# AP/AD Runes vs. Pen Runes; A formula and table for any champion

#Intro
I was disappointed that there has yet to be an easy way to decide whether to run AP or AD runes instead of flat penetration. **People say high base damage champions should run penetration, but what if high base is coupled with high scaling? What if it's low scaling but low base? It's so arbitrary.**
I made it not arbitrary. **Please don't be intimidated by the tables; the rest of the post will be giving practical examples on how to use the table quickly!**
***
#Tables and Graphs
##Marks
[Ability Power vs. Magic Penetration](http://i.imgur.com/dUxfNPX.png) - [GRAPH](http://i.imgur.com/F75Aj3d.png)
[Attack Damage vs. Armor Penetration](http://i.imgur.com/lGQvtMZ.png) - [GRAPH
](http://i.imgur.com/BStvJDH.png)
##Glyphs
[Ability Power vs. Magic Penetration](http://i.imgur.com/sYlbCUW.png) - [GRAPH](http://i.imgur.com/IDWMOCf.png)
##Quintessences
[Ability Power vs. Magic Penetration](http://i.imgur.com/ZpeoVHM.png) - [GRAPH](http://i.imgur.com/SMQAazy.png)
[Attack Damage vs. Armor Penetration](http://i.imgur.com/r9zQQj8.png) - [GRAPH](http://i.imgur.com/ybLtuJD.png)
***
# These Sure Look Fancy! How to Use?
I'll be giving some real examples in a moment, but here's a step by step guide.
1. Find the **total base damage** of the spell or combo
2. Find the **total ability scaling** of the spell or combo
3. At the top of the table, find the corresponding base damage
4. Go down that column until you find the first number smaller than the spell/combo's scaling
5. This tells us "Above x MR, AP/AD Runes will deal more damage than Penetration Runes"
##Example: Karthus - Lay Waste
I play a lot of **Karthus**. Let's find out whether I should be running **ability damage Glyphs** or not!
For simplicity, I'm going to check each of Karthus' spells individually. [Let's start with Lay Waste.](http://i.imgur.com/tUIitpQ.png)
At Rank 3, Lay Waste has a Base Damage of 80.
Lay Waste has an ability scaling damage of 0.30.
Since I'm testing Glyphs, I pull up the AP Glyphs table.
[Lay Waste has a base damage of 60, so I look for the "60" column.](http://i.imgur.com/KcyE0Q4.png)
I look for the first number smaller than Lay Waste's scaling. In this case, Lay Waste has a scaling of 0.3, so I look for the first row smaller than 0.3. [The first number smaller than the scaling occurs on row three, which is on the 50 MR line.](http://i.imgur.com/DznkGHE.png)
So I have my answer: **Ability Damage adds more damage than Magic Penetration to any target above 50 MR, for a Rank 3 Lay Waste.** Not too shabby for mid game!
##Example: Karthus - Defile
[Let's check out Defile next!](http://i.imgur.com/Ugmjog8.png). **At rank 5, Defile has a Base Damage of 110 with an AP Scaling of 0.2.**
110 doesn't fit neatly into the table but 100 is honestly a close enough approximation. Check the 100 base-damage column, go down until a number smaller than 0.2 appears. That happens a little around 160 MR (estimating).
**Ability Damage will add more than Penetration on Defile Rank 5 to any target above 160 MR.** Yikes; that's some pretty bad scaling.
After knowing how to use the table, further evaluations are pretty fast!
##Example - Karthus: Requiem
[One final spell to check on Karthus, Requiem.](http://i.imgur.com/yQCuS98.png)
Checking at Rank One. 250 base, 0.6 Scaling. Table tells us that AP only starts doing more damage after 120 MR; eh.
In conclusion: **Ability Marks increase the Lay Waste's Rank 3 Damage against Targets above 50 MR, while only increasing the damage of Defile and Requiem on targets above mid-100 MR.**
***
##Example: Orianna QWR Combo
Let's try something for another of my champions. What does the chart tells us for a full spell combo?
At maximum rank, a full QWR combo from Orianna will deal 730 Base Damage.
To find the AP Scaling, simply add up the AP scalings of each individual spell.
Command Attack has a 0.5 Scaling. Dissonance has a 0.7 Scaling. Shockwave has a 0.7 Scaling. In total, that's a total scaling 1.9.
QWR has 730 base damage and 1.9 Scaling.
For marks, there's never a point where the 700-Base column shows a lower number than 1.9, meaning **pen marks are superior for Orianna's burst combo on any champion.**
For glyphs, the first lower number appears at 100 MR. **This means Ability Damage Glyphs will add more damage than pen to Orianna's combo to any target above 100 MR**.
***
##Example: Orianna QWQ Combo
What happens if casting the same spell multiple times? The same principle applies.
Command Attack has base 180 and Scaling 0.5.
Command Dissonance has base 250 and Scaling 0.7
But we cast Command Attack twice. So we simply add its base **and its scaling** twice.
180 + 250 + 180 = 610 Base
0.5 + 0.7 + 0.5 = 1.7 Scaling
For Marks, AP never beats Pen. For Glpyhs, AP deals more damage to targets above 90'ish MR.
***
#Example: Zed Early-game QE-AA-AA Combo
Attack Damage champions follow the same principles outlined above but with one twist: **Every autoattack is essentially a spell of [Champion's AD] damage with a 1.0 Scaling.**
Since this is early game, I'm using Rank 1 Q, and E, testing on a Level 3 Zed who has 60 Base AD.
Q Base 70, Scaling 0.9
E Base 60, Scaling 0.8
Autoattack Base 60, Scaling 1.0
**Two autoattacks, so AA-total Base 120, Scaling 2.0**
Total Base of 250, Scaling 3.7
Attack Damage Marks and Quints always add more damage than Penetration Marks; Nice!
***
##Caveats
* There are more uses to Ability Power than just raw champion damage. Waveclear is one of the big benefits provided by AP that penetration does not provide.
* These tables should not be used to test magic penetration from items. Items have their own slew of considerations, the biggest being gold cost. It doesn't tell us much if we can't compare their gold.
* Be sure to test Rank 1 and Rank 5 spells, instead of only one or the other. Ability Power is favored early on due to the lower base damages, but if it's not favored by 40 MR, then penetration will still be the best choice for champion damage.
***
##Thanks for reading! I hope you'll find this useful.

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