### Math regarding Zileas' N^y formula

xavarn

Senior Member

Quote:
Originally Posted by Viro Melchior
Upvoted for good discussion even if arguing against it!

That is why I admit that MR scales strangely.
However, if you are Annie and worried about a 250 MR target, you'll want to scale your damage up with a Void Staff, retaining your N^3 scaling ability.

250 MR means you are doing 28.6% damage.
Dropping them to 150 MR with a Void Staff gives you 40% damage, a 40% increase in damage (ignoring the AP it provides).
Since that 40% increase still multiplies any damage values you gain from AP or CDR, it is therefore N^3.

But MPen % and MPen are two totally different stats. One that increases in usefulness as MR increases the other one having the opposite effect, especially now that Mpen is applied before MPen % (not sure if you were around for that patch or not).

I totally agree with your math btw, just pointing out a little meaningless factor in your explanation and possibly supporting why Zileas left out the N^3

Holy Malevolence

Senior Member

I'm tired, but this thread reminds me of this.

Anhi

Senior Member

This is why I like League. Cuz once the math goes down, then we get to debate.

For instance Lux

Huge AP lazer that can nuke out running away targets returning gold through kills, following tower pushes and or dragons and open farmable lanes. VS. CDR Lazer that does no damage but fires ever 25 secs giving gold through direct farming. Which one is better?

Holy Malevolence

Senior Member

Quote:
Originally Posted by Anhi
This is why I like League. Cuz once the math goes down, then we get to debate.

For instance Lux

Huge AP lazer that can nuke out running away targets returning gold through kills, following tower pushes and or dragons and open farmable lanes. VS. CDR Lazer that does no damage but fires ever 25 secs giving gold through direct farming. Which one is better?
Ap/CDR laser that does damage every 25 seconds.
It just needs items to be possible. Beyond Nashor's.

Texas Snyper

Senior Member

Quote:
Originally Posted by Anhi
This is why I like League. Cuz once the math goes down, then we get to debate.

For instance Lux

Huge AP lazer that can nuke out running away targets returning gold through kills, following tower pushes and or dragons and open farmable lanes. VS. CDR Lazer that does no damage but fires ever 25 secs giving gold through direct farming. Which one is better?
or you stack both and get the multiplicative factor that the OP is talking about. Maybe a 30-35 sec CD laser that does more than just tickle?

Anhi

Senior Member

Quote:
Originally Posted by Texas Snyper
or you stack both and get the multiplicative factor that the OP is talking about. Maybe a 30-35 sec CD laser that does more than just tickle?
You'll want both. But OP says getting AP after will get more "damage" out of the money spent on AP. The fun crafting comes in demonstrating that while getting CDR before AP will increase overall damage during the game it will decrease the damage you typically want. Like he said, most caster want burst damage versus sustained. And none of these calculations take into account the cost of your spells. For instance, the more AP a spell has the cheaper the damage becomes. You can have your Lazer off cool down all you want but with no mana pool to support it, its just as usefull as the longer CD AP lazer

Viro Melchior

Senior Member

Quote:
Originally Posted by xavarn
But MPen % and MPen are two totally different stats. One that increases in usefulness as MR increases the other one having the opposite effect, especially now that Mpen is applied before MPen % (not sure if you were around for that patch or not).

I totally agree with your math btw, just pointing out a little meaningless factor in your explanation and possibly supporting why Zileas left out the N^3
Yes they are technically different stats, but they both scale against each other, not with. Previously (when % reduction occured first), Annie could be considered N^4.
However, even at that time, 3 of her N's were fairly limited in scope. In comparison, there are very few ways to scale the crit damag on a carry style champion. They tend to be quite potent (like CDR in terms of sustained damage), but limited in availability.

The reason why *every* strong caster wants Penetration is because of how powerful it is.
If your targets are low MR, you want the boots and/or a Guise. If they are high MR (above 100), you want a Void Staff because the scaling ratios make flat penetration weak. However, even at 250 MR, Annie is N^3 with flat penetration. The issue is just that one of those N's has a TERRIBLE ratio.
Looking at the AP:CDR comparison, why wouldn't you ever just stack CDR? It will always give you a better total damage level than AP. That is why it is hard-capped. Additionally, some champions scale better with CDR than others. Such as Ryze vs Annie.

Just because 1 stat is better than another doesn't mean the weaker stat is useless.
Take a look at the 3 carry stats I listed. Attack Speed is flat out the best, and Critical Chance the worst. Yet if you mix and match, you get better benefits. AP, CDR, and Penetration (either flat or % based) are the same.
If you stacked 6000g of just penetration (flat if they are low MR, % if high), you'd be doing 100% damage all the time, but you're numbers would be at the base levels, and you'd never do more than 1035 damage to your target. Considering everyone gets over 1700 health by then, you'd never be able to burst someone down, and at 0% CDR, you'd then be waiting several seconds before you'd get to do anything but auto-attack them for 100 damage/second (before armor).
If you stack 6000g of AP, you would be doing 54% more damage in burst, and once your abilities come off cooldown.
If you stack 6000g of CDR, you hit the cap, so it's kinda moot. Your sustained damage still is going up by 52% (effectively it's lower though because 1/3 of her damage is on a huge cooldown).
If you stack 2000g of each, you get maxed CDR, 18% damage from AP, and your penetration.

For Annie alone (with her .09 N value per 1000g from AP), and a value of 575g = 20 penetration (1000g = about 35 pen), we can make the following statements:
Flat Penetration increases in value until the target has 0 MR.
Inversely, Flat Penetration becomes less valuable the higher MR your target begins with.
AP scales at a set rate indefinitely.
Therefore, there is a point where Flat Penetration is no longer a better value than stacking AP.

1 Penetration increases your damage by:
(100 / [99 + X]) / (100 / [100 + X])
Since 35 penetration is costed equal to 50 AP, 1 penetration is equal in gold cost to 1.42 AP. 1.42 AP provides Annie a damage increase of .002556 (.09 / 50 * 1.42),or .25%.
So, at what point does our Penetration formula reach .25%?

(100 / [99 + X]) / (100 / [100 + X]) = 1.0025
X = 301. So, until they break 300 armor, flat penetration STILL does more damage than AP.
So unless I screwed up, penetration is good. And I did this at late night, so I very well may have messed up.

Viro Melchior

Senior Member

Formula for use on any champion:

X = Dmg / (1.42 * A)
Solve for X. Subtract 99 to get the MR breakpoint.
A is the champion's AP ratio
Dmg is the sum of their 0 AP burst damage (rank 5 abilities added together).
This assumes that you have no % penetration.

Annie comes out to 283 MR
Sion comes in at 114 MR

Lower base damage an/or better proportional scaling (Sion has really low total base damage since his ult isn't a nuke, but excellent ratios on his Q and W) means that they will benefit from AP over flat penetration easier.
Also, do to the prevalence of 15% penetration (mastery), the actual in-effect numbers is lower than these by a bit.

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