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.
pc In Fallout 3, the extra 15% critical chance does not work without the help of the unofficial Fallout 3 patch. [verified]
pcps3xbox360 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. There is a bug with the calculations with all three perks active, depending on the order in which they were granted, as follows:
Right now the only solution for ps4 and xboxone 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.
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 PC version, a fix for this and the above issue is available here.