Runaan's Hurricane or Phantom Dancer on Caitlyn?
Her passive allows to do 150% damage every 5 AAs and ignores 50% of target's bonus armor. With Runaan's, that's ever 2 AAs (the on-hit effect applies, I confirmed) unless you're attacking in a bush, in which case that's every AA.
Every 150% damage on every 2 AA and armor penetration AND bunch of AoE damage sounds pretty good on paper, but I'm not sure if it's worth getting instead of another crit item.
I tried to do some math but I failed. Can someone help me?
EDIT: I'm doing some math again. I'll add a tl'dr after each section.
I'm gonna assume
for the build (most popular and highest winrate build minus PD), and add PD or Runaan's.
I'll also ignore runes and masteries for the sake of simplicity, and assume level 18.
Caitlyn's Base Stats AD: 101 AS: 0.625+68% CC (Crit Chance): 0%
build
AD: 301
AS: 0.625+128%=1.425
CC: 55%
AD: 301
AS: 0.625+173%=1.699
CC: 20%
Unique Passive (Runaan's proc)
I'll calculate how much damage would be done over 5 AAs, and calculate DPS later by dividing it by how much time it would take to do that much damage. Also, I'll make multiple cases for whether passive crits or not. I'm assuming 3 crits for PD (55% rounded up to 60%) and 2 passive procs for Runaan's (2.5 rounded down to 2).
DPS (case 1)
3 crits: 3012.53=2257.5
1 regular attack: 3011=301
1 non-crit passive: 3011.5=451.5
Total: 3010/3.509 seconds=~858 DPS
DPS (case 2)
2 crits: 3012.52=1505
2 regular attack: 3012=602
1 crit passive: 3011.5*2.5=1128.75
Total: 3235.75/3.509 seconds=~922 DPS
DPS (case 1)
3 regular attack: 3013=903
1 regular passive: 3011.5=451.5
1 crit passive: 3011.52.5=1128.75
Total: 2483.25/2.943 seconds=~844 DPS
DPS (case 2)
2 regular attack: 3012=602
1 crit: 3012.5=752.5
2 non-crit passive: 3011.52=903
Total: 2257.5/2.943 seconds=~767 DPS
tl;dr: In terms of raw damage, PD build does much more damage.
What if we account for armor?
Let's say the enemy has base armor of 90 and bonus armor of 150, which is approximately 2 armor items. More armor they buy, more damage your passive will do.
This means the enemy will have total of 240 armor. With
, 35% of the armor is ignored, so that's total of 156 armor. The passive ignores 50% of bonus armor, so with the passive, that's 165*.65=107.25 armor.
156 armor reduces physical damage by ~61% (39% goes through), and 107.25 armor reduces physical damage by ~52% (48% goes through).
If the enemy builds more armor, Runaan's build will be less affected by than PD build.
DPS (case 1)
3 crits: 3012.53=2257.5 reduced to 880
1 regular attack: 3011=301 reduced to 117.39
1 non-crit passive: 3011.5=451.5 reduced to 216.72
Total damage to tank: 1214.11/3.509 seconds=346 DPS
DPS (case 2)
2 crits: 3012.52=1505 reduced to 587
2 regular attack: 3012=602 reduced to 234.78
1 crit passive: 3011.5*2.5=1128.75 reduced to 541.8
Total damage to tank: 1363.58/3.509 seconds=389 DPS
DPS (case 1)
3 regular attack: 3013=903 reduced to 352.17
1 regular passive: 3011.5=451.5 reduced to 216.72
1 crit passive: 3011.52.5=1128.75 reduced to 541.8
Total damage to tank: 1110.69/2.943 seconds=377 DPS
DPS (case 2)
2 regular attack: 3012=602 reduced to 234.78
1 crit: 3012.5=752.5 reduced to 293.475
2 non-crit passive: 3011.52=903 reduced to 433.44
Total damage to tank: 961.695/2.943 seconds=326 DPS
tl;dr: So even if the enemy is tanky, PD build does more damage. The gap is much smaller now, so with more armor, Runaan's may do more DPS to someone with, say, 200 bonus armor (300 total armor).
What if we account for Runaan's bolt procs? The goal of ADC is to do consistent damage, and that isn't necessarily single-target. Consider that the bolts will most likely hit more squishy targets instead of tanks.
DPS (case 1)
3 crits: 3012.53=2257.5
1 regular attack: 3011=301
1 non-crit passive: 3011.5=451.5
Total: 3010/3.509 seconds=~858 DPS
DPS (case 2)
2 crits: 3012.52=1505
2 regular attack: 3012=602
1 crit passive: 3011.5*2.5=1128.75
Total: 3235.75/3.509 seconds=~922 DPS
DPS (case 1)
3 regular attack: 3013=903
1 regular passive: 3011.5=451.5
1 crit passive: 3011.52.5=1128.75
Runaan's bolts: (10+0.5*301)*10=1605
Total: 4088.25/2.943 seconds=~1389 DPS
DPS (case 2)
2 regular attack: 3012=602
1 crit: 3012.5=752.5
2 non-crit passive: 3011.52=903
Runaan's bolts: (10+0.5*301)*10=1605
Total: 3862.5/2.943 seconds=~1312 DPS
tl;dr: total damage is much better with Runaan's, although single target damage is still bad.
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