AP Users: Your runes, Magic Pen, MR and Build

In one of the latest trends in LoL, it has become increasingly popular to run Magic Resist runes on everybody, including AP mids. A rare but increasing trend is to replace MPen marks with flat MR marks providing the extra durability while giving up some damage. Froggen is credited for bringing this set-up to popularity and has influenced other players such as Reginald of TSM to include it in his repertoire. Today I'll be taking a look at how efficient this set-up is.
What you see above is an example of a page that Froggen runs. He gives up the extra damage from his marks for durability. The following is a more standard set up that you'll come across more often.

Let's take a look at how these set-ups compare and apply what we learn to our item builds and damage outputs. Read on!

 The Runes

 Firstly, to kick off the analysis - let's take a look at the rune types and what they give you.
It's possible to kick off with over 22 Magic penetration with the 10% from the Arcane Knowledge mastery.
It's possible to start off with 43.65 bonus MR purely from runes and masteries which would put you at a pretty 73.65 MR at level 1. 73 MR negates 42% of incoming magical damage which is nothing to scoff at.

Magic Penetration and Magic Resist

Magic Penetration and Magic Resist can be considered to negate each other. Each point of MPen discounts one point of MR from your enemy. Now here's a graph showing that exact relationship. It takes into account the Arcane Knowledge mastery, assuming that the enemy's base MR is 30 and is therefore not exactly linear but very close to.

The damage increase is in percent. So if you see an indication of -10, it means you will do 10% less damage you would than if you didn't have MPen and enemy didn't have bonus MR. The base case is that you don't have any MPen and the enemy has no extra MR on top of his base 30 (the origin). As an example, if you have no magic pen but your enemy runs 30 bonus MR, they fall flatly in to the green area which indicates that they will take 10% less damage than they would have if they had no bonus MR.
If you want to look for a time when enemy has 80 MR, just look at 50 on the X axis above.
Considering the fact that you have 30 base MR and 0 flat magic penetration at the origin of this graph, we can see that if you buy Sorc shoes and take Magic Pen marks while the enemy neglects any MR - you'll be dealing true damage (white area of the graph) as your magic penetration is equal to enemy MR.
It's quite a simple graph, with MPen and MR effectively balancing each other out.
Froggen's Set up = ~19 MR and 0 Magic Pen
Standard Set up = ~12 MR and 8.55 Magic Pen
No runes set up (aka control) = 0 MR and 0 Magic Pen (origin of graph)
When faced with each other, the players will deal less/more damage depending on enemy's rune set up. The following table summarises this nicely.
If you're running Froggen's setup, not only do you take 5.4% or 9.3% less damage, you deal equally less damage at either 6.17% less or 9.34% less. This is a question of personal preference, would you rather deal ~5% more damage or negate ~5% damage.
Now that the graph explanation is out of the way, let's talk build paths and scalability into late game. A big part of this is the Void Staff - which we'll cover later in this post.


Here's where things get interesting though: You can itemise for MR in numerous ways, you can't do that as easily with Magic Penetration.
If we take a quick look at common items that a mage may get MR from:
 - Abyssal Scepter
 - Aegis of the Legion
 - Mercury's Treads
 - Banshee's Veil
 - Quicksilver Sash
 - Guardian Angel
Similarly, common items that mages get MPen from:
 - Sorcerer's shoes
 - Haunting Guise
 - Abyssal Scepter (magic reduction strictly speaking, but it's rare to get an enemy below 0 MR)
 - Void Staff
Before I talk about Abyssal and Haunting Guise as viable choices for AP carries, we need to take a look at Void Staff, since it is a common buy for AP carries being the equivalent of a Last Whisper.

The Void Staff

The Void Staff not only gives you a significant 70AP boost, it gives you 40% magic penetration. A common argument against stacking flat Magic Penetration is that its usefulness drops off once you buy a Void Staff as they counteract each other.
For those not in the know, flat magic penetration applies before percentage magic penetration. So if you have a target whose MR is 100 and you penetrate 20 flat and 10%. The end result of their MR would be 72 which is (100-20) * 0.9. The percentage magic penetration contributes to 8 Magic penetration of the 28 penetrated.
If you had the same target who had 100 MR and had 10% Magic Pen, then they would have 90MR as 100 * 0.9 - 90. The same 10% magic pen contributes to 10 magic penetration. As you can see, this is an improvement for the percentage penetration effectiveness.
It is due to the 20 flat magic penetration that the % penetration is less effective and this is where that argument comes from. Having understood that, let's take a look at the same rainbow graph from above, except with the magic penetration of the Void Staff added on to the Arcane Knowledge penetration.
As you can see, the same flat magic penetration that resulted in damage increases of ~25% now only results in an increase of ~10%. Anything beyond 20 flat magic penetration is severely diminished in effectiveness.

Void Staff Conclusions

If you're planning to build a Void Staff relatively early in your build - eg: Sorc Shoes, Deathcap, Void Staff - I would recommend taking flat MR marks. The ~5% reduced damage early can be extremely useful in surviving laning phase and I'd be happy to give up ~5% damage late game for it, otherwise I'd leave out the MR marks for the Magic Pen marks.

I conclude the above with the advantage of foresight (the advantage that I know the results of the following calculations being the author). The most common way to increase your magical damage is through stacking Ability Power, however how effective is it compared with MPen? I decided to find out.
Note: I spent a good few hours looking at ways to represent 4 dimensions of data, they all seemed reader-unfriendly and thus I decided to use a calculator that I've embedded below. Change the values of the first five rows and the 10th row will show you the amount of extra AP required to increase the damage by the % you have inputted.
As you can see, the amount of AP required to match the damage increase given by a few points of Magic Penetration is quite high. As an example, it takes ~20 extra AP to increase the damage you deal by 5% when your APR is 0.7, base damage of ability is 200 and your current AP is 100. The scenario is a realistic one and not made to look outrageous.
20 AP is an Amplifying Tome.
You can get that same damage increase with roughly 10 points of magic penetration (variant on enemy MR, check out rainbow graphs above).
Now having made that conclusion - I want to talk about other magic penetration items.

Haunting Guise and Abyssal Scepter

Haunting Guise

Now we come to the part where you guys tell me "Haunting Guise is a pointless item" and I tell you, "Sorta".
Regardless of what the numbers may say above, Haunting Guise is simply terribly built. It suffers heavily from the lack of an upgrade option.
It results in a significant boost in damage. For ~1500 gold, it gives you around the same damage as a Needlessly Large Rod and even durability - but it is simply a tough buy for me. You lose out on building other items and that is the biggest con to it. You can buy a Haunting Guise sure, but by the time you spend building it, gives the opponent valuable time/gold they can use to buy more effective items, eg. Zhonya's Hourglass. They will have the Hourglass minutes before you and items like Hourglass can make or break fights. A Haunting Guise simply does not offer that same power.
My suggestion for this item: 
Give it a full offensive upgrade path. The upgraded Haunting Guise should have a significant AP value, and a damaging active/passive. Make it feel like an item that is raw, untamed power because that's what it is right now (until you have to sell it!). Give it Malady's or Wit's End passive, except make it work off spell damage and not Auto Attacks. Make it feel like by throwing your spells out there, you have done serious damage and you also gain rewards as a result - because that's what the item should be. 

Abyssal Scepter

Abyssal Scepter on the other hand, is a very very strong item. I've written an article on Abyssal Scepter vs. Deathcap in the past. The video version of that post is below.
Not only does this item benefit you with damage and durability, it also reduces MR as an aura, helping your whole team a lot more damage. Having your whole team do 5-10% more magical damage to your enemies is an amazing boost and is something that should be valued more.
tl;dr Abyssal is awesome.

The Conclusion

There is a fine line between building AP, MPen and MR. Every game has different factors involved and you should change your build accordingly but if you asked for my opinion on what I should/would run:
 - MR marks (if you're rushing Void Staff early, as 3rd/4th item - else MPen marks)
 - Choice seals
 - MR Glyphs (however I'd take 6 flat and 3 scaling if you're goign with MPen marks - you don't need more than 8.55 MR at level 1 to counter their MPen)
 - AP Quints (it gives you enough AP to justify choosing over MPen)
As for item builds:
 - Abyssal is incredibly strong.
 - Keep in mind that Deathcap scales every point of AP you have.
 - Haunting results in a significant damage increase but has to be sold or not bought at all, it has no utility like an Hourglass could give. If it had some utility, would be amazing buy.
 - Void Staff is an important buy, you can delay it a bit if you buy items like Abyssal/Haunting/Sorc, but should be bought as an essential item for AP carries.

There is a lot that went into this article and I hope you enjoyed it. I've made a video version for this article as well - since there's a lot of things that are to be interpreted from these.
I'll be running a giveaway if I hit 1k subscribers on YouTube and after that 5k. My goal is to get to 5k subs by August - help me make it happen!
(After a couple of hours spent making the video I realised that I made an error in the "AP required" calculator section of the video. I made an error in the calculations and listed the AP required as 120 instead of 20 - resulting in me exaggerating the weakness of AP. I've fixed up the calculations within the post and annotated the video with the error. The conclusions remain the same however!)
 - DiffTheEnder
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