Advanced Training 101: 969 and FCFS Theorycraft

[jere]

Those are based on the boss's actual swing timer, so they would be post-JotJ/parry haste/whatever else affects his swing timer. Also edited the previous post to correct "The boss attacks that many times per second or more" to "The boss's swing timer is that much or less"

so that would bring the values to:

1.050
0.525
1.067

swing speeds before you take JotJ into account, respectively

[Jerey-Darkspear]

Bit late on this. Nice write-up, but towards the end, when you split it into two rotations with Queue1 and Queue2, there was a substitution you didn't account for that will yield 100% HS uptime, approximately the same JotJ uptime, and slightly higher threat (or greatly higher if glyphed) than the standard 969 rotation.

Queue2

Cons > HS > AS > JoV

It's probably only a 25 TPS increase (unglyphed for either J or AS), 6 TPS increase (glyphed J but unglyphed AS), or 222 TPS increase (glyphed AS but unglyphed J); however, it does meet the other requirements of 100% HS and JotJ. I don't have Matlab to confirm this, but I don't see why it wouldn't be the case.

[Kriskringle]

it does meet the other requirements of 100% HS and JotJ

We must keep 100% Holy Shield uptime
We want to cast Judgement as often as possible to minimize the chance that JotJ will expire

The difference between the requirements you're considering and the requirements listed by theckhd boils down to the assumption that we won't miss a judgement. Your rotation will allow for 20 second intervals with only one chance for JotJ to refresh, which doesn't "minimize the chance that JotJ will expire" if that judgement can miss. Theck mentions this when he sets up the "Building the Queue" section:

Let's try and craft our FCFS using the same rules as 969: We want 100% Holy Shield uptime, and we want to cast Judgement as often as we can to minimize JotJ drop-off. Thus we'll start our priority queue with:
#1: HS > JoV

Any "acceptable" FCFS under theck's requirements/assumptions has to start this way, then evolve without reducing the amount of Judgement casts we can make. There's been some discussion about the validity of those requirements, and the majority of folks (at least the ones who post about it here) tend to support them.

[Jerey-Darkspear]

it does meet the other requirements of 100% HS and JotJ

We must keep 100% Holy Shield uptime
We want to cast Judgement as often as possible to minimize the chance that JotJ will expire

The difference between the requirements you're considering and the requirements listed by theckhd boils down to the assumption that we won't miss a judgement. Your rotation will allow for 20 second intervals with only one chance for JotJ to refresh, which doesn't "minimize the chance that JotJ will expire" if that judgement can miss. Theck mentions this when he sets up the "Building the Queue" section:

Let's try and craft our FCFS using the same rules as 969: We want 100% Holy Shield uptime, and we want to cast Judgement as often as we can to minimize JotJ drop-off. Thus we'll start our priority queue with:
#1: HS > JoV

Any "acceptable" FCFS under theck's requirements/assumptions has to start this way, then evolve without reducing the amount of Judgement casts we can make. There's been some discussion about the validity of those requirements, and the majority of folks (at least the ones who post about it here) tend to support them.

Not every other. Every fourth. Miss chance of it being gone for 7 seconds; miss chance squared of it being gone for 16 seconds; miss chance cubed of it being gone for 25 seconds or permanently.

[Kriskringle]

I never used the phrase "every other", but you're right about the dropoff chance. That's why your suggested queue doesn't fit with that section of work in the OP - the initial dropoff chance must always be miss chance squared for a queue to fulfill the listed requirements.

[kysu]

The math he does is what I do every pull, I shall never be a threat cap.

[Weimdog]

Hey all, my first post. I'm not a pally tank, I've never even played a pally.
So now that I've qualified myself to question the OP.....

It's clear from the first plot that ShoR, Consecration, and HotR are our highest-damage abilities. However, since HotR is on a 6-second cooldown (as opposed to Consecration's effective cooldown of 9 seconds), it's higher DPS than Consecration

Am I the only one who has a problem with this math/logic? If an ability has a shorter cooldown, but and does a TINY bit less damage than our 9-second cooldown friend, "whatever of the righteous justice" (how the hell pallies remember all these names is beyond me), it seems to me that putting the 9 second ability on CD first will be more beneficial, as it will be available 1 GCD sooner. In my eyes, its not the ability CD's determining DPS, its whatever damage you can get out of the GCD.

Now maybe you need to use the 6-second CD ability because 9 seconds (or whatever it is) later you need to use a mitigation ability "vengeful shield of holy righteousness" or whichever you need. IF that's the case, my argument is bunk, but the quoted logic is still false.
Also if using consecration on CD clips the damage ticks then that's a separate issue.

I'm looking forward to seeing my cooldowns differently

Weimdog

[Zobel]

You're a confused necroposter. All he was saying is that in isolation, the ability that does the same damage but on a shorter cooldown provides higher dps than the ability that does the same damage but on a higher cooldown. That's basic arithmetic, and it is as true today as it was a year and a half ago when he said it.

[theckhd]

Am I the only one who has a problem with this math/logic? If an ability has a shorter cooldown, but and does a TINY bit less damage than our 9-second cooldown friend, "whatever of the righteous justice" (how the hell pallies remember all these names is beyond me), it seems to me that putting the 9 second ability on CD first will be more beneficial, as it will be available 1 GCD sooner. In my eyes, its not the ability CD's determining DPS, its whatever damage you can get out of the GCD.

It would seem that way, but it turns out not to be right. There are some caveats involved in that though.

First of all, some clarifications:

1. you can't cast Consecration at 8 second intervals if you're casting something every GCD. Your next available cast window is always at 9 seconds. The only way to cast it every 8 seconds is to "skip" your 7.5s GCD and wait for Cons to come off of cooldown, but that will always end up being a DPS loss. So Consecration is without question a 9-second cooldown ability.
2. The passage you quoted was only describing the DPS of each ability, it didn't say anything about how to use that to build the queue. So there's nothing "wrong" with the math, unless you're suggesting I don't know how to divide by 9.

But of course, later on in the article I do build the queue based on DPS, so the question you asked is worth spending some time on - Why did I build the queue based on highest-DPS?. Note that a lot of this is covered in the "Building the Queue" section of the article if you give it a thorough read-through.


Let's look at basic FCFS mechanics. You traditionally build an FCFS based on DPS rather than DPCT (damage per cast time, aka damage per execute time). This is consistent with the way Retribution FCFS was first modeled, though it's no longer a "strict" DPS-based queue anymore (we'll see why shortly).

The reasoning for this comes down to cooldown clashes. If you have two spells that do identical damage, but one has a shorter cooldown than the other, you get more total damage output by giving priority to the short-cooldown one and fitting the long-cooldown one within the gaps. If you don't, you usually end up with lower overall damage because you tend to run into more clashes, which means you're "pushing back" more of your spells.

Protection is a bit special thanks to the "orthogonal" nature of our rotation. Our skills can't clash once you've chosen the cast order - you'll never hit a GCD where you get to choose which one to cast, as long as you're casting each as soon as they're available and limiting yourself to the five basic abilities.

However, for a simple example let's consider two abilities A and B. We assume they do the same amount of damage, but the cooldowns are different (one's a 6 second and one is a 7.5 second, or 4 and 5 GCDs respectively).

Everything starts off available, so you'd get the following possible queues:
AB--A-B-A--BA---X
BA---X

X is where we hit our first clash. You see that with the "higher DPS" queue, you go longer until you hit a clash, whereas the "longer cooldown" queue hits it earlier. Let's see where these queues lead if we keep going (bold indicates a clash):

AB--A-B-A--BA---AB--A-B-A--BA---AB--A-B-A--BA---AB
BA---BA---BA----BA---BA---BA---BA---BA

So we can see immediately here what's happening - in the second priority system, we're constantly pushing A back a GCD, which means we've effectively increased it to a 5-GCD cooldown.

Since the pattern is pretty clear, we can also calculate DPS for each of these queues. In the first, we get 4 A's and 3 B's every 16 GCDs, for a DPS of (expressed per GCD rather than per second):

(4A+3B)/16 = A/4 + 3*B/16 = 0.25*A + 0.1875*B.

In the second, we get one A and one B every 5 GCDs, for a DPS of:

(A+B)/5 = 0.2*A + 0.2*B.

Again, we said that A and B do identical damage, so the first queue does 0.4375*A while the second does only 0.4*A, or about 9% less total DPS. For the second sequence to out-dps the first, we'd need B to out-damage A by:

0.2*A + 0.2*B > 0.25*A + 0.1875*B
0.0125*B > 0.05*A
B > 4*A

In other words, B would have to do 4x the damage of A for that rotation to win out, and since the cooldown is only 20% longer, this would by far make it the higher-DPS option. This statement also gives us a clue as to why the Retribution queue isn't strictly built on DPS - even if B is slightly higher-DPS than A, prioritizing it can end up being lower total DPS because of all the clashes with A.

So what really matters is the cooldown. By prioritizing the shorter-cooldown abilities you usually prevent the most clashes, thus pushing back the fewest of your spells and packing the most damage into your sequence.

Now of course, once you add more spells into the mix this gets very complicated. Every spell does a different amount of damage, can have a different cooldown, and may have other non-damage effects to consider (keeping up a % damage buff like Glyph of Life Tap or returning mana via JotW being prime examples). That's why we usually turn to simulations like the one I wrote to try out all sorts of different queues to figure out what gives us the highest damage output.