Why we use 969
Paladin tanking moves are all instant-cast, on the GCD, and have cooldowns. Most of our abilities are pure threat moves, Holy Shield is excellent mitigation, we want close to 100% uptime (it also provides decent threat). Judgement is one of our weaker threat moves, but also applies a variety of debuffs on the mob and also procs our tanking Libram (the BV one is the only tanking Libram at the moment).
We have more moves than we can actually use - under most boss-tanking circumstances, every single GCD will be used. The 969 rotation can be mathematically proven to be the best possible TPS rotation - Psiven has done this in his monumental TPS sticky. What follows is a very brief summary of his findings. Credit his, mistakes mine.
Although I talk about "best" and "worst" moves in this section, our worst move (HotR-single-target) still does 75% of the DPS/TPS of our best move (ShoR), so it isn't worth losing half a second to dead time to switch from worst move to best move. Given that a half-second delay in order to go from worst->best isn't viable, ANY tanking rotation with dead-time in it is automatically a non-optimal rotation.
Dead-time = mathematically non-optimal TPS rotation. Any suggestions of "I use a weird rotation and just take a 0.5 second break every so often" cannot be as much TPS as 969.
The GCD is 1.5 seconds, and is checked client side, so Internet lag/ping is a non-issue (within reason - past about 500ms everything goes to hell). Human reaction time doesn't change the results either.
We have two moves that are on 6 second CDs, which is 4 GCDs - HotR & ShoR. Both moves are very good - ShoR in particular is our best DPS move. HotR is weak single target, but amazing for 2+. So that's half our GCDs gone. So we have half our GCDs left.
We have three moves on 8-10 seconds CDs - roughly 6 GCDs: Consecrate, Judgment & Holy Shield. We want HS to have 100% uptime, but it has 10-sec duration and 8 sec CD, and 9 seconds = 6 GCDs, so we use HS every 6 GCDs.
So we're using some things every 4 GCDs and some every 6 GCDs. Which lines up in 12 GCDs - our rotation is 18 seconds long. Once we get HotR, ShoR & HS in, we end up with just enough GCDs left over to get Consecrate and judgement in every 6 GCDs as well.
The base CD of Judgement is 10 seconds - that's more than 6 GCDs - so we have to talent it to 9 seconds. But we've already shown that dead-time reduces our TPS under all circumstances, so there isn't any point dropping it to 8 seconds, because 8 isn't divisible by 1.5. We have a GCD at 7.5 seconds - but we can't judge then, too early. And we don't want dead-time, so we use something else and now we get to judge at 9 seconds. Thus: 1/2 Imp Judge.
Once Judge is in, we're down to one GCD free every 6 GCDs. We insert Consecrate, with 8 sec CD, and we get to 8/9 uptime - about 89%.
Psiven did a whole pile of analysis trying various different options using 8 second Judge/Consecrate, and there was no solution that provided higher DPS than judging/consecrate on 9 sec CD.
This has been confirmed (again) in compelling and accurate detail by Theck. Go read his sticky.
How to do 969
OK, so all our GCDs are full in theory, how do you actually execute 969?
Short Version: Watch this YouTube Vid:
YouTube - Protection Paladin TPS / DPS Tanking Rotation
Long version follows...
Well, we know our cycle is 18 seconds / 12 GCDs long, and that 4 GCD abilities use half and 6 GCD abilities use half. These abilities are referred to by the CD length - 6 seconds and 9 seconds.
We want no dead-time, and we know we're using every single GCD. So what order to use abilities?
If you work it out, you discover that the only way to avoid "GCD collision" (two abilities coming off CD at the same time) is to swap back and forth between the 6 sec and 9 sec abilities. If you start with 6699, you shortly hit a point where either two abilities com off CD at the same time or no abilities are available at all. It's the latter one that stuffs you - you just had a whole GCD of dead time.
So you have to go "969" (or 696). Short-Long-Short-Long. If you do that, you will always have an ability to use every GCD, and will be able to use each ability immediately it comes off GCD.
The exact order doesn't matter - you can tune it to suit your personal preferences or the boss/trash mechanics. Just make sure you start with short-long-short-long and after that you're locked into 969 - just hit each ability as it comes off CD.
You can macro it to two buttons if you want - you have a "short" button and a "long" button, and your tanking rotation becomes 12121212. There are pros and cons - I don't do it, I prefer flexibility of order, and the ability to totally control when I use Consecrate.
Should you weave long CD moves into 969?
Need to find all the references? They're here in the MATLAB thread.
Maintankadin • View topic - Theck's MATLAB TPS analysis (A Jonesy derivative work)