I've seen allot of discussion over speed vs. damage, and crits vs. damage. So, I decided to put three builds of each (crits, AS, AD) through a testing sequence to determine which is better.
Each build consists of 3 popular items from each category, put on a level 18 Ashe with no other masteries, runes, buffs, etc.. I chose Ashe because I tend to see her being used as a base for other tests like this, and because she can use Runaan's for the speed build. Each build's stats were calculated, then raw damage and damage w/ armor & MR were calculated.
The builds are as follows:
-Critical Chance Ashe:
---Phantom Dancer
---Atma's Impaler
---Infinity Edge
-Attack Speed Ashe:
---Runaan's Hurricane
---Zephyr
---Nashor's Tooth
-Attack Damage Ashe:
---The Bloodthirster (Fully Stacked)
---The Black Cleaver
---Last Whisper
Here's the stats for each build:
-Crit Ashe:
---AS = 1.65816
---AD = 167.6
----Atma's = 27.255
-----Total AD = 194.855
---Crit Damage = 487.1375
---Crit Chance = 70%
-AS Ashe:
---AS = 2.984688 (Capped at 2.5)
---AD = 122.6
----Nashor's = 24
-----Total Damage = 146.6
---Crit Damage = 269.2
----One Runaan's Bolt = 71.3 (+ Nashor's = 95.3)
-AD Ashe:
---AS = 1.10544
---AD = 287.6
---Crit Damage = 575.2
----Armor Reduction = 0->5->10->15->20->25%
-----Armor Ignored = 35%
------Armor Penetration = 10
Here's the raw damage values (before applying armor/MR):
~~Each Ashe gets a free 'Focused' attack before the tests.~~
~~For AS Ashe, Runaan's total damage is included to show total damage give-out.~~
~~Also for AS Ashe, the damage from each individual bolt of Runaan's is included.~~
~~AS Ashe also could exceed the AS cap of 2.5 per sec., so I included that for fun.~~
-Crit Ashe:
---Focus = 487.1375
----100 Attacks >> [487.1375 x 70 (Crits)] + [194.855 x 30] + [487.1375 (Focus)] = 40,432.4125
----10 Sec. of Attacks (17 Attacks) >> [487.1375 x 12 (Crits)] + [194.855 x 5] + [487.1375 (Focus)] = 7,307.0625
-AS Ashe:
---Focus = 269.2
----100 Attacks >> [146.6 x 100] + [269.2 (Focus)] = 14,929.2 {+ [190.6 x 100 (Runaan's)] = 33,989.2}
------100 Attacks from Runaan's >> [95.3 x 100] = 9,530
----10 Sec. of Attacks (25 Attacks) >> [146.6 x 25] + [269.2 (Focus)] = 3,934.2 {+ [190.6 x 25 (Runaan's)] = 8,699.2}
-----10 Sec. of Attacks w/o Caps (30 Attacks) >> [146.6 x 30] + [269.2 (Focus)] = 4,667.2 {+ [190.6 x 30 (Runaan's)] = 10,385.2}
------10 Sec. of Attacks from Runaan's (25 Attacks) >> [95.3 x 25] = 2,382.5
-------10 Sec. of Attacks from Runaan's w/o Caps (30 Attacks) >> [95.3 x 30] = 2,859
-AD Ashe:
---Focus = 575.2
----100 Attacks >> [287.6 x 100] + [575.2 (Focus)] = 29,335.2
----10 Sec. of Attacks (12 Attacks) >> [287.6 x 12] + [575.2 (Focus)] = 4,026.4
By this point, my testing shows that AS Ashe is a very poor choice for damage give-out (although for DPS, AS Ashe has a higher ratio than DPA), and AD Ashe does about 75% of crit Ashe's damage. However, AD Ashe has both The Black Cleaver and Last Whisper, so when facing a target with armor and MR, AD Ashe could pull ahead. Here's my final calculations against a test target.
Actual damage values (calculating armor and MR):
~~Test target has 100 Armor and Magic Resist and no other buffs.~~
~~Btw, 100 Armor and MR gives exactly 50% damage reduction.~~
-Crit Ashe:
---100 Attacks >> [40,432.4125 x 0.5] = 20,216.20625
---10 Sec. of Attacks (17 Attacks) >> [7,307.0625 x 0.5] = 3,653.53125
-AS Ashe:
---100 Attacks >> [14,929.2 x 0.5] = 7,464.6 {+ Runaan's = 16,994.6}
-----100 Attacks from Runaan's >> [9,530 x 0.5] = 4,765
---10 Sec. of Attacks (25 Attacks) >> [3,934.2 x 0.5] = 1,967.1 {+ Runaan's = 4,349.6}
----10 Sec. of Attacks w/o Caps (30 Attacks) >> [4,667.2 x 0.5] = 2,333.6 {+ Runaan's = 5,192.6}
-----10 Sec. of Attacks from Runaan's (25 Attacks) >> [2,382.5 x 0.5] = 1,191.25
------10 Sec. of Attacks from Runaan's w/o Caps (30 Attacks) >> [2,859 x 0.5] = 1,429.5
-AD Ashe:
---100 Attacks >> [371.11904 (Focus)] + [189.5284 (1 BC Stack)] + [193.66984 (2 BC)] + [198.0126 (3 BC)] + [202.52792 (4 BC)] + [207.27332 x 96 (5 BC)] = 21,053.09652
---10 Sec. of Attacks (12 Attacks) >> [371.11904 (Focus)] + [189.5284 (1 BC Stack)] + [193.66984 (2 BC)] + [198.0126 (3 BC)] + [202.52792 (4 BC)] + [207.27332 x 8 (5 BC)] = 2,813.04436
The results? Well, an AS Ashe with just these 3 items clearly needs some help (maybe some Bloodthirsters?), and in terms of raw damage, crit Ashe wins over AD Ashe. However, against an actual in-game target w/ 100 armor & MR, AD Ashe really catches up. After 1 Focused attack and 100 more attacks, thanks to armor reduction/penetration, AD Ashe outdoes crit Ashe by about 800 damage. However, crit Ashe still has higher AS, so crit Ashe wins out by ~800 damage in 10 seconds of attacks.
Still, crit Ashe's success depends on whether she actually gets 70 crits out of 100 attacks, and AD Ashe would just build more AD to out-do crit Ashe. However, crit Ashe could also build more AD, and get another Phantom Dancer for 100% crit chance. AS Ashe still has a chance as well (just throw in some Bloodthirsters/Blade of the Ruined King).
Also, there are other builds out there, so AD Ashe could be built differently and get more damage. Crit Ashe could build a Statikk Shiv for magic damage, and AS Ashe could easily pick up some AD to capitalize on that max attack speed. These are just base builds, and could even be combined (70% crits that do 700+ damage?!).
Anyway, these are just my findings and opinions on the topic. If you guys have any better builds, or even different champs to test, or a more specific test target, feel free to make suggestions. I'll gladly test any other set-ups, so just ask if you want it tested.
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