Runnings the Numbers on Shaco - by Phoebus

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Shaco is a character with a lot of percent-bonus-damage attacks. This makes it slightly unclear exactly how his abilities interact with certain items. Specifically, I have always been curious exactly how well Sheen, Trinity Force, and the Infinity Edge work in a DPS Shaco build. I just played a practice game to run the numbers, and thought I would share the results! To start things off...

Baseline Values
The abilities I am considering are:
Backstab (passive): "Shaco deals 25% bonus damage when striking from behind"
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Level 5 Deceive ('q'): "Shaco instantly stealths for 4 seconds, and teleports to target nearby location. If he attacks while stealthed, the attack is guaranteed to crit for a bonus 130% damage."

The Items:
Sheen: after ability use, next physical attack deals "100% extra base damage"

Trinity Force: "+20 Attack Damage... On attack, increases your base attack damage by 150% for one attack"

Infinity Edge: "+80 Attack Damage... Critical hits now deal 250% damage instead of 200%"

I also used a Tiamat to speed up the farming phase. Tiamat adds 42 Attack Damage.

*At level 18, Shaco's base attack damage before item modifiers is 113

**Tests were performed on release v

The Experiment
At level 18, with various combinations of the above items, I recorded attack damage vs 0-armor creeps from the front and the rear. Here's what I got:

Weapon: Front Attack; Front Deceive; Rear Attack; Rear Deceive

Tiamat Only: 155; 356; 193; 445;

Sheen: 155; 469; 193; 558;

Infinity Edge: 235; 658; 293; 822;

IE + Sheen: 235; 771; 293; 935;

IE + Trinity Force: 255; 883; 318; 1062;

What this means...

First off, Sheen and Trinity Force get no benefit from any of Shaco's skills. Their damage portion does not increase when attacking from behind, and they do not add damage to Deceive attacks beyond their standard contribution. Because of the different wording in their tooltips, I thought it possible that TF would scale with crit even if Sheen didn't, but that's not the case. Sheen always adds 113 damage, and TF always adds 169.5 to Shaco's attack's. (Remember Shaco has base 113 damage. This all makes sense.)

Now Infinity Edge, on the other hand, does get a benefit from both Deceive and Backstab. The IE bonus is additive to the Deceive bonus and multiplicative to the Backstab bonus. This will be easier to explain with equations....

Damage = (Attack Damage)*(Crit Coefficient)*(Backstab Coefficient)+(Sheen Bonus)

Normally, Crit Coefficient = 2.0 for normal crits and (2.0+0.5)=2.5 while wearing IE. 
For Deceive, Crit Coefficient = 2.3 for normal strikes and (2.3+0.5)=2.8 while wearing IE.

This makes the complete equation for Deceiving from behind with Trinity Force:
Damage = (255)*(2.8)*(1.25)+169.5 = 1062.0

In short, Infinity Edge is extremely effective in a DPS Shaco build. Sheen and Trinity Force, while still nice due to his frequent casting, do not scale with any other items or abilities. I hope this was helpful to some. Happy hunting!