The perk works correctly. It has random bonus damage [i]and[/i] extra precision damage when firing from the hip. The ads precision damage you are seeing is the random damage boost from the first half of the perk, which will also increase body shot damage as well, but you probably didn't notice it.
With aggressive ballistics, the bonus shot will hit for 111 precision damage, making the gun a two shot kill weapon at random and staying in line with what the first half of the perk says. The hip fire bonus damage is also there but is highly unlikely because getting a headshot from the hip is difficult. If anyone has a number for this damage please let me know, I have yet to see it.
The most bonus shots I have had in a row are two, and the frequency of these bonuses is low, possibly 2 to 6 per match. Because of this, and tlw's unreasonably low range, it is a strong but balanced weapon. It seems overpowered because the large maps have been removed from most playlists, turning crucible into a run and gun close range war zone. If two to three larger maps were reintroduced into crucible you would likely have less TLW users and less complaining posts about game mechanics that [i]seem[/i] broken, but aren't.
English
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Hip fire critical head shot is 111.