PSA: flat pen vs% pen. How to calculate Armor and MR
I'm tired of hearing people say things like "Tanks are broken, I built magic pen/armor pen and yet i still do no damage to them." And then I look at their build only to see they've built 
and 
as their "Magic pen" or 
items expecting to crack open a 200 armor 
or 
or any pure tank. So as a public service I'm going to teach you how resistances work in this game. Feel free to link this page to anyone who really doesn't get how this is done.
Armor/Magic resistance
- For those of you who don't know the more Armor/Magic resistance you build, the less actual resistance you're gaining. Here's the equation for anyone who's interested. [(http://leagueoflegends.wikia.com/wiki/Armor)]. Basically you can plug in the Armor/MR into this calculation in order to figure out the %resistance the tank is gaining.
100 x {1 - [100/ (Armor or MR + 100)]}
- Armor and MR are very strange stats in the game because they, like many other stats have a diminishing return. What does that mean? If you have 0 Armor for instance you get 0% physical damage reduction, if you have 100 armor you gain 50% physical reduction, and at 200 armor you don't get 100% reduction, but instead 66% reduction
MATH
IF they have 0 Armor/MR: 100 x [1 - (100/0 + 100)] = 100 x [1 - (100/100)] = 100 x [1 - 1] = 0% reduction If they have 100 Armor/MR: 100 x [1 - (100/100 + 100)] = 100 x [1 - (100/200) = 100 x [1 - .5] = 100 x .5 = 50% reduction If they have 200 Armor/MR 100 x [1 - (100/200 + 100)] = 100 x [1 - (100/300)] = 100 x [1 - .333....] = 100 x .66 = 66% reduction TL:DR every point of armor/MR gained is worth less than the last
Flat pen Tank vs Squishy
- Let's say you've got the most possible flat magic penetration in the game, and you wanna kill the enemy
.
- Assuming she's full build and builds no MR, giving her 38.5 MR late game.
- Let's also say you've built the max flat magic penetration possible with
- With those values you're dropping her MR from 38.5 to -1.5 meaning she goes from resisting 28% magic damage reduction to making her take 2% bonus magic damage from you. That's a 30% increase in damage! You're dealing more than true damage to her a that at point.
- But lets say you're up against a
with just a
and conditioning at the same stage in the game. At that point Malphite has around 128 MR. And that's a serious lowball for late game Malphite build. But lets go with it.
- **With the same build you drop His MR from 128 to 88 or from 57% reduction to 47% so only 10% extra damage. That's REALLY shitty compared to the 30% bonus damage you had on Xayah. **
- And keep in mind that's still low balling it, that's not including if Malphite built any other Items that grant him resistances like
{{item: 3512}} etc..
- TL:DR Flat penetration, even when added up to max, Is terrible against High MR numbers.
But lets say instead you only build a 
instead of all the flat penetration.
- Keeping the example of
- Keep in mind that Voidstaff negates 40% of all MR champions have, leaving them with only 60% of their total MR
- Starting with Xayah's MR voidstaff cuts 38.5 MR down to 23.1 MR bringing her from 28% to 19% reduction. only a 9% increase in damage
- Wow that sucks, that's worse than the exmpale with Malphite with just flat penetration. But let's actually do Malphite's math for a quick second.
- Malphite's 128 MR build is cut down to 76.8 MR with voidstaff bringing him from 57% reduction down to 44% reduction, or a 13% increase, still pretty small. But better than before.
- So lesson learned tanks are dumb because even % Reduction does jack shit right? wrong.
- Remember, we're lowballing Malphites build in terms of MR, assuming he only builds one item that gives MR. With that build on Malphite any AP mage could still chunk him, maybe not Burst him down due to his HP, but definitely make tanking impossible.
- So lets actually do a normal late game build, and because he's an ARMOR tank, let's use the tank that can get the most MR in the game. . .
- (what you expected
?? damage reduction =/= as Armor or MR.
Big math's
So for fun, because mAtH Is FuN, I'm going to calculate a full build
Plus her W and conditioning, and compare the resistances she gets there with The Voidstaff vs the flat penetration items
Lets see here: (113.4_lvl18 with W on_ + 25 + 55 + 60 + 80 + 10 conditioning bonus) x 1.26 conditioning bonus and Leona W% equals a whopping 346 MR or 78% magic damage reduction. Alright now onto the real math.
FLAT PEN
- 346 MR - 40 magic pen = 306 MR
- 100 x (1 - (100/ 100 + 306)) = 100 x (1 - (100/406)) = 100 x (1 - .246) = 75% reduction
- wow from 78% reduction to 75% reduction. Only a full 3%. That's it, tanks are busted. BROKE--- wait... we gotta do voidstaff.
% PEN
- 346 MR x .6 MR left after voidstaff = about 208 MR
- 100 x (1 - (100/ 100 + 208)) = 100 x (1 - .324) = 68% reduction
- so now we go from 78% to 68% a flat 10% reduction from 3% on flat.
- And remember this is one of the biggest case scenarios (at least for magic damage). And you're still negating enough armor to turn a full MR tank
who is squishier by comparison.
And this is why you build for tanks and for squishy champions. I hate hearing "Oh boo hoo! tanks are broken! there's nothing I can do against them! Boo hoo!" OR " Oh damage champs are bullshit right now! Way too much damage before I can even kill them!Oh woah is me!" There's so many chances for counter play in this game, yet I see people make some of the dumbest decisions when building against the things they claim are bullshit. So here is my PSA. Have a wonderful April fools ya bunch of bonobo's
