Q: What are masterwork rolls?
A: Most legendary weapons are capable of being Masterworked. The masterwork system is a way for you to upgrade your favorite weapons to their maximum potential.
Q: What does it take to upgrade a weapon to a masterwork?
A: Upgrading your weapons, in broad terms, takes a small amount of glimmer, legendary shards, and, most importantly, Enhancement Cores.
Depending on what Tier your weapon is at, the requirements to raise it to the next tier increase the closer the weapon is to being fully masterworked (Tier 10).
Q: What benefits do I get for masterworking a weapon?
A: Each tier that you increase your weapon will grant a small buff to a single stat, chosen randomly when the item drops.
Beyond that, at Tier 5 you gain access to a kill tracker. At Tier 10, your multi-kills will generate orbs of light.
Q: So what are these "masterwork roll" stats?
A: These are the possible stats that upgrading your weapon will grant a bonus to. Depending on what tier you are at, you can grant anywhere from 1-10 additional points in any of the stats listed to your weapon.
Q: Any catch with this?
A: The Bungie API currently says that all weapons can potentially roll with all stats as their masterwork stat. This obviously isn't accurate, as Blast Radius isn't applicable to, say, Auto Rifles.
The list you see on this page is trimmed to only show stats that actually appear on the weapon. However, it is possible that Bungie has additional logic behind the scenes that further filters these
possibilities to, for example, prevent certain items from being able to have an Impact masterwork. Until Bungie modifies the API files to 100% accurately display which masterwork stats are possible on
each item, take what you see here with a pinch of salt.
This perk's main use seems to be on LFR's and Snipers for PvP as an offensive counterpart to No Distractions; you time holding your aim ahead of time very briefly to get an added benefit - in this case, a higher-damage headshot. This, like No Distractions, is already an incredibly niche advantage however, as - unless you're using a weapon roll with the minimum possible Range and firing from an entirely different area code - both of these guns already kill a player in a single headshot. Thus, its only use is breaking through thicker Overshields - an increasingly-uncommon situation with how many times Ward of Dawn and Bastion have gotten nerfed at this point, and how rare it is to see someone using another Overshield-giving source in PvP otherwise - or killing a Guardian in their Super, in which case... this perk is completely outclassed by Vorpal Weapon? Vorpal gives you a hideous +60% damage boost on Primaries and +20% to all others when attacking a Super-ing Guardian, which, while potentially lower than +1.00 to the gun's headshot multiplier, 1) should already be plenty enough damage to blow a Berserker or Dawnblade's head off, and 2), *doesn't require a headshot*, meaning you still have a chance to get the kill if you miss the head if you have the ammo and distance for a follow-up.
That last part is really Box Breathing's biggest problem, and also part of what holds it back in PvE; in exchange for having to not shoot for even longer than No Distractions, you not only get *one shot* with an admittedly good damage bonus, but it's all or nothing, because if you miss the head and hit the body, this perk does nothing. No, increased effective range is not comparable to a damage bonus. In any situation where you'd use this perk in PvE, it's completely outclassed by... literally anything. Dedicated single-target DPS? Add-clearing? Invader-killing? A flexible weapon that can do multiple of these things? Again, each weapon probably has ~2 damage perks per each of those categories that leave Box Breathing in the dust. Literally the only time I can think of that you'd seriously be trying to use Box Breathing in PvE is because... you're seriously committed to using the Komodo (which was recently unset), because I guess you really need a Solar LFR, but can't use Sleeper, still know better than to use Man O' War, and just don't have Corsair's Wrath, Briar's Contempt, or Cataclysmic.
So much of this could just be fixed, in my opinion, by changing the bonus from "+1.0 to headshot multiplier" to "+80-100% damage". No need to change anything else. The trait still wouldn't be great, but then at least, it'd be usable outside of... one and a half situations in one singular corner of the game.