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Mpen quints on mid laners

Creator: PsiGuard June 29, 2012 11:06pm
PsiGuard
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Lugignaf wrote:
I would change based on the client but I'm planning on doing this important thing called "sleep" real soon.

Sounds overrated.
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Am I the only one that uses Greater Quintessence of Movement Speed on my mids? >.>
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No, but it's irrelevant to this discussion.
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PsiGuard wrote:

No, but it's irrelevant to this discussion.


I run 2 magic penetration blue's to do true damage to enemy mid's without defense runes.

But i'm actually not even sure if it's good.
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^ Lol xD

BUT ya dem Hybrid quints is gud~ :3
Lugignaf
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True love is found only in yourself.
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You know, some reds don't know their own game.^^
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But that thread's about marks.
I wanna know about quints.
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1.89 Magic pen
1.89x3= 5.67% magic penetration
5.67%x30= 1.701
24-1.701= 22.299
100x22.299%= 22.299
100-22.299= 77.701

Magic Pen ~ 77.701 damage




4.95 AP
4.95x3= 14.85
14.85x1/2= 7.425
107.425x24%= 25.782
107.425-25.782= 81.643

AP ~ 81.643




Side notes:
For the AP runes, I used a .5 ratio on the spell.
This was based on all champions having 30 magic resist.
30 magic resist ~ 24% reduction
This was based on 0 Base AP and 0 Magic Penetration.
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^That is totally wrong. Magic Penetration does not work like that. Moreover, you have to use real numbers, since changing the amount of MPen or AP from other sources can change the numbers dramatically.

But anyway, Psi, I'll bite. Math time.

To simplify the number of variables I'm looking at, instead of using any actual skills base damages and ratios, I'm going to instead use the number Ability Damage (AbDam), which will be the base damage plus the damage gained from AP. I'll translate it out of these terms after some maths, of course.

Assuming standard mage masteries, flat AP glyphs, and a boots 3 start, then, we have AbDam_MPen * (100 / ((.9)(100 + MR - .95*9 - 2.18*3))) for MPen quints, versus AbDam_AP * (100 / ((.9)(100 + MR - .95*9))) for AP quints. Setting AbDam_MPen * (100 / ((.9)(100 + MR - .95*9 - 2.18*3))) >= AbDam_AP * (100 / ((.9)(100 + MR - .95*9))) and simplifying, we get that AbDam_MPen * ((91.45+MR)/(84.91+MR)) >= AbDam_AP. Now, keep in mind that ((91.45+MR)/(84.91+MR)) > 1 for all positive MR, so what we're looking at is what percentage AbDam_AP needs to be greater than AbDam_MPen in order for AP quints to do more damage. Or, rather, what percentage of AbDam_MPen the AP bonus from AP quints cannot exceed in order for MPen quints to do more damage.

Now, I know that a lot of mids don't build much (if any) MR in the early game, so I'll look first at MR=30. For this, we get that AbDam_AP needs to be no more than 5.691% higher than AbDam_MPen in order for MPen quints to do more damage. Using Lux's Light Binding at level 1 as an example, AbDam_MPen is going to be 60 + (.7)(4 + 1 + 10.71) = 70.997. AP quints provide .7 * 14.85 = 10.395 AbDam, which is a bit over 14.6% of AbDam_MPen. Thus, AP quints provide more damage.

Looking at Lux's Lucent Singularity, which has lower scaling, AbDam_MPen is 60 + (.6)(4 + 1 + 10.71) = 69.426. AP quints provide .6 * 14.85 = 8.91 AbDam, which is a bit over 12.8% of AbDam_MPen. Thus, AP quints provide more damage.

For Lucent Singularity, with no other MPen, and against 30 MR targets, AbDam_MP needs to be at least 156.56 in order for MPen quints to be more effective. This is to say that the skill needs to be rank 3, or to be rank 2 and Lux to have built at least 69 AP.

For Light Binding, with no other MPen, and against 30 MR targets, AbDam_MP needs to be at least 182.66 for MPen quints to be more effective. This is to say that the skill needs to be rank 4, or to be rank 3 and Lux to have built at least 11 AP.

For Finales Funkeln, AP quints provide .75 * 14.85 = 11.1375 AbDam. Therefore, with no other MPen and against 30 MR targets, AbDam_MPen needs to be at least 195.71. This will be true as soon as you take the skill.

A short list of how much AbDam Lux's skills need for MPen quints to be more effective, using the same assumptions as above, follows:
  • 50 MR: 4.848%
  • Q: 214.5 AbDam
  • E: 183.8 AbDam
  • R: 229.8 AbDam
  • 100 MR: 3.537%
  • Q: 293.9 AbDam
  • E: 252 AbDam
  • R: 314.9 AbDam
  • 150 MR: 2.784%
  • Q: 373.4 AbDam
  • E: 320.1 AbDam
  • R: 400.1 AbDam

I'll be happy to look at what the numbers look like after Sorcerer's Shoes and against higher MR values, as well, but I think this post is long enough for the moment. If there are any specific MR values you want me to math at, Psi, let me know.

TL;DR: MPen quints are less effective than flat AP quints at low levels, by a pretty wide margin. With starting items only, MPen quints may have a slight lead for most Q, W, or E skills starting at rank 3. Abilities with very high base damage and mediocre or worse scaling, like Lux's Finales Funkeln, seem considerably better at all stages of the game with MPen quints.
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