10 replies to this topic

[Suzaku910]

I'll be calculating the damage increase of 15 AD via Flat AD Quints and Marks vs. 25 Armor Penetration via Armor Penetration Marks and Quints. We'll also be assuming that both runesets are used in combination with 21/x/x masteries, adding an additional 6 + 10% armor penetration and 3 damage.

We'll use this against Level 5 Tristana with Flat Armor seals, so 43 armor, as level 5 Ashe, so 61 base damage.

Flat AD:

• First we start by calculating total damage without runes: 61 + 3 from masteries = 64.
  
• Now we calculate the total armor she is going to deal damage against: (43 - 6 from masteries) - [.1*(43 - 6)] from masteries. Ashe's damage will be calculated against 33.3 armor.
  
• 33.3 armor reduces 33.3/(100+33.3) damage. Ashe's 64 AD will be reduced by 24.9812%
  
• So 64 - (64*.249812) = 48.012 total damage.
  
• Now we will calculate how the additional 15 damage from runes will affect this. Ashe now has 79 total AD. 79-(79*.249812) = 59.2648 total damage.
  
• We now calculate the increase: 59.2648 - 48.012 = 11.2528 (rounded down to 11).
  
• Ashe gains 11 damage from going Flat AD Quints and Marks with 21/x/x against a target with 43 armor.

Armor Penetration:

• Again we will calculate Ashe's total damage without runes: 61 + 3 from masteries = 64.
  
• We will again calculate the total armor that is going to be dealt damage against, but not including runes so we can see the damage increase. We have done this before: Ashe deals 48.012 damage without penetration runes.
  
• Now we will calculate the total armor that is going to be calculated against including runes. Ashe will have 31 total armor penetration + 10% after that calculation: (43-31) - [.1*(43-31)] = 10.8. Ashe's damage will now be calculated against 11 armor.
  
• 11 Armor reduces damage by: 11/111 = 9.9099%
  
• 64 - (64*.099099) = 57.65 or 58 damage dealt after penetration
  
• 57.65 - 48.012 = 9.638 damage (rounded to 10)
  
• Ashe's damage is increased by 10 with Armor Penetration runes vs. 43 armor.

Conclusion:
Ashe deals more damage at level 5 with flat AD runes than with armor penetration runes on targets with 43 armor or less.

What was not considered:

• Targets with more armor
  
• Flat AD helps last hit
  
• Abilities that scale with AD at a ratio other than 1

Edited by Suzaku910, 26 February 2012 - 06:37 PM.

[Josidiah]

now pls do the same for caitlyn pls

Jokes aside; useful info for me. Proves why I feel better while using my ArPen page. So ty.

Edit: When I say "proves", I mean it in a way that "it explains why I feel the way I feel".

Edited by Josidiah, 26 February 2012 - 08:42 PM.

[Drunkard]

In all honesty, AD runes have been better for quite a while. Going full AD page for last hitting then grabbing a Last Whisper or Black Cleaver for Ranged Carries has been standard.

[Josidiah]

 Drunkard, on 26 February 2012 - 07:24 PM, said:

In all honesty, AD runes have been better for quite a while. Going full AD page for last hitting then grabbing a Last Whisper or Black Cleaver for Ranged Carries has been standard.

I know that, and have done so myself a lot of times lately. But for whatever the reason, I perform better with Arpen. The only way to explain it to myself is that I avoid LW until my IE and PD are done. So I feel that during the time it takes from lets say, Zeal to finishing PD AND LW (midgame???), I deal better damage with ArPen runes. Please note that I am not saying anything definitive, its just what I feel like.

And on those rare occasions when games just dont end, I get double PD instead of LW, esp if enemy has strong chasers with Ghost (Singed, Udyr, Vayne). Fk me if I ever try to kill that 300 armor tank instead of any other 4 enemies out there.

As for lasthitting: I have probably over 700 games with Ashe alone. Im so used to lasthitting with no extra AD (not even Dorans, just the +4 damage on minions from old mastery tree) that AD runes barely effect my farming, if at all.

TL;DR Each to his own. I know flat AD runes are great and work fine, its just ArPen does it better for me

[Belfador]

Hi, Long time read first time poster.

I noticed a few issues with your theory. If you are compaining flat AD (+quints) to armour pen (+quints), why did you include the additional 13 armour from yellow runes (tristana only has 30 armour at lvl 5). If you are including these you should also include the additional 3.87 (rounded to 4) dmg for flat yellow dmg runes. (I havent done the maths on this yet)

Or you remove the additional yellow armour runes you'll be doing 52 dmg base dmg not 48. (see below).

Note: if you include the additonal .5 / lvl from the deadliness mastery if does not effect the difference between the output of FLAT AD and ArPen.

Flat AD:

• First we start by calculating total damage without runes: 61 + 3 + .5/lvl from masteries = 66.5 or 64 (Rounded up).
  
• Now we calculate the total armor she is going to deal damage against: (30 - 6 from masteries) - [.1*(30 - 6)] from masteries. Ashe's damage will be calculated against 21.6 armor.
  
• 21.6 armor reduces 21.6/(100+21.6) damage. Ashe's 64 AD will be reduced by 17.763%
  
• So 64 - (64*.17763) = 52.631 total damage.
  
• Now we will calculate how the additional 15 damage from runes will affect this. Ashe now has 79 total AD. 79-(79*.17763) = 64.967 total damage.
  
• We now calculate the increase: 64.967 - 52.631 = 12.336 (rounded down to 12).
  
• Ashe gains 12 damage from going Flat AD Quints and Marks with 21/x/x against a target with 30 armor.

Armor Penetration:

• Again we will calculate Ashe's total damage without runes: 61 + 3 from masteries = 64.
  
• We will again calculate the total armor that is going to be dealt damage against, but not including runes so we can see the damage increase. We have done this before: Ashe deals 52.631 damage without penetration runes (only masteries).
  
• Now we will calculate the total armor that is going to be calculated against including runes. Ashe will have 31 total armor penetration + 10% after that calculation: (30-31) - [.1*(30-31)] = -0.9. Ashe's damage will now be calculated against 0 armor (as runes are armour pen not reduction).
  
• 0 Armor reduces damage by: 0% (or true dmg)
  
• therefore he dmg would be 64.

Comparing the diference Flat AD would increase your dmg by .336.

This is really a insignificat amout without adding additional items or armour.

If you taking into account alot of low elo players and normal games (majority of all games played) most characters (yes I know I'm generalizing) fail to buy armour (not icluding your tanks) whilst staking heavily on additional dmg items you would be better with the ArPen runes into late game, as you item dmg would not be reduced by the 17% reduction.

or for the difference:
with flat AD you will do an additional 64-52 = 12 dmg;
or with ArPen 64-52 = 12.

To summarise:
With armour pen (31 using your figures below) & you will do true dmg to Tristana @ lvl 5. or 64,
With flat AD (15 dmg) or 64 (rounded up) - again using your formulas.

Note: I've copied your formulas to make comparison easier

I would like to see how the runes effect things at late game, but as I'm at work I dont really have time to complete the maths for a few standard builds.

[Suzaku910]

 Belfador, on 27 February 2012 - 12:13 AM, said:

Hi, Long time read first time poster.

I noticed a few issues with your theory. If you are compaining flat AD (+quints) to armour pen (+quints), why did you include the additional 13 armour from yellow runes (tristana only has 30 armour at lvl 5). If you are including these you should also include the additional 3.87 (rounded to 4) dmg for flat yellow dmg runes. (I havent done the maths on this yet)

Or you remove the additional yellow armour runes you'll be doing 52 dmg base dmg not 48. (see below).

Because flat yellow AD is not common. The largest reason people take flat armor pen is to counter armor seals early game, which is why I included the armor yellows. Additionally, most AD carries use flat AD yellows since there really isn't anything else useful to put there (13 Armor vs. 4 Damage....armor is better). Besides that, it's just an arbitrary number. Doesn't matter if you add the yellows or not; champions will reach 43 armor at one point in the game or another.

Quote

Note: if you include the additonal .5 / lvl from the deadliness mastery if does not effect the difference between the output of FLAT AD and ArPen.

Then why did you include it?

Quote

Flat AD:

• First we start by calculating total damage without runes: 61 + 3 + .5/lvl from masteries = 66.5 or 64 (Rounded up).
  
• Now we calculate the total armor she is going to deal damage against: (30 - 6 from masteries) - [.1*(30 - 6)] from masteries. Ashe's damage will be calculated against 21.6 armor.
  
• 21.6 armor reduces 21.6/(100+21.6) damage. Ashe's 64 AD will be reduced by 17.763%
  
• So 64 - (64*.17763) = 52.631 total damage.
  
• Now we will calculate how the additional 15 damage from runes will affect this. Ashe now has 79 total AD. 79-(79*.17763) = 64.967 total damage.
  
• We now calculate the increase: 64.967 - 52.631 = 12.336 (rounded down to 12).
  
• Ashe gains 12 damage from going Flat AD Quints and Marks with 21/x/x against a target with 30 armor.

You screwed up here. You calculated the Deadliness mastery in the first part to calculate her total damage, but didn't take it into account anywhere else in the mathcrafting, specifically where you calculated her damage against Armor without the runes and when you calculated it with the runes.

Quote

Armor Penetration:

• Again we will calculate Ashe's total damage without runes: 61 + 3 from masteries = 64.
  
• We will again calculate the total armor that is going to be dealt damage against, but not including runes so we can see the damage increase. We have done this before: Ashe deals 52.631 damage without penetration runes (only masteries).
  
• Now we will calculate the total armor that is going to be calculated against including runes. Ashe will have 31 total armor penetration + 10% after that calculation: (30-31) - [.1*(30-31)] = -0.9. Ashe's damage will now be calculated against 0 armor (as runes are armour pen not reduction).
  
• 0 Armor reduces damage by: 0% (or true dmg)
  
• therefore he dmg would be 64.

Again, you counted the Deadliness mastery in the first part of the Flat AD calculations but didn't mention it anywhere in this part.

Quote

Comparing the diference Flat AD would increase your dmg by .336.

Except you didn't count any extra armor, when Armor Yellows are incredibly common.

Quote

This is really a insignificat amout without adding additional items or armour.

Which isn't encountered often except in low elo and sub-30 play.

Quote

If you taking into account alot of low elo players and normal games (majority of all games played) most characters (yes I know I'm generalizing) fail to buy armour (not icluding your tanks) whilst staking heavily on additional dmg items you would be better with the ArPen runes into late game, as you item dmg would not be reduced by the 17% reduction.

Perhaps, but I see some armor built or at least defensive masteries + armor yellows.

As for the rest...well, you rounded at some parts but not at others.

Without all your rounding, Flat AD still increases Ashe's damage by .967 (rounded up to 1 in-game) over Armor Penetration runes if Tristana has no additional armor. This is only slightly less than with the armor calculations.

[Belfador]

I realise it is yellow Armour is a common build, but for comparsion sake I feel you should be comparing like for like, unfortuantely as you stated is does effect things.

 Suzaku910, on 27 February 2012 - 12:55 AM, said:

Then why did you include it?

Sorry about the added deadliness, I started to change the data when I realised it didnt make a difference, I thought I had removed the references in the maths components. I obviously missed bits.

As for why I included the other yellows, they could very well be AS runes. It still effects total dmg.
I should put a disclaimer and say I rarely play ad ranged, more ad melee or ap caster. So Im not sure how common AS runes on a ad ranged would be. So I'll go by thoughts as to how common this would be.

As for the round up and down I only did that on screen, on the calculator I used the the number to the 8th decimal place.

no I didnt calcuate extra armour, but I didnt calculate extra dmg either. I could add a frozen heart at 100 armour and full BT at 100 dmg and re run the maths. I think that would give a better comparison in mid game.

As for "Which isn't encountered often except in low elo and sub-30 play." My experience has shown me in normal play even at lvl 30 most ppl dont by armour or magic resistance unless the side is heavily stacked or as a last item.
EDIT: I say most, but I refer to signifcant expenditure. ( not merc treads for example ). So much so that I usually work towards (70% of the time) a magic reduction build (extra dmg) and sell my sorc pen boots.

And whilst you do get defensive masteries and armour, you also have ppl building brutilizer and other items to compensate. I wasnt trying to get bogged down in possibilities, just pointing out that there is very little difference in either rune set. (Even @ 1 dmg difference per hit... it's not going to make or break you.)

On a side note isnt it that same maths to calculate Magic pen vs AP, yet its considered normal to get magic pen runes over AP runes for blue. (this might also be because of sorc boots coming into play early)... just at thought tho.

Edited by Belfador, 27 February 2012 - 02:15 AM.

[Suzaku910]

 Belfador, on 27 February 2012 - 02:10 AM, said:

On a side note isnt it that same maths to calculate Magic pen vs AP, yet its considered normal to get magic pen runes over AP runes for blue. (this might also be because of sorc boots coming into play early)... just at thought tho.

Actually, AP/level blues are more common than Mag Pen blues.

AP/Level, flat AP, flat CDR, and CDR/level, MR/level, flat MR are the "common" blues.

[Belfador]

 Suzaku910, on 27 February 2012 - 02:28 AM, said:

Actually, AP/level blues are more common than Mag Pen blues.

AP/Level, flat AP, flat CDR, and CDR/level, MR/level, flat MR are the "common" blues.

Fair enough. I'll stand corrected.

[Feanor]

Take crit, give shits about Armor.

On a more relevant note:
AD runes are better overall, not only do most AD carries' skills scale with AD, if you have a Black Cleaver you will be hitting harder than a Last Whisper against targets up to ~130 armor (assuming you have the 10% armor pen from the offensive tree). Also, Ashe benefits even more from AD runes because her passive makes her lethal early on, first hit + W goodbye 50% of your health.