http://wowwebstats.com/4j1spmy66miog?s=189155-221438&a=x7d94c8#abilities
DPS: 3923
DTPS: 4164
Kill time: 2:48
Gear: Full tanking gear with str or str/stam gems and a DMC:G (second trinket was Repelling Charge). Uncrittable (no defense buffs) and block capped (I let one unblocked through either through slow rotation or holy shield just getting knocked off.)
Disclaimer: Cheating with tricks of the trade, which is probably worth 100 dps. Used 50 str / 800 ac elixirs and 40 str food. Took DPS talents including the epic failure that is reckoning. One Avenging Wrath. I also won the crit RNG on ShoR with 35%, although HotR failed at 16%.
@OP:
First of all, did you have full raid buffs (including a Draenei in your group for the hit)? Missing any buffs is huge, and was assumed when I said you "should" do 7k+TPS on Patchwerk.
I also assumed that your raid would have comparable gear (as in, mostly 25man) so you'd have reasonably fast kill times. It was already mentioned that faster kill = increased uptime on AW / Heroism / trinket activations (if you're using one).
As for your WWS in particular: Your kill time was 3:38, 50 seconds longer than mine of 2:48. However, let's compare primary ability usage:
ShoR: You had 28 ShoRs, I had 26.
HotR: You had 28 HotRs, I had 25.
In an extra 50 seconds you should get ~8 more of each. It could be lag, or just not mashing the buttons as soon as they come off cooldown (assuming you're running 969), but I'm definitely getting more actions per minute than you are.
It also looks like you're weaving a non-glyphed AS into your rotation, which isn't generally a good idea, although you did get lucky and it crit 3 of 4 times.
Of course my damage per ability is much higher but that's because of the strength gems and DMC:G combined with the aforementioned tricks of the trade cheating and avenging wrath use. Strength >> BV for dps.
The main thing I'd work on is tightening your rotation up. In simple terms, and sacrificing a bit of time ( 8 seconds) to allow for Patchwerk to get to you and for your rotation to get going, we have:
For me:
2:40 worth of time to run a rotation, allowing for 160/6 = 26.7 ShoR and HotR casts. I had 26 ShoRs and 25 HotRs. A bit of time lost to lag / slow button mashing, but that's pretty much unavoidable.
For you:
In 3:30 you can use ShoR and HotR 35 times each in a "perfect" environment with no lag. If you go from your use of 28 of each to 35 of each, that's 25% more casts of your two primary threat abilities (and I assume, also all the other abilities in your rotation). That alone is enough to push you well over 7k.