ToTS Haste Plateau-Esque: Dissecting Marksmanship

The following represents a continuation of my look into Haste Plateaus in Warlords of Draenor. Click here for the introduction.  None of this information is necessary to playing a hunter well, but if you're really into min-maxing your play, or you just happen to enjoy dissecting numbers, check it out.

In Search Of Haste Plateaus

My first task in looking at MM's potential for any Haste plateaus, was to look at some basic cast times of our cast shots, and just see where any interesting combinations occur.  The numbers/sums we're interested are those which can result in a whole number of seconds, which would mean no wasted time and no delay to our signature shot.  We'll start off by just looking at individual shots' cast times.  Note that the haste values here are your haste value after a buff, they are not assuming that you will add any on top of what's already there, except for the case of Rapid Fire and Ancient Hysteria.  Also: RF = Rapid Fire and AH = Ancient Hysteria/Time Warp/Bloodlust/Hero.

Steady Shot:
Base cast time:2 sec
1.5 sec cast time:33.3% haste
1 sec cast time: 9.9% haste + RF & AH
42.8% + RF
53.8% haste + AH
Aimed Shot:
Base cast time:2.5 sec
2 sec cast time:25% haste
1.5 sec cast time:19% haste + RF
28.2% haste + AH
1 sec cast time:37.3% haste + RF & AH
Base cast time:3 sec
2.5 sec cast time:20% haste
2 sec cast time:50% haste
15.4% haste + AH
7.1% haste + RF
1.5 sec cast time:53.8% haste + AH
42.9% haste + RF
9.9% haste + RF & AH
1 sec cast time: 64.8% haste + RF & AH

After looking at individual shots, I made up a little spreadsheet of shot combinations.  The results are as follows:

8 Second Combos
10.6%3 AiS, 2 SSAH12.5%2 AiS, 2 SSNone
11.6%5 AiSRF18.7%3 AiS, 1 SSNone
12.5%2 AiS, 2 SSnone25.0%5 SSNone
15.4%4 AiS, 2 SSAH25.0%4 AiSNone
18.7%3 AiS, 1 SSnone31.2%1 AiS, 4 SSNone
20.2%5 AiSAH37.5%2 AiS, 3 SSNone
20.2%7 AiSAH + RF43.8%3 AiS, 2 SSNone
25.0%5 SSnone10.6%3 AiS, 2 SSAH
25.0%4 AiSnone15.4%4 AiS, 2 SSAH
25.0%4 Ais, 2 SSRF20.2%5 AiSAH
29.4%5 AiS, 1 SSRF34.6%4 AiS, 2 SSAH
31.2%1 AiS, 4 SSnone39.4%5 AiS, 1 SSAH
33.9%6 AiSRF44.2%6 AiSAH
34.6%4 AiS, 2 SSAH20.2%7 AiSAH + RF
37.3%8 AiSAH + RF37.3%8 AiSAH + RF
37.5%2 AiS, 3 SSnone11.6%5 AiSRF
39.4%5 AiS, 1 SSAH25.0%4 Ais, 2 SSRF
43.8%3 AiS, 2 SSnone29.4%5 AiS, 1 SSRF
44.2%6 AiSAH33.9%6 AiSRF

And just for funsies, I put in some 7 second combos, which could, possibly, be useful if you want to fit in a Glaive Toss and its GCD. 

7 Second Combos
Haste ShotsBuffs
21.4%1 AiS, 3 SSNone
28.5%2 AiS, 2 SSNone
35.7%3 AiS, 1 SSNone
42.8%4 AiSNone
42.9%5 SSNone

So here, we have a good idea of how many shots we can fit into the space between Chimeara Shots, which just required a little basic arithmetic. Our next task, however, is a bit more complicated and will require us to spend a bit of time looking through logs.  

Below represents the values of my shots wearing all 630 gear (gear was scaled down, but that should be about what our dungeon gear looks like when we start WoD raiding) in a normal Highmaul run in beta, killing the Butcher (a Patchwerk style, totally single target, pretty much just stand there kind of fight).  The three Aimed Shots are a normal Aimed Shot, Aimed Shot with Careful Aim, and Aimed Shot with Careful Aim and TotH.

MM Hunter at Lvl 100, ilvl 630, w/ LW, TotH, Brg, Crows:

AbilityHitCritPer cast avg:Focus CostCast/GCDDPCTDPFDPCT/F
Chim Shot372608059659631.635160705.101734.431734.43
Kill Shot353007443048391.20148391.20n/an/a
Aimed Shot191585398029756.2502.2413284.02595.12265.68
Aimed Shot 191585398050649.4302.2422611.341688.31753.71
Aimed Shot 191585398050649.4102.2422611.345064.942261.13

Now that we know about how hard each of our abilities are hitting, we can go ahead and compare some different scenarios.  There are several different ways to compare the value of a particular ability.  When considering for the purpose of our rotation / priority system, I like to use Damage per Cast Time per Focus.  That's not of particular help here, because when we're talking about delaying a shot for a second or less, we're not really talking about missing out on the shot all together, just pushing it back.  

We could look, instead, at the total damage over a set period of time. Perhaps go as far as looking at an entire fight, call it 240 seconds, or 300 seconds, and work this out for each different fight, and depending on the group we have with us, which would seem more accurate, but we don't really know down to the second how long our fight will last, especially when we're progressing through a raid.  

So what I'll do instead, is just assign a fractional value to my signature shot, and call that the DPS loss from delaying it.  What I mean is, if I delay my Chim Shot 9 seconds, I have lost the entire damage from one Chim Shot.  If I delay it one second, we don't really know whether or not I've lost any damage, because we don't know on exactly which second the fight is going to end.  Since I have a 1 in 9 chance to not get to cast an additional Chim Shot, will just call that losing one ninth the value of Chim Shot, or 11.11%.  To further clarify, in case it's unclear, the reason I'm calculating the damage loss with an average like this is because we're not ever talking about just delaying Chim Shot once,  we're talking about doing it multiple times over the course of the fight.  So if x equals the amount of time I've delay Chim Shot, and Chim Shot is doing 60k damage (yes, I'm rounding 59,631.6 up to 60k, for brevity's sake), then "x*60,000/9" represents the damage loss.  

Why would we ever take a loss of damage?  Well we wouldn't, but we're not just losing total damage from Chim Shot, we're also gaining total damage from fitting in whatever ability is delaying Chim Shot.  For example, my Aimed Shot, under normal conditions (not with Careful Aim), averages around 30k damage (neat, I hadn't even noticed how close Aimed Shot was to exactly half of Chim Shot at this gear level), so as long as 30k*((2.24-x)/2.24) > (x/9)*60k, then we'll want to squeeze in that extra Aimed Shot (assuming we have enough focus for both shots, otherwise we'd have to add to "x" the time it takes cast enough Steady Shots to have enough focus to cast Chim Shot).  

At my haste level in 630 gear (only 11.6% buffed), that break point is a really high 1.496 seconds.  That is to say, I can delay my Chim Shot an entire 1.496 seconds to use an Aimed Shot and still come out ahead in total damage.  It's important to remember, however, that this is comparing the loss of Chim Shot damage, and doing nothing; what I mean is let's say we have one second left on the CD for Chim Shot, we can either A. do nothing until Chim Shot, or B. use an Aimed Shot, delaying Chim Shot by 1.24 seconds.  If these are our only two options, then, since 1.24 < 1.496, we'll be better off to go ahead and squeeze in that Aimed Shot, delaying Chim Shot (this is where the old adage "ABC: Always Be Casting" comes from). However, using Aimed Shot or doing nothing are not our only options!

We've also got this pesky Steady Shot.  Steady Shot, of course, does considerably less damage than AiS or Chim Shot, but it gives us more focus, allowing us to cast more Aimed Shots at a later time. This is where the algebra gets a bit more complicated than I want to describe here (not actually complicated like hard, just takes up a lot of room), because we're looking at combination of shots: x Steady Shots and y Aimed Shots.  What we need to do, is plug our Aimed Shot/Chim Shot Delay equation into my "shot combination at various haste levels" spreadsheet. The result looks a bit like this:

MM hunters haste plateaus in Warlords of Draenor

So there we go! Done!

Well, perhaps I can be a bit more elegant than that.  Let's revisit our chart from earlier.  It now looks like this:

CombosHaste Range +SS+AiS
2 AiS, 2 SS5% - 12.5%16.4%22.3%
3 AiS, 1 SS5% - 18.7%22.3%28.2%
5 SS5% - 25%25.0%34.2%
4 AiS5% - 25%28.2%34.2%
1 AiS, 4 SS10.5% - 31.2%34.2%40.2%
2 AiS, 3 SS16.4% - 37.5%40.2%46.2%
3 AiS, 2 SS22.3% - 43.8%46.2%n/a
4 AiS, 1 SS28.2% - 50%n/an/a
5 AiS34.2% - 56.2%n/an/a
What it's show, is first, obviously, the combination of shots.  The second column, "Haste Range", is the point where you have enough haste to where this combination is worthwhile (for example, with less than 16.4% haste, you shouldn't ever cast 2 Aimed Shots and 3 Steady Shots in between Chim Shots). The second number in this range is the point at which haste no longer benefits this combination of shots; you may still use that combination at a little bit higher Haste level, but you'll have some dead time.  The "+ SS" column represents the Haste point where adding in an additional Steady Shot becomes a DPS gain, and the "+ AiS" column represents the Haste point where adding in an additional Aimed Shot becomes a DPS gain.  And there we have it.  

It's becoming clear at this point, that I really need to stop saying "Haste Plateau", as it really doesn't describe, at all, what we're talking about here.  Before knowing these numbers, it's unclear how many might line up, and if there would be a clear-cut point where haste is really beneficial, and where it's much less beneficial, but at this point, we can go ahead and say no to plateaus.  

That doesn't mean this information isn't useful.  I'll at least continue to use that chart to sort of map out where my rotation will change through-out various haste levels.  I'm not going to post anymore spreadsheets, as this is already a bit to long, but for those curious how the numbers look during Careful Aim, the ranges are even more extreme for when it's best to delay Chim Shot.  That is to say, since the value of Aimed Shot goes up so much (averaging about 83% of Chim Shot's damage), having any down time will be a pretty big DPS loss.  So even if there's only a half second left before Chim Shot is off CD, you'll still be DPS ahead by casting an Aimed Shot.  

Over the next few days, I'll be looking at Survival and Beast Mastery rotations to see if there's any info there that'll help us.  Hopefully it'll be a bit simpler since there will only be one shot with a cast time.  

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