaves a comment (good or bad) will receive a +rep!

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wrote:

Im very torn... For you see, even though i like theory crafting and finding the loopholes through theorys and blasting people away with superior knowledge... FML so much MATH!!!!

The gist of it is that each point of armour/MR matters more the less you have of it, so while 20 + 8 flat pen will completely screw a guy with only 30 MR it will do virtually nothing to a guy who has 200 MR. Hence, flat pen is most effective against targets with a low amount of resistance and percentage pen is most effective against targets with a high amount of resistance.

It sounds pretty obvious but I've seen a ton of people in this very forum recommend people buy Brutalizer to counter early armour stacking which is completely ***-backwards if you actually think about it for five seconds.

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wrote:

It sounds pretty obvious but I've seen a ton of people in this very forum recommend people buy Brutalizer to counter early armour stacking which is completely ***-backwards if you actually think about it for five seconds.

<3

3 dorans LW rush is pretty OP on a bunch of guiz :)