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“The Ninja perk grants you the power of the fabled shadow warriors. When attacking, you gain a +15% critical chance on all Melee and Unarmed attacks. Additionally, Sneak attack criticals do 25% more damage than normal.”— Fallout 3 in-game description
Due to Covert Operative affecting the sneak attack multiplier of unarmed weapons, using Covert Operative 3 and Ninja 3 will yield a x3.5 sneak attack multiplier on unarmed weapons.
In Fallout 3, the extra 15% critical chance does not work without the help of the unofficial Fallout 3 patch. [verified]
In Fallout: New Vegas, Ninja multiplies your critical chance by 1.15 instead of adding a flat 15%, unlike all other perks/traits that modify critical chance. For example, a character with a critical hit chance of even 25% would have it be increased to only 28.5% rather than to 40% as it should. (25% * 1.15 = 28.75% vs 25% + 15% = 40%) [verified]
In Fallout 4, the bonus to the actual sneak attack damage multiplier on silenced weapons provided by this perk is known to behave erratically when interacting with Cloak & Dagger and Mister Sandman. Patch 1.4 tried to address this bug, so that you could no longer reach a 6.3x multiplier. However, there was still some variance depending on the order you obtain the three perks. The current multipliers are:
Sandman 3, Ninja 3, Cloak = 4.4x
Ninja 3, Sandman 3, Cloak = 4.7x
Sandman 3, Cloak, Ninja 3 = 4.7x
Ninja 3, Cloak, Sandman 3 = 4.8x
Cloak, Ninja 3, Sandman 3 = 4.8x
Cloak, Sandman 3, Ninja 3 = 4.8x
Right now the only solution for and appears to be selecting/receiving these perks in the "correct" order. The reason these differences happen is because, although Cloak & Dagger and Mister Sandman both use multiplication, Ninja is set to use addition. Because order of operations matters when both are mixed, results from having all three perks can vary.[verified]
In Fallout 4, the Ninja perk works very oddly with melee attacks. One-handed weapons are always treated as melee, and unarmed are always treated as ranged attacks. Rank one doesn't affect two-handed melee weapons at all, rank two treats two-handed weapons as ranged weapons, and rank 3 finally treats two-handed melee weapons as melee weapons. This results in a very bizarre sneak attack damage progression for two-handed melee weapon users, and a very low one for unarmed users. On the PC version, a fix for this and the above issue is available here. [verified]