Sorry this took so long. There was a lot of misinformation out there, so after [b]100+ hours[/b] of testing, animating, and editing, here you go <3 The video has all this info. If you prefer, you can just read through this. I do use Figures and Silhouettes in the video though :3 easier to look at. The figures come in at the 2 minute mark in the video.
Focused Fire increases damage by 33%, and decreases Rate of Fire by 33%, but only on High and Low Impact auto rifles. On Mid Impact Auto Rifles, the RoF nerf is [b]40%[/b] (from 600 RPM to 360). I've seen ppl claim the RPM is 400 or 300, but it's really 360.
This means a shot is fired at the start of every 5th Frame. This is where Destiny's Frame Rate comes in. There is no such thing as half a frame. Unless you're running a game with some ridiculously amazing FPS (120+), your Frame Rate is gonna create inconsistencies with RPM. The lower the frame rate, the more this is a factor. This does not mean only certain RPMs can exist in a game, but it does mean that RPMs divisible by 3 will have to most consistent Rates of Fire. This is most likely why Mid Impact ARs have a 40% Drop in RoF, cause a 33% drop would put it at 400 RPM.
(This next part is speculation, for there does not currently exist a 400 RPM weapon in Destiny, to my knowledge)
A 400 RPM would result in shots firing every 4th OR 5th frame. These things do exist in other shooters, but the margin of inconsistency is decreased with higher Frame Rates, allowing for these minor hiccups.
The numbers on AR's with & w/out Focused Fire below, as of March 2016.
Btw,[b] TTK = Time to Kill[/b]. Please, please, can we [u]stop calling The Taken King, TTK[/u].
Low Impact: 900 RPM - 16 Precision Damage / 13 Body
TTK:
[b]0.86 - 1.00[/b] (0.80 - 0.93 Against Low Armor)
Focused Fire: 600 RPM - 21/17 Damage
TTK:
[b]0.90 - 1.20[/b]
Shots to Kill:
13-16 (12-15 low armor)
10-13(FF)
High Impact: 450 RPM - 25/20 Damage
TTK:
[b]0.93 - 1.20[/b]
Focused Fire: 300 RPM - 33/27 Damage
TTK:
[b]1.20 - 1.40[/b] (1.00 - 1.40 Against Low Armor)
Shots to Kill:
8-10
7-8 (FF)(6 Precision low armor)
Mid Impact: 600 RPM - 20/16 Damage
TTK:
[b]0.90 - 1.20[/b]
Focused Fire: 360 RPM - 26/21 Damage
TTK:
[b]1.16 - [u]1.50[/u][/b]
Shots to Kill
10-13
8-10 (FF)
Low Impact:
Arminius-D [Gunsmith / Häkke]
Doctrine of Passing [Trials]
Doctrine of Passing (Adept) [Trials]
Medium Impact:
Red Spectre [Crucible Drop](The stat chart lies, does no more damage than these other weapons)
Paleocontact JPK-43 [Dead Orbit]
Haakon's Hatchet [Iron Banner]
Righteous VII [New Monarchy / Suros]
Zarinaea-D [Gunsmith / Häkke]
SUROS ARI-41 [Suros]
High Impact:
Anguish of Drystan [Raid / No Focused Fire]
Harrowed Anguish of Drystan [Raid / No Focused Fire]
An Answering Chord [Vanguard / Suros]
Questing Beast [Vanguard / Awful Range]
Does Not Bow [Shadow Thief Strike]
Antipodal Hindsight [Crucible Vendor]
The Dealbreaker [Crucible Vendor / Häkke]
SUROS ARI-45 [Gunsmith / Suros]
Focused Fire slows down your Time to Kill (which is bad), across all weapons. The advantages are more Aim Assist / Magazine Size (due to archetype, not perk), but decreased range (also due to archetype). Focused Fire is definitely not for High Level Players.
Mid Impact ARs are hurt the most. In my opinion, [b]Focused Fired Mid Impact ARs are the worst legendaries in the game[/b], on par with High Impact Hand Cannons (e.g. Timur's Lash).
Compared Stats: Mid Impact FF - Non-FF High Impact AR
Mid FF: 26/21 Damage High Base: 25/20 Damage
Both Kill with 8 Precision, 10 Body shots. But since the High Impact has a 450 RPM, and Mid has 360 w/FF... Terrible TTK and DPS for the FF Mid.
The Xerxes-C Machine Gun is a Green Quality weapon that can have Focused Fire. With Smart Drift Control AND Aggressive Ballistics, the damage is the same. This [u]could be a glitch[/u] or it could mean that weapons have a [b]damage cap[/b] when they aren't buffed (e.g. Weapons of Light / Final Round). You probably already know about the Xerxes, so I won't get into that. If not, it's in the video :D
TL;DR - Focused Fire is good for sustained fire and plays to the average player's style, but is detrimental to High Tier players that want pure TTK (Time to Kill). Mid Impact ARs have an extra 7% loss in Rate of Fire from Focused Fire, resulting in some of the worst possible DPS in Destiny.
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Good stuff. However, to gripe with your gripe at the end: TTK = The Taken King, ttk = time to kill.