Showing posts with label tier 8. Show all posts
Showing posts with label tier 8. Show all posts

Wednesday, June 3, 2009

Casting & Consequence with 4T8

I've been trading views with Xiera over at The Moonkin Repository lately over the value of the 4T8 set bonus in relationship to both cycles. The real concern is the 4T8 bonus's synergy with the precasting phase of the Lunar rotation and the Eclipse phase of the Solar rotation. As many of you know, Graylo recently posted on the DPS increase his model shows for 4T8 on both rotations. I think (or hope) that everyone agrees at this point that when the change goes live, 4T8 will be beneficial and deserves a place in any BiS list.

Today, I took a look at the semantics of using a 4T8 proc at the "wrong" time. My initial gut feeling was that it would be worthwhile to use a 4T8 proc under the effects of Solar Eclipse but would result in a decrease if used in a precasting phase of a Lunar rotation and caused the wrong Eclipse to proc. Let's start with the simpler case, the Solar Eclipse proc.

Solar Eclipse


Even though the Starfire from 4T8 is instant, it still evokes a GCD. Since Wrath has a cast time equal to the GCD, I am going to say that for all practical intents and purposes the 4Tb proc and Wrath have the same cast time. I am also assuming that the Idol of Steadfast Renewal is equipped.

Because we have 4T8, we naturally have 2T8 (durrrr statement, I know, but I forgot it in my initial calculations). We expect to see a 45% increase to damage for all Wrath cast under the effects of Eclipse. Since Wrath and the 4T8 proc have the same cast time, we need only show that the average Starfire is greater than or equal to the average Eclipsed Wrath. If that is true, then it would always be a benefit to consume the 4T8 proc during a Solar rotation. So here's a graph of damage calculations at varying levels of Spell Power from 2000 to 4000.
Google Chart
As we can see, the graph shows that Starfire gains an even bigger advantage over Wrath as we gain Spell Power. Thus, it is my recommendation to always use a 4T8 proc during a Solar Eclipse, regardless of time remaining.

Lunar Precasting Phase


In the precasting phase, we are casting Wrath. I will assume that the Idol of the Shooting Star is equipped. I will also be using a druid equipped in Graylo's choices for BiS as he calculated his BiS for a Lunar rotation as I did mine for a Solar rotation.

We only experience a problem when Starfire crits and procs a Solar Eclipse, changing our rotation from the desired Lunar Eclipse. I will be comparing the difference of a crit Starfire vs average Wrath to the DPS gain/loss of proccing the incorrect Eclipse.

Average Wrath: 4832.183
Average Crit Starfire: 12030.23
Damage During Lunar Eclipse phase: 75884.2460
Damage During Solar Eclipse phase: 75382.0508
4T8 Damage gain: 12030.23 - 4832.183 = 7198.047
Eclipse Damage gain: 75382.0508 - 75884.2460 = -502.1925
Net Damage gain through 4T8: 7198.047 + -502.1925 = 6695.8518

Surprisingly, I did not notice a very large difference between the Solar Eclipse with the wrong idol and the Lunar Eclipse with the correct idol. I was initially bothered by this until I recalled that all of this was in a perfect Spell Queuing environment and the value of the Solar Eclipse would decrease with every Wrath cast that did not queue properly. So theoretically, my advice as per the numbers is to use the 4T8 proc whenever you can.

TL:DR


The short version of my work here was that no matter when you receive a 4T8 proc, it is appears advantageous to use it.

I wanted to push these results out first because I have the suspicion that my next bit of work might take some time to complete. I want to look into the effects of the spell queuing system and adjust the worth of the Solar Eclipse based on both latency and player reaction time.

Please do not walk away from this post saying that you should always cast 4T8 whenever it procs. This is only true for a perfect environment with zero latency and a 0ms reaction time.

Monday, May 11, 2009

4 Piece Tier 8 Bonus

Debates are raging! Procs are being watched! Combat logs are being combed through! Cowpies are being hurled with precarious disregard! And all the while we're wondering what the final judgment will be.

Here's what we know: It's a 15% chance to proc a GCD Starfire every time that Insect Swarm ticks. There is no internal cooldown.

I will be using a slightly uber druid for stats because with 4T8, I'm assuming you've garnered some good gear. Therefore, my druid has 3k spell power, 45% crit, and 389 haste rating. As always, there is a TL:DR for those of you looking for the "express" ride.

Math Stuff


Chances to proc: Insect swarm ticks 7 times over 14 seconds. So I have
(0.15 * 7)/14 = .075 procs per second
Thats 4.5 procs per minute. To even out the numbers, I'm going to be looking at 120 seconds (two minutes) so that I would get 9 procs.

Nature's Grace Uptime: I will be using Starfire's NG uptime for this so
(1 - (1 - .45)^2) = 0.6975 uptime.
GCD:
GCD w/NG - 1.5 / ((1.2 * 1.05 * 1.03 * 1.03)(1 + (389 / 3297)) = 1.004
GCD w/o NG - 1.5 / ((1.05 * 1.03 * 1.03)(1 + (389 / 3297)) = 1.204
Average GCD - (1.004 * 0.6975) + (1.204 * (1 - 0.6975)) =1.065
Average Starfire Cast Time:
Starfire w/NG - 3.0 / ((1.2 * 1.05 * 1.03 * 1.03)(1 + (389 / 3297)) = 2.007
Starfire w/o NG - 3.0 / ((1.05 * 1.03 * 1.03)(1 + (389 / 3297)) = 2.409
Average Starfire Cast Time - (1.004 * 0.6975) + (1.204 * (1 - 0.6975)) =2.129
Average Starfire Damage (assuming SF idol and moonfire buff to crit):
Regular Starfire - ((1285 + (3000 * 1.2))(1.1 * 1.04 * 1.03) = 5756.09
Crit Starfire - ((1285 + (3000 * 1.2))(1.1 * 1.04 * 1.03)(2.09) = 12030.23
Average Damage - (5756.09 * (1 - 0.48)) + (12030.23 * 0.48) = 8767.68
I would get 9 instant Starfires @ an average GCD of 1.065 seconds for a total of 9.585 seconds of casting time. In this time I would normally do an average of 4.5 Starfires.
Net Damage of Instant Starfires - (9 * 8767.68) = 78909.12
Net Damage of Normal Cast Starfires - (4.5 * 8767.68) = 39454.56
Net Gain of Instant Procs - (78909.12 - 39454.56) = 39454.56
Net DPS gain of Instant Procs - (39454.56 / 120) = 328.78

TL:DR


My theoretical druid picked up 328.78 DPS through his 4T8 piece bonus assuming that the buff never overwrote itself and wasn't consumed by the casting bug. That, to me, is a significant increase in DPS and warrants the inclusion of the 4T8 bonus into the BiS gear.

A small note on all of this: The benefit of the proc decreases as Haste increases. Logically, this makes sense because there is less gain in casting time per proc as you cast faster. In Bloodlust and Heroism situations my druid is popping off Starfires at a rapid 1.434 seconds per cast. Here, the DPS boost of the proc is minimal. I speculate that Solar rotations will make heavier use of the 4T8 than Lunar rotations using high haste. For example, a druid with 700 haste will find himself gaining around a mere .9 seconds of cast time through the proc. My druid was gaining well over 1 second per proc.