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.
Basically it's either 1 or 4 stars depending on the weapon, and viable mainly against champions.
On a Heavy weapon (only Cataclysmic LFR) this perk is quite underrated. For boss damage you might do better with Focused Fury, but for champions it's easier and faster to proc (especially with damage over time effects like Le Monarque or Witherhoard paired with anti-champion Primary) while giving the same 20% damage buff. Additional inconvenience is that you can't refresh the duration while it's active, but for champion's it doesn't really matter.
On Special it would be good, but it requires you to use Heavy weapon somewhat often which makes it a lot worse for anything except champions and maybe boss damage, both of which you do rather occasionally on the weapons that can roll this perk (Deliverance FR, Forbearance GL and Lubrae's Ruin Glaive).
On Primary weapons just skip it and take OFA, Frenzy or sth like that instead.