### Attack damage vs Armor Penetration runes

DorifitoX

Senior Member

So I have have spent the past few hours crunching numbers because a friend said that "ArP Runes are always better than AD runes." And then I searched with google to find if there was any good discussions on this topic. The only thread I saw was one from a month ago or so and it seemed like everyone said that exact same thing. So I decided to take some time and actually figure it out with numbers to see which is actually better and these are the results I've found:

Against 30 armor with a base of 73.65 AD and assuming you have 7 marks for either (I am level 22 so I only have 7 spots open to me currently though the math shouldn't change as you get to 9 marks) you will do about 56.65 damage per hit with no runes or items taken into affect.

This is based on the equation Armor reduction is 100/(100+Armor) = actual damage dealt. In this case you have 100/130 = .7692...etc. So you are dealing about 77% of your damage to someone with armor 30 and no armor pen. Now with 7 T3 runes you can either get 11.62 Armor Pen or 6.65 AD. So lets add those in:

With the ArP Your target's effective Armor is 18.38 (30-11.62) which puts your damage reduction to (100/118.38) .8447 Or around 84%. So let's plug that with your base damage above of 73.65 (73.65 * .8447) giving you a effective damage of 62.21.

Now with the AD your target's Armor is again 30 so we are back at the .7692 effective damage and you are now adding 6.65 damage to your total which is equal to 80.3 (73.65+ 6.65) When we multiply that by the reduction of .7692 we see 61.77 damage.

So the damage change for ArP is .44 damage. Not exactly the startling change I was expecting for something that cannot scale abilities on any champion.

So I decided to test this against two more examples all using Warwick as the attacker and one as Annie as Defender and one as Shen as defender at different levels. I am going to go a bit quicker over the math for these parts as this post is incredibly long already but basically it went like this:

Annie is mid and level 7 with 32.5 armor.

Warwick has been jungling and is 5 with 70.75 AD

With the Armor Pen The effective damage against Annie is (Armor 20.88 = .8273 effective damage) 70.75 * .8273 = 58.53 damage

With AD runes the effective damage against Annie is (Armor 32.5 = .7547 effective damage) 77.4 * .7547 = 58.41 damage. A change of a .12 damage, wow.

The next is Warwick v Shen both at level 7. No items,

Shen 42 Armor WW has 77.03 AD

With ArP The effective armor is 30.38 or .7669 effective damage giving us a total damage of 77.03 * .7669 = 59.07 damage

With AD The effective armor is 42 or .7042 effective damage giving us a total damage of 83.68 * .7042 = 58.92 damage

This gives us a total improvement of .15 so slightly better against a higher armor target.

My last two examples are just arbitrary numbers so we will use Attacker and Defender:

Attacker has 250 AD and Defender has 300 Armor

With ArP the effective damage is going to be .2574 * 250 = 64.35

With AD the effective damage is going to be .25 * 256.65 = 64.1625

So now we see a whole .1875 change in damage.

Lastly is Attacker has 50 AD and Defender has 12 Armor.

With ArP the effective damage is going to be .9962 * 50 = 49.81

With AD the effective damage is going to be .8928 * 56.65 = 50.57 damage

So we see that the effective damage is actually higher when you get lower on the total armor of the subject.

I obviously did not do any numbers for someone with lower than 11.62 Armor as we all know that once you drop a targets Armor to 0 ArP does nothing.

So the TL:DR is honestly AD is better than ArP. In no example does ArP actually result in a single point of damage higher and AD will scale off quite a large number of abilities where as ArP does not.

So tell me what you think? Also I am not the greatest at this game so if I possibly messed up the math feel free to Critique and enlighten me as I mostly did this to try to determine whether I should use ArP runes vs AD runes for my Jungle WW. After I spent the greater part of the Afternoon doing it I decided to share it with all of you.

Happy posting!

ReeYAwN

Junior Member

Uh... 90% of the abilities that scale w/ AD are physical abilities, thus they are also subject to armor, and arp runes would be beneficial.

Also, arp (due to the nature of the formula used to calculate damage based on armor) is increasingly powerful the more you have. where as ad is a flat increase. My point being the lower you can get a targets armor (using a combination of arp runes, items, and possiblities) the higher you damage increases.

I don't feel like doing the math, but better players than you and I are using arp runes. No offense but at level 22 w/ some napkin math you aren't proving anything.

I'll also note that in every example the damage was higher w/ arp, with the exception of 11.62 armor which nobody has.

TLDR: arp is better

UknowsI

Senior Member

I did similar calculations with Udyr earlier, and in my example flat AD runes was better that arm pen both at level 1 and 18. However, I only build him with 1-2 ad items. If I used more AD items armour penetration would end up better against anything except tanks at level 18.

But in my opinion, ad runes are better for a number of characters who build tanky, and for characters who have mixed physical and magic damage.

DorifitoX

Senior Member

Quote:
Originally Posted by ReeYAwN
Uh... 90% of the abilities that scale w/ AD are physical abilities, thus they are also subject to armor, and arp runes would be beneficial.

Also, arp (due to the nature of the formula used to calculate damage based on armor) is increasingly powerful the more you have. where as ad is a flat increase. My point being the lower you can get a targets armor (using a combination of arp runes, items, and possiblities) the higher you damage increases.

I don't feel like doing the math, but better players than you and I are using arp runes. No offense but at level 22 w/ some napkin math you aren't proving anything.

I'll also note that in every example the damage was higher w/ arp, with the exception of 11.62 armor which nobody has.

TLDR: arp is better
Well that was a bit rude, however upon further thinking I realized I hadn't done a sample involving a high atk damage vs low armor

So we will assume again we are using Trynd who has one of the highest base attacks in the game.

At level 18 he has 111.62. Against a Fiddlesticks who has a base of 56 armor at 18. Now we are going to assume the Trynd build is going to involve an Infinity Edge for +80 AD and a Bloodthirster for an average of 80 AD. And a Last Whisper which gives +40 AD and 40% armor pen. So total we have 311.62 damage (Estimate. Obviously you can build into a second bloodthirster and keep max stacks so it could be substantially higher but in a real game you are likely to get 3 or 4 of your items and you will need at least one PD in there)

We will also assume that Fiddlestick's isn't totally ******ed and notices a well built trynd killing everyone so he will get a Guardian Angel for some protection putting him to 119 Armor

So 311.62 damage with either 14.94 ArP (For 9 runes) or 8.55 AD.

Now with a 119 armor -40% armor pen is 71.4 - 14.94 = 56.46 armor. So your effective damage is .6391 with against 311.62 damage is going to be 199.15 damage.

Now the same calculation with AD will look like 119 - 40% armor pen is still 71.4 giving you an effective damage of .5834. Starting now with an AD of 320.17 which means that your damage will be 186.78

So the total change will be about 12.37 which is indeed a pretty valid change. However all of this said, for heroes with AD modifiers that deal magic damage, which you will find is a fairly large number, having AD will help add damage to them while Armor Pen will not.

So again TLDR: Armor Pen scales well against squishies late game if you take a lot of AD items however if you plan to use AD modified magic abilities (Like Katarina's dagger/ult or Tryndamere's Spin attack) you will probably see greater benefit from your AD runes. And if you aren't taking a large amount of AD in items, (Say under the 150 mark) You will probably notice almost no difference between ArP and AD.

FROM WINNIPEG

Senior Member

In the case of Katarina at least, magic pen trumps AD easily... You would never take a mark or quint of AD over magic pen. This will hold true for any champ that deals damage this way.

Tierren

Senior Member

Well, which would help more champs? AD or ArP? Or would any champ that wants AD also want ArP?

preparetobeowned

Senior Member

Try the math again with 9. Having only 7 skews the results due to it making the gap closer.

FIatulence

Recruiter

Armpen >

Not many items gives it but this stat is as needed as attack damage, best is if u have a good ratio ad/armpen.

Don't get ad w/o armpen its like having a super fast processor w/o memory

mekabar

Senior Member

Using ArP marks, Quints and masteries you can get to as much as 31 Arp at lvl 1, which negates almost any starting armor. Not to mention ArP Scales a lot better than a measly amount of attack damage later on.

Duril

Senior Member

arpen packs a punch early, and scales better later on.

9 marks will give you a whole 8 damage. A hero like Ashe would go from 53 to 61 damage. a 15% increase at level 1 (assuming you aren't using doran's).

9 deso runes gives you 15 arpen, which should give you 31 total (at level 30). so without them, you only have 16. That's fine at lvl 1 vs very squishee people, but let's assume a 31 armor character. Instead of no bonus EHP, they now have 15% bonus EHP vs physical. This means the arpen would give the same effective bonus to damage.

That's at level 1. As things scale your damage goes up, with many pushing 300ish AD by end game. 8 extra damage is a whole ~3% bonus. The added arpen will be much higher.

Take a 300 dmg character vs a 100 armor character. Assume no additional arpen (which favors straight damage).

Against AD marks, they have 84 armor or they take 54.3 % of damage (45.7% reduction)
Against arpen marks then have 69 armor or they take 59.2 % of damage (40.8% reduction)

AD marks hits for 308*.543 = 167 damage
arpen marks hit for 300*.592 = 177 damage

And now realize that with more arpen this advantage grows even larger.

I even tried AD/per level runes and they come out behind arpen.

There simply isn't any way for those AD runes to come out ahead, except precisely at lvl 1 when your arpen may exceed their armor significantly.

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