When is more advantageous to choose magic penetration over ability power?
Solution 1:
Magic resistance stacks additively, and is calculated via this formula (assuming positive MR):
Damage taken = Raw damage * (100 / 100 + MR)
25 magic resistance → ×0.8 incoming magic damage (20% reduction).
100 magic resistance → ×0.5 incoming magic damage (50% reduction).
source
Magic penetration is applied in this order:
- Flat magic resistance reduction
- Percentage magic resistance reduction
- Flat magic penetration
- Percentage magic penetration
source
Magic penetration stacks multiplicatively. Void staff (40% magic pen) and the Arcane Knowledge mastery (10% magic pen) together equal 46% magic pen. source
We can see that the types of magic pen are very important, because buying flat magic pen (sorcerer's shoes) makes % magic pen (void staff) less effective. Unless the enemy has a lot of MR (ex: Galio), it's not worth it to buy multiple types of magic pen.
Compare some examples with a base MR of 30. With 0 magic pen, 100 magic damage does ~77 damage. With Arcane Knowledge, we ignore 10% of 30 MR (27 MR total) and deal ~79 damage. With sorcerer's shoes, we ignore 20 MR (10 MR total) for ~91 damage. With shoes and arcane knowledge, we ignore 20 MR + 10% of 10 MR (9 MR total), or ~92 damage.
We can see that for low values of MR, increasing Magic Pen provides very little gain. It also shows how effective flat MR is vs low amounts of MR, whereas percent reduction is not.
Now let's consider a large MR, say 200 and 500 magic damage. With 0 magic pen, that's ~167 magic damage. Arcane Knowledge reduces the MR to 180, or ~179 damage. Sorcerer shoe's are the exact same here. With shoes and arcane knowledge, we ignore 20 MR + 10% of 180 MR (162 MR total), or ~190 damage. If we add a void staff to these 2 (discounting it's bonus AP for simplicity), we get 200-20-72-11 (97 MR total), or ~254 damage.
It's safe to say at this point that unless the champion is stacking MR, you'll do more damage buying AP instead of Magic pen. A notable exception to this rule is Soraka, because her passive provides a substantial MR aura.
tl;dr: Runes, masteries, and sorcerer's shoes provide enough magic pen vs most champions. Only buy additional magic pen if the enemy champion has over 100 MR.
Solution 2:
Generally you'll want to build AP until you see the enemy team start to stack magic resistance. You'll get some magic penetration already from a few things:
1) Your Runes (I typically run magic pen reds)
2) Your Masteries (Assuming you put at least 9 points in offense)
3) Sorcerer Boots
As you can see, if you run a standard AP build you'll already have a good amount of magic penetration. So my general rule of thumb, is if they're not building magic resist, then you don't need to build magic penetration.
Now there are exceptions.
If a champion is known to not scale well with AP items (E.g. Malphite, Katarina), yet their abilities scale with level, then you should consider building a heavier magic pen build.
It's pretty common to see someone play AP Malphite mid with heavy magic penetration runes. This is because stacking enough MPen on a champion will result in them doing "True" damage, whereas building straight AP on Malphite would result in less damage.
Solution 3:
Here is a little theory crafting. As an AP Carry, you are first typically going to be laning against another AP carry. Champions in lower levels will have roughly 30 MR base unless they happen to rune for it, such as they desire a more passive farming lane. By getting Magic Pen Marks and Sorc boots, a common choice if you wish to deal more damage - no boots provide any AP, this will give you close to 30 MPen, which means that you get to do true damage as no damage will be mitigated by the champion's Magic Resist. This helps you win your lane.
Depending on the AP ratios of your abilities, the damage gained by building AP versus building MPen can vary.
Suppose you already have sorc boots and runes to get you 30 flat MPen with 10% MPen mastery. From runes+masteries you have 25 AP and just hit level 6 as Annie. You have gold and wondering between Needlessly Large Rod or Haunting Guise. Your opponent has 50 MR on them, so 20 MR effective after your MPen (or take 83% of your damage)
You have 1 pt in Disintegrate, 3 in Incinerate, 1 in Molten Shield, and 1 in Tibbers. Note: Disintegrate has 0.7 AP Ratio, Incinerate has 0.75 AP Ratio, Tibbers has 0.7 AP Ratio with a 0.2 AP Ratio burn.
If you take the Haunting Guise, you'd have 50 AP, but do true damage with the MPen:
Disintegrate: 85 + 35 Incinerate: 180 + 37.5 Tibbers: 450 + 35 with 35+10 burn
Tibbers and 3 seconds of burn with full spell combo is 485+45*3+217.5+120 = 957.5 damage done
With Needlessly Large Rod, you'd have 105 AP, but they take 83% of the damage from MR:
Disintegrate: 85 + 73.5 Incinerate: 180 + 78.75 Tibbers: 450 + 73.5 with 35+21 burn
full spell combo is (523.5+168+158.5+258.75) * 0.83 = 920.2 damage done
So even with the extra gold spent to get Needlessly Large Rod and less health you get as Haunting Visage gives you 200 health as well, you end up with more damage done.
In summary, it varies on the situation and what the champions' AP ratios are. But you want enough MPen to nullify your targets' MR as much as possible. If the AP Champ has worse ratios than Annie, definitely favor MPen over AP. If the AP Champ has better ratios than Annie, then perhaps consider more AP. Of course, it always feels good seeing a large number as a stat for AP when you are playing the carry.