Parlley Mechanics - by Heat n Serve

The gadget spec URL could not be found
 wanted to demystify the multitude of game mechanics that go into figuring out the damage that is dealt by parrrley and how it interacts with target champions. This is based on release v1.0.0.74. My complete Gangplank guide is linked below, if you want to see build details. This thread is purely for parrrley mechanics.

Additional thanks to:, Akanei, Wildstorm.

EDIT: 1/29/2010
The gadget spec URL could not be found
full Gangplank guide has won 2nd place in the guide contest! Thanks to all who voted!

EDIT: 2/5/2010
The Gangplank guide has hit the 10,000 views mark! Hooray!

EDIT: 2/10/2010
I have updated this to reflect the recent patch, but I have not really tested it. I am assuming the same mechanics apply. If anyone finds anything different, post here and I will modify the guide accordingly.

The red numbers that appear above a target's head when you parrrley them can be calculated as follows, rounding to the nearest whole number:
base => Gangplanks's base attack value (your damage without items/runes/masteries/etc)

total => Gangplank's total attack value (your damage with items/runes/masteries/etc)

AP => Ability power of your champion

Pdmg => Damage based on parrrley level (1-5): 20/55/90/120/150

critdmg => Default is 2, but can be increased with crit damage modifiers (example: with infinity edge critdmg=2.5), set this to 1 for the case of no-crit

armor => target's armor value, applying debuffs in proper order (see next section)

armorpen => amount of armor penetration from items, runes, and masteries (can be of a fixed value or a percentage of the target's resist, or the sum of both)
For positive values of armor:
with nothing
[(1.1 * total + Pdmg) * critdmg] * 100/[100 + max(0, armor - armorpen)]

with sheen
[(1.1 * total + Pdmg) * critdmg + base] * 100/[100 + max(0, armor - armorpen)]

with triforce
[(1.1 * total + Pdmg) * critdmg + 1.5 * base] * 100/[100 + max(0, armor - armorpen)]

with lichbane
[(1.1 * total + Pdmg) * critdmg + AP] * 100/[100 + max(0, armor - armorpen)]
For negative values of armor:
with nothing
[(1.1 * total + Pdmg) * critdmg] * [1 - armor/(100 - armor)]

with sheen
[(1.1 * total + Pdmg) * critdmg + base] * [1 - armor/(100 - armor)]

with triforce
[(1.1 * total + Pdmg) * critdmg + 1.5*base] * [1 - armor/(100 - armor)]

with lichbane
[(1.1 * total + Pdmg) * critdmg + AP] * [1 - armor/(100 - armor)]
A word on magic resist reduction and spell penetration...
Armor reduction and armor penetration are applied in this order:
1. % reduction (Bushwack)
2. Flat reduction (Black Cleaver debuff, Puncturing Taunt, etc)
3. % penetration (Last Whisper)
4. Flat penetration (The Brutalizer, Sunder Mastery, Runes of Desolation)

Apply 1 & 2 to get the enemy target's new armor value, which you and your teammates will see. Apply 3 & 4 to that new value based on what armor penetration you possess.

What if I don't see red damage numbers when I parrrley? What if I see "dodge" or "miss"?
Dodge is fairly self explanatory, any target with a non-zero chance to dodge could avoid taking damage from your parrrley. Jax, Sivir and Katarina are the most likely champions to do this to you because of their naturally high chance to dodge.

Misses are caused by having debuffs on your character that reduce your chance to hit:
  • Corki's phosphorus bomb reduces your chance to hit by 35%
  • Shaco's two-shiv poison reduces chance to hit by 20%/22.5%/25%/27.5%/30%
  • Teemo's blinding dart reduces your chance to hit by 100%
  • Heimerdinger's CH-1 concussion grenade reduces your chance to hit by 100%
  • Exhaust summoner ability reduces your chance to hit by 100%

After playing a few games, I believe Banshee's Veil still blocks Parrrley, which is horribly stupid in my opinion, since the damage is now physical.

Putting it altogether in a real battle situation:
You're a level 10 Gangplank with 82 base damage, 162 total damage and 40 armor penetration. You have a Sheen and an Infinity Edge. Let's assume your total chance to crit is 40%. While under the effect of Corki's phosphorus bomb, you cast level 5 parrrley on a level 10 Jax with 59 armor who has a 27% chance to dodge.

If my assumptions are correct about how the game rolls for crits and then checks against miss chance and dodge, then:
There is a 28.47% chance that you will hit Jax for 303 damage.
There is a 18.98% chance that you will crit Jax for 654 damage.
There is a 52.55% chance that Jax will take no damage from the parrrley.
The expectation of the damage is about 210, so from a statistical standpoint, you are better off casting your parrrley on a different target. 

What does this mean in terms of strategy?
There is no real strategy anymore. Just get armor pen. Prior to the patch, there was an art to playing this champion. There was strategy that could greatly optimize how useful you could be on a team. It's why I loved playing him. Whatever. Thanks to everyone who supported my guides over the past few months. As a courtesy to you, I will keep these guides up to date based on the strategies that I follow most often.