What are the best anti-tank kits for mid laners? I'm not saying who's better in this patch but overall. Is it better to force a Liandry + Rilay's on certain mages you would normally build full ap?
TehNACHO4 votesFor builds, absolutely build CDR Boots, Liandry's, and Void Staff. Flat Penetration isn't as effective against higher resistances (though Liandry's gets around this due to obvious reasons) so you might as well take the CDR.
I heard Malzahar is a really stupid anti-tank mid laner.
12tales1 votesFlat Penetration isn't as effective against higher resistances (though Liandry's gets around this due to obvious reasons) so you might as well take the CDR.
C/Ping myself from another thread, since this is a really common misconception.
This is a myth. Flat armor pen has nothing to do with the enemy's total armor.
Math reasoning, if you care:
There are two approaches to representing the affect of armor on incoming damage. The first is the approach that Riot takes in game, where armor/mr is represented as percentile damage reduction. The formula for this is 1/(1+.01Armor). For example, a champion with 100 armor will have their armor represented as 1/(1+1), or 50% damage reduction.
I personally don't like this approach, mostly because decimals are ugly. I prefer to use Effective Health. This is a value equal to HP(1+.01Armor). For example, that same champion with 100 armor would have an effective health value of HP(1+1), or double his base health. If he has 2000 base health, his armor gives him 4000 effective health against physical damage. This is basically identical to the percentile reduction method that Riot uses, but I find it easier to work with because you can subtract damage values of abilities/auto attacks directly from effective health, so you only need to do actual math once.
Let's factor in Armor Penetration, now, using Effective Health. Assume that you have a Brutalizer - the effective health of the enemy you're attacking can be represented as HP(1+.01(Armor-10)). Thanks to the Distributive Property, we can break that down like so - HP(1+.01(Armor)+.01(-10)). This is just a slightly more long winded way of expressing the exact same equation.
However, we can break it up even further using the Distributive Property, because our equation is basically HP(X+Y+Z), and that's equal to HP(X)+HP(Y)+HP(Z). Applying that process here, we get -
HP(1)+HP(.01Armor)+HP(.01(-10))
Simplify, and we get
HP+HP(.01Armor)-.1HP
From this, we can see that the value of armor penetration is only multiplied by Health, not armor. A 2000 health target will have their effective health decreased by the exact same amount, whether they have 10 or 1000 armor.
Even tho, if you use Riot's method, it looks like Armor Pentration has a bigger effect on the damage reduction of low armor targets, this is deceptive. The value scales exclusively with health.
TehNACHO2 votesMmhmm, that's great, but have you ever graphed the damage in relation to gold efficiency?
x: Enemy Resistance y: Damage dealt
What ACTUALLY happens is that when you build flat penetration, the graph moves towards the right along the x axis. That's just it however. It's not that the graph is taller, it's that it's shifted.
This is important because of slopes. Flat Penetration in the form of Sorc Shoes falls off just as fast as without any items at all. On the other hand, if you focused on raising your base multipliers (AD, AP, CDR, etc.), you stretch the graph to be taller than it should be, and this effect lasts even as you climb in armor.
What this means is that, in relation to raw stat items like Deathcap, Flat Penetration falls off late.
Now, let me reiterate just so that we are perfectly clear. This effect is noticeable relative to stat items. You are right in saying that in a vacuum, flat penetration doesn't fall off. Relatively, however, its effects drop off faster against higher forms of armor.
12tales1 votesWhat ACTUALLY happens is that when you build flat penetration, the graph moves towards the right along the x axis. That's just it however. It's not that the graph is taller, it's that it's shifted.
Not really. Values change when you shift a graph. If you have a negative slope and shift it to the right, the values along the left increase. 'Get taller,' if we want to use that terminology.
This is important because of slopes. Flat Penetration in the form of Sorc Shoes falls off just as fast as without any items at all. On the other hand, if you focused on raising your base multipliers (AD, AP, CDR, etc.), you stretch the graph to be taller than it should be, and this effect lasts even as you climb in armor.
What this means is that, in relation to raw stat items like Deathcap, Flat Penetration falls off late.
I've read this a dozen times and showed it to my more math-inclined friends, and none of us have any idea what you're talking about. Could you maybe rephrase or clarify your reasoning?
Relatively, however, its effects drop off faster against higher forms of armor.
To an extent, sure. It scales with the enemy's health. It will be less effective against a tank that built Frozen Heart and Thonrmail than one that built Randuin's and Warmog's. That's not because the enemy has higher armor values, tho - it's because they have lower health values.
Relatively, AP, AD and CDR also drop off faster against higher forms of armor/mr/hp. That's just how defensive statistics work - it's why people with low stats are called squishy and people with high stats are called tanks. Literally every damage multiplier out there is relatively less effective as you add armor/mr. The only thing special about flat penetration is that it scales exclusively with health, rather than with a combination of health and resistances. It's basically identical to %HP damage in that regard, and who thinks that falls off late game?
TehNACHO2 votesI'm silly, I'm commenting on graphing and I don't even show you a graph.
Here's a WIP I'm doing to calculate a build for Annie. I can explain in exact detail if you ask, but the tl;dr is that the red-black line is Abyssal Scepter, the green line is Void Staff, and the blue line is Rabadon's.
If you look particularly at the slopes of the graphs, you'll notice a few things. Firstly, it if weren't for how negative penetration works, the black line would exceed the power of Rabadon's at extremely low MR levels. As I've stated, this is due to the Abyssal Scepter's graph being shifted to the right. As I've also stated, flat penetration (this time for Abyssal Scepter) falls off faster than straight AP. This can be represented by the fact that the Rabadon's Deathcap exceeds the damage of the Abyssal Sceptor as MR rises, and then stays ahead into infinity.
This is what I mean. Flat Penetration (well this specific example is reduction, however I haven't plugged in the items to have that be a substantial difference), is much stronger while the opponent has less resistances, but falls off faster than straight up stat items. This is due to how shifting works vs plugging in bigger numbers.
12tales1 votesIf you look particularly at the slopes of the graphs, you'll notice a few things. Firstly, it if weren't for how negative penetration works, the black line would exceed the power of Rabadon's at extremely low MR levels. As I've stated, this is due to the Abyssal Scepter's graph being shifted to the right. As I've also stated, flat penetration (this time for Abyssal Scepter) falls off faster than straight AP. This can be represented by the fact that the Rabadon's Deathcap exceeds the damage of the Abyssal Sceptor as MR rises, and then stays ahead into infinity.
Deathcap is a significantly more expensive item than Abyssal Scepter, and a greater percentage of its cost is spent on offensive stats. Unless you're isolating the variables of MR Reduction and AP, and adjusting them for the price of the stats, the comparison only tells you about those specific items on those specific champions, not Magic Pen vs. AP in general. I would expect Deathcap to provide the highest damage output of almost any item for most mages.
Also, it's worth mentioning that AP is only a multiplicative stat to the extent that a champion scales with it. Magic Pen increases Zed's damage; AP literally does nothing. Even if you can come up with a proof that Magic Penetration is less gold efficient on Annie than flat AP against a specific set of opponents, the relative value of those two statistics is going to change for every champion with different base values and ap scaling than Annie. A champion with higher base damages and lower scaling than Annie (such as, say, Vel'Koz) is going to get significantly higher benefit out of Magic Pen relative to AP.
TehNACHO1 votesActually, all you'd need is to double the value of x that any BotRK vs another item gives you due to how DPSing works in the first place, at least for a general idea of what the calculations should suggest...
And also, I have gone through many champions to see this point time and time again. I've done similar numbers with a large assortment of ADCs, and published a few with Twitch and Azir. Funnily enough, Azir's numbers already calibrate for cost. If you read the notes about penetration in the damage build, you'll notice I put an alternate build containing Sorc Shoes for all enemies with 71 or less MR, whereas Azir favors Berserker's Greaves for DPS against any enemies with even higher MR. Berserkers Greaves vs. Sorc Shoes, a case where the items already are the same price. In other words, your complaints about price is null. In this case, between Flat Penetration (not just Magic Pen in general) and Attack Speed, with a completely and totally different champion like Azir, we once again see the same pattern: Flat Penetration is stronger against lower MR targets, but stat items scale harder against higher MR targets.
And please note, these damage calculations are based off the opponent's true HP, AFTER the damage is reduced by their resistances. In other words, it doesn't matter how much Effective Health the opponent has, these calculations are already getting around the armor portion of that stat anyway, so we are looking at barebones HP damage here.
On one hand, we have a burst champion with solid base values and scaling, and a DPS champion with bad base values but some emphasis on scaling. I may concede if I ever calculate a champion like Vel'Koz, but as of right now, I think I've proven enough to at least say that stat items tend to out scale Flat Penetration as the opponent's resistances get higher and higher.
12tales1 votesYeah, I figured out the bit about effective hp a few minutes after I posted about it.
Anyways, I'm not surprised to learn that there are champions that scale better with AP or AS than MPen. Similarly, there are champions that scale better with MPen than AP or AS - I raised Zed as a (somewhat tongue in cheek) example of a champion on whom MPen will outdamage AP at literally every possible MR value.
So, while I'll accept that the relative value of flat penetration will decrease as resistances increase, I don't accept that 'AP/AD/CDR/Whatever outscales flat Penetration' or 'AP/AD/CDR/Whatever is more useful than flat Penetration against high resistance targets' is a valid conclusion to draw. Very much dependent on the champion.
TehNACHO1 votesYeah I guess I'm bad at phrasing that, pfft.
But yeah, looks like we both got a bit out of this. Had fun seeing another point of view in this subject, sometimes I feel like I'm the only one who ever analyzes these things~
12tales1 votesAppreciate you taking the time to explain yourself.
And I can sympathize - I've got a huge collection of spreadsheets on optimizing item builds for various champions that I never get to share with anyone. Such are the trials of those who care about math, I suppose.
GreyXpelliarmus1 votesFor builds, absolutely build CDR Boots, Liandry's, and Void Staff. Flat Penetration isn't as effective against higher resistances (though Liandry's gets around this due to obvious reasons) so you might as well take the CDR.
I heard Malzahar is a really stupid anti-tank mid laner.
Hey thank you al guysl, I've read everything you wrote. I'll definitely try malzahar, cdr boots? I feel like I should've come up with that but I'm so used to the meta pen boots. Very helpful thanks
7ha7guy7772 votesi'm pretty sure malzahar is up there. high base damage aoe silence with a .8 ap scaling, 5 seconds of aoe % max health in magic damage, high base damage .8 ap scaling 4 second DoT, and a suppression ult that deals moderate damage with 1.3 ap scaling. as well as minions who can tank skill shots and turret shots that spawn every 4 spell casts
Apostasy Now2 votesLearn AP Kog'maw mid. Also, Malzahar is good. Cassiopeia is good. Fizz is good. Champions that have %HP damage in their kit. Champions that benefit from building Morellonomicon and Liandry's.
The only issue is keeping the tank from sticking to you. Lux and Morg are good at this, so is Xerath and to some extent Orianna but she doesn't have as consistent of a hard cc.
12tales1 votesOrianna does really well against dive-oriented tanks like Shyvana. Syndra and Zyra, too. Less so against hand holding tanks, tho.
Basically, any champions with very linear movement patterns is gonna have a rough time against those champions, since predictable movement against any of them is going to turn into guaranteed CC and insane burst.
Going for Liandry's is occasionally a solid choice (I believe GBM popularized the Nuker build on Orianna, going Double Doran's into Sorc Boots and Haunting guise to maximize early damage), but Rylai's is generally a champ specific pick, not so much a situational pick for all mages.
2000boxes1 votesumm i would say zed because you build atleast 2 high armor penetration items on him and you still do a decent amount of damage plus his passive helps and he has low cooldowns for a melt if the tank survives the combo and he builds lifesteal so he won't die in a fight against say a maokai.
YOURGE3001 votesFrom me, a 
main, this to me can't be more true. His burst is just so massive and his escapes and plays can be simply orgasmic...
pacifishstick1 votes
Tsen1 votesMalzahar is the most obvious choice (10+% max hp per tic of pool) Brand is nice as well due to his passive.
Otherwise, someone with cc to keep the tank at bay while you demolish their carries, then either finish off the tank or he escapes. That's team fight stuff though, I'm not sure about 1v1ing tanks. Usually blowing all your cooldowns only gets them down to 25-40% health, assuming you aren't fed, have void/last whisper and are +2 levels up or somethin.
Merxamers1 votes
is a good choice against many tanks, and that's why you see her top lane sometimes; she obliterates 
in lane with her harass, for example. Plus, Liandries is a good item for her.
GreyXpelliarmus2 votes
I LOVE Lissandra, her capabilities to cc and/or deal dmg are amazing