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.
Like Spike Grenades, Liquid Coils and Impact Casing, this perk shouldn't exist in its current state. Any weapon with a barrel, magazine, etc. that's automatically better than all the others is bad game design. Like how those two magazines' damage bonuses should be applied to all Grenade Launchers, Fusion Rifles and Rocket Launchers (and then made to do something else other than increase damage/charge time), Elastic String's charge speed should be factored in to the base stats for all Bows, and it should be made to do something else in return (as should all bowstrings that modify charge time). But for now, this is our lot, and like the other three "always-better magazine" examples, we just have to work with it.
Elastic String lets you use any Masterwork whilst still hitting the draw time floor.
Polymer String with a Draw Time Masterwork gives you +15 Accuracy over Elastic String, making Elastic + Accuracy Masterwork an almost always bad choice, though the +5 Handling of Elastic String is technically a positive of that combo.
Flexible String is essentially a less extreme Elastic string with higher Handling - with a Draw Time Masterwork, Flexible String gives the lowest maximum Accuracy of the three, but still has +5 over Elastic String with a non-Accuracy Masterwork. It also has +5 Handling over Elastic String with a non-Handling Masterwork, and +10 Handling over Polymer String. I would say this is, by a significant margin, the weakest of the three, but it is still a viable choice (less so after the recent update 7.3.5 - arrows are a lot harder to land at low Accuracy now)
My personal preferred roll on Lightweights is: Polymer String / Compact Arrow Shaft / Unique Perk 1 / Unique Perk 2 / Draw Time Masterwork. I find this to be just as, if not more, viable - compared to Elastic String with any combination of other perks.