The Iron Colonel

Warning: wild speculation ahead
My feelings on the best way to model that would be to use an alternating series that accomodates for the delay from previous shots. My gut reaction is that because you're using sine/cosine to model shot time (which is continuous) but are really more interested in discrete events (shots) you would use a series that is essentially a time function that accounts for the time delay on the nth shot - for this case it would be a relatively (note: heavily stressing relatively) easy task to determine shot delay. As alluded to before, at this point I can only speculate on possible methods to account for delay, since I haven't worked out the math yet. Hopefully you kind of see where I'm headed with this line of thinking, though.

Despite all the mathematical masturbation, I maintain that discrete simulation is just going to be better than a generalized model. Likewise, empirical evidence from gameplay will surpass simulation in accuracy. It's just the order of things, really. Nonetheless, it would be valuable to have a reasonable model of shot rotations that does not rely on time averaging (which, unfortunately, appears to be a nontrivial task).

As for iAotH, here are my feelings: if you want to use average time of non-proc streaks, you're using time averaging. The 10% proc rate is only a valid number for extremely large sample sizes. Given that, as I understand it, your goal is to eliminate time-averaged accounting for haste effect and replace it with a more accurate model (which I can only gather would have to be discrete), you're on the wrong foot here. I can only echo the thoughts of others: I dislike modeling iAotH as a time-averaged percent increase in haste, but I don't have an alternative model that doesn't rely on simulation. I think Glau more or less did the best work possible in terms of describing it generally - if you want more accuracy, you have to independently simulate it for yourself.

 

Cheeky

The idea I'm currently working on regarding IAotH would be to have the user specify 2 shot rotations. One with no Quick Shots and one with. We can then determine the uptime of Quick Shots (pretty simple function) and ratio the DPS between the 2 rotations by that value.

This wouldn't be exact, but it does cover the cases where you don't clip in non-Quick Shots, but do clip when you look at the current averages. BM Hunters could specify a every-other auto/special QS rotation, where MM could drop down to 1 special/auto for QS rotation.

It also has the benefit of seeing the exact effects of Rapid Fire, Beast Within, trinkets, and racials both in and out of QS. Just playing around with the rotations could let you know exactly when to pop what.

It wouldn't be too hard for me to add, but might be a large pain in the ass to configure 2 rotations. I could add in buttons to speed that up with some standard stuff like I have now.

I figure uptime is calculated no different than Frenzy or Expose Weakness would be, and we seem to have a pretty solid handle on those abilities.

Any thoughts?

Cheeky of Havoc

 

The Iron Colonel

I may be misunderstanding you, but I'm not sure I see the added value of this method. We already know (maybe not? My impression is that we've accepted converse probability as a method of determining uptime as a community at large) that the average up-time on iAotH is 1-0.15^floor(10/ attack speed under QS) so I'm not sure how the ratio of the dps between the two rotations would be any different. If you're modeling Quick Shots as % uptime * % haste to get the average haste and using that as a flat increase in dps (as a consequence of being a flat increase in haste) then the ratio of the two rotations is going to be just % uptime * % haste.

More clearly, let
A = rotation dps w/o QS
B = % uptime * % haste for QS = average haste benefit of QS
A*B = rotation dps w/ QS

(A*B)/(A)=B

Am I grossly misunderstanding what your intention is or is there some breakdown in communication? I'm not sure this would give us any more information than we have now - other than providing redundant sets of data for QS and non-QS rotations.

As for just providing the option for a second rotation while under haste, it might be nice to have something like a checklist of haste buffs - as BM I frequently have stacked haste, resulting in small attack speeds. Thus, having the ability to tune theoretical rotations under a variety of circumstances would be beneficial.

 

• Glaurong

How about, since quick shots is such a pain in the ass to model and variable haste effects screw us up they just change it.

Improved Aspects - While you have Aspect of the Hawk or Aspect of the Viper active your auto shots have a chance to trigger Focused Shots. While under the effect of Focused Shots your auto shots will do 3/6/9/12/15% more damage.

They could change Rapid Fire as well.

Rapid Fire - When Rapid Fire is active each of your shots has a chance to immediately trigger a second shot.

Adjust the %chance to trigger as needed.

 

Norwest

Right, but the average is 10, correct?

 

Cheeky

What you have is pretty much exactly what is done now. The only problem is you take a weapon with speed X, then figure that IAotH adjusts to Y over very long periods of time. And that's fine, as far as auto shot DPS goes.

But in reality you have either X or Z (X/1.15) all of the time, you never actually see Y in game. Tuning a rotation around Y is problematic because that is a timing pattern that doesn't exist.

Right now my spreadsheet says you'll do D DPS using a Steady + Special/Auto rotation, but it's not really true. For some bows the Quick Shot proc prevents you from actually maintaining anything more than auto/special. While it probably doesn't have a huge effect in the grand scheme, of things my entire methodology in the spreadsheet breaks down for very fast bows. It makes them look better than they already are. I'd like to explore some ideas on fixing that.

Cheeky of Havoc

 

The Iron Colonel

Ah now I understand. As far as the 'never attained speed' argument, I wholeheartedly agree. The problem with modeling iAotH as a time-averaged haste increase is that it isn't. You never see the speed you calculate as average because your data set is bimodal - either the speed is hasted or it isn't. Using the mean doesn't really reflect reality IF you have to alter the shot rotation (if you don't, then you could actually model iAotH as a flat haste increase and get away with it).

I'm starting to see your point about differentiating shot rotations based on haste. Let my reiterate what I understand your idea to be and see if I'm following you now: construct two rotations with and without haste and determine the dps of each. Determine the time under effect for iAotH as a percentage of time as a whole, then weight each of the rotations accordingly and add them together to get total dps. Is that close?

Assuming the last paragraph is true (or close to true) I'd like to propose a more general method (although strongly based on your last post - admittedly I misunderstood your idea originally and I want to acknowledge that this is strongly based on your post). My suggestion would be to allow a user to select gear/buffs that you have previously modeled to establish time under effect. For example, abacus of violent odds and iAotH; You can easily determine the average time under effect for either of these. What I would then suggest is determine the percentage of time, on average, that you would be under the effects of each permutation thereof - either iAotH, abacus, both, or none - and assign shot rotations to each permutation (and thus to each state of haste). Then weight each rotation based on percentage of time under effect. The sum of these weighted values might more accurately reflect the rotation mechanics while still maintaining their respective weights for up-time.

Thoughts?

 

Cheeky

That's exactly what I was going for. I probably could have been clearer in my earlier post.

This becomes an unbounded problem as more and more haste effects are possible. IAotH is something 95%+ of Hunters seem to have, so it makes sense to have special consideration for it. But you could have Abacus, Dragonspine, Kiss of the Spider, etc. that all come into play. And you could have them stack. I'm not sure I want to add the complexity of modeling them all as separate rotations. It doesn't scale well.

I provide for triggered effects right now from trinkets. The chance procs are a pain in the ass. And it seems like there is becoming more and more of them around. I've already decided it's probably worth it to handle IAotH. (I'm sure if that fucking Abacus ever drops for me I'll be in more of a hurry to include it too.) Could we generalize that at most 2 other "on chance" haste effects could come into play - based off of only trinkets exhibiting this property? If so I can include an additional sheet for those and crunch the permutations you discuss. I just want to make sure I don't work beyond the point of diminishing returns with this tool, there is a good chance I passed that line a while ago.

Cheeky of Havoc

 

The Iron Colonel

I certainly understand the problem of scaling the modelling problem. The only limitation I see is the limit of only two trinkets available during combat (lets pretend feign/switch doesn't exist, because then you're correct - the problem has no practical upper bound). Perhaps I was overly general in stating the requirement to calculate for all permutations of gear. Rather, calculating based on what gear the player has more or less dictates that there will only be at most 2 on chance haste effects possible (are there non-trinkets that effects ranged haste or proc from ranged attacks? I'm not sure they exist). I do realize that's a tremendous amount of work - I don't honestly expect you to implement that kind of over-arching calculation to the spreadsheet (although it sounds like accomodating iAotH is a feasible option). From a purely theoretical standpoint, however, weighting rotations for time is probably more accurate than modeling iAotH as a flat haste increase.

Thanks for indulging me in the conversation of that - I realize I occasionally get long-winded.

 

Cheeky

I put a version 13 up. This has a few asked-for items I've gotten pms for here and on other boards.
- SSC, Mag, Kazzak loot (leather & mail)
- new gems in 2.1
- specifying rank of KC now allowable, and mana use accounted for.

If none of those interest you there are very few item corrections to worry about.

Cheeky of Havoc

 

• Glaurong

All well and good for theorycraft but I'd venture that 99% of the time if you tried to drop into new rotations when quick shots came up, being in a variable place in another rotation, you will lose DPS overall.

Also people keep mentioning that you can be firing so fast that you have to stop steady, why? Suggesting you stop steady unless you are firing an auto shot every ~0.75 seconds is a drop in DPS.

If you find yourself in an extreme haste situation (firing shots faster than the global cool), most of the time it is best to drop into spamming your steady/auto macro with a reset of 2 and stopping to toss a special when you can/if you want to. You won't get a shot off in between every auto and you will delay some autos but your overall damage is much, much higher.

 

Nightarcher

I have a question regarding the differences between the 2 spreadsheets we have now. I've been using Lactoses table to get a ratio of which item is better upgrade and which gems to use. But if for example I would use Cheeky's spreadsheet the differences are quite big. For example:
Lactose's table for MM spec 1 AGI = 1.59 RAP while Cheeky's 1 AGI = 2.08 RAP (Personal hunter DPS). You can understand the difference is quite huge making the choice of gems for the gear different. Can anyone comment on this?

 

• Keltan

The latest version of Cheeky's spreadsheet attempts to model the new 2.10 Kill Command. Since Kill Command is fueled by crits, crit rating (and the crit part of agility) become massively more valuable in 2.10 if you plan on spamming Kill Command everytime it's up. Lactose's spreadsheet still uses current game mechanics, so it doesn't value crit nearly as much.

That's most likely where the majority of the difference is coming from.

For my gear and build pre-2.10, stat priority based off itemvalue cost was:
Hit Rating > Agility / AP > Crit Rating

Using Cheeky's spreadsheet with 2.10 Kill Command Mechanics, this has changed to:
Hit Rating / Crit Rating > Agility > AP

I'd predict this is where the major difference is coming from for you.

 

Nightarcher

No the figure I gave was about hunter's personal dps, I on purpose ignored the merged dps in order to see the difference between the 2 spreadsheets since Lactose's doesn't calculate pet damage.

 

Cheeky

If you are a Survival build the new Expose Weakness rates make Agility very, very valuable. It increases your chance to keep EW up, and increases the benefit from it.

Survival Hunters are pretty much going to be stacking Agility like hasn't been seen since 1.X again. The advantages to it just scale so well now. You reach a point where each point of Agility is effectively 1.15 * 1.25 * 1.04 = ~1.5 RAP effective on target.

I break down the differences between character sheet RAP, and the effective RAP on target. Are you seeing changes in the character RAP that are out of line? I won't discount the possiblity of bugs in the sheet, there have been a lot of changes, and not nearly enough time for me to test all talent combinations.

Cheeky of Havoc

 

Kolusius

Moved to Hunters/Haste thread.

 

Nightarcher

No I'm comparing pure pve MM builds. For Surv both show that +8 AGI > 16 AP for example. But for MM Lactose: 16 AP > 8 AGI but yours other way around. Thats what boggles me. The difference isn't minor.

What I'm using is comparing the dps change compared to no socket, 8 agi socket and 16 AP socket and see the ratio between the difference. While Lactose's table already have in installed (*hint* wish list ) And shows it I had to do it manually.

I actually just noticed you are using new Imp mark (440 rap) so I put it in Lactose table. I notices there is a huge difference about fighting 0 mitigation mobs (not using arcane for rotation) So I entered 32% mitigation for both tables:
Lactose: 1 agi = 1.66 RAP (Straight from table)

Using Cheeky's (Data for hunter only)
+1 AP = 0.183758864 dps
+1 AGI = 0.380008956 dps
AP to AGI ratio: 2.067976194

Merged with pet dps:

+1 AP = 0.205799736 dps
+1 AGI = 0.439491411 dps
AP to AGI ratio: 2.135529521

As you see HUGE difference.

Now here is something interesting. Removing all mitigation from all calculations (Make Cheeky spreadsheet remove Arcane shot from rotations, and do that same to Lactose by forcing rank 0 on the shot)

Lactose 1agi = 1.84 rap

Cheeky (hunter only) 1 agi = 2.068073999 rap
Cheeky (Merged with pet) 1 agi = 2.135723783 rap

This is more inline.

 

Dibbler

I have been having this exact discussion on the WoW boards and the specualtion is very confusing. I see it is just as confusing within these forums as those.

Nightarcher - I see the exact same results as do you from Lactose's spreadsheet, AP > Ag.

I am not gifted enough in the math department to argue the finer points but wanted to say a big THANKS to all that are attempting to.

 

Cheeky

It's interesting that you are trying to ratio the DPS gains of the 2 types of stats that way. I don't think I would have thought to do so quite like that.

Are you using the exact same numbers of the different shots in your rotations? Fundamentally the way we compute damage should be identical based on individual shots, RAP, crit%, talents, etc.

Did you factor in the +44 more RAP Master Marksman gives you on the new Hunter's Mark?

To be honest I haven't looked at Lactose's HICS in a while. Looking over it now, he and I use different assumptions in the frequency of shots. I don't think you'll have an easy time lining up much more than a Steady/Auto rotation between the two of them.

Looking at the way Lactose computes things he handles the combat results table better than I do. Mine allows for you to only crit what hits, instead of treating your crit% as absolute and misses coming from non-crit shots. If anything though, that should increase the value of Agility in his tables.

I also cannot find any place that Improved Aspect of the Hawk is covered in HICS. It shouldn't really make much of a difference in a steady/auto rotation since it's just a % increase if shots don't get clipped. Your ratios of Agility to RAP to DPS should remain fairly constant.

Ok, after punching my gear stats, talents, and weapon into Lactose's HICS & setting 0/5 IAotH in mine I get the following results:
HICS - 930.98 DPS, mine - 950.18 DPS - Pretty damn close. I'll investigate what average shot values are later.
HICS - 1 Agility = 2.01 RAP
Cheeky - 1 Agility = .44 DPS, 1 RAP = .24 DPS, 1Agility = 1.83 Agility

So there is a 10% difference in there. I'll try and delve into the guts of both spreadsheets and see where any discrepencies lie.

Cheeky of Havoc

 

Nightarcher

Can I see what data you used for your HICS to get 1 Agility = 2.01 RAP?

For example mine: (This is Self buffed data no raid buffs)

RAP 2770 (Include 440 rap from Mark)
19.34% crit
6,6% hit

Using Sunfury Bow (157-292dmg, 2.9 speed)

Focused Fire: (0-2) 2
Efficiency: (0-5) 5
Mortal Shots: (0-5) 5
Improved Arcane Shot: (0-5) 5
Barrage: (0-3) 3
Improved Barrage: (0-3) 3
Ranged Weapon Specialization: (0-5) 5
Master Marksman: (0-5) 5
Careful Aim: (0-3) 3
Combat Experience: (0-2) 2
Slaying vs Target: (0-3) 3

Quiver haste: 0.15

In terms of damage gained...
1 Agility = 1.45 Crit Rating
1 Agility = 1.664881656 RAP
1 Crit Rating = 1.14521204 RAP

Maybe we are using different bows?

 

◊ Lactose

Keep in mind some of my averages are messed up, and use 100% crit on some abilities for some weird reason, as well as ignore Focused Fire.
Other than that I can't think of anything right now that would result in the discrepancy.
Locally, I've made a number of changes though, so if there is an error on my part I might have fixed it ages ago :P

And yeah... my suggested rates of firing skills is completely messed up, don't look too much into that.

Look, Lactose, we'd rather you didn't eradicate the whole human race.
- Sam & Max

 

Cheeky

My numbers before included a screwup on the ammo DPS I put in for HICS.

Also, HICS does not factor in Focused Fire to damage totals, using the correct ammo and my gear HICS computes the average autoshot to 1099.61, mine 1121.92. Thats 102% plus some rounding errors. Steady Shot averages are HICS - 1144.97, mine - 1168.19.

The downside to my shot rotation mechanic is that it is finite. After 50 shots it ends the time computations. This is going to skew the DPS calculations a tad. For the example here of a auto/steady rotation the Shot Rotation grid computes a time of 60.24 seconds for 25 Autos, 25 steadys. With the damages computed above this is 950.42 DPS. Just calculating DPS based on a 2.43 second cycle forever yields 942.43 DPS. I figure 1% difference is enough of a sacrifice in accuracy to allow for complicated shot rotations.

HICS DPS is 921.88, which is pretty much exactly what you'd get in my sheet by disabling FF and factoring in the Shot Rotation rounding.

Ok, so we've established Lactose and I are using almost identical formulas for shot damage. Now lets look at how we handle additional stats.

HICS adds in an additional RAP * LR * CE * MM to the RAP value. He then modifies the crit percentage based on one more agility * LR * CE. HICS computes average autoshot to 1000.18, disabling FF mine is 1000.15. Steady is 1145.55 to 1145.52 to mine. Sicne my sheet derives everything from gearing I don't have anything special to handle an extra stat. It just uses the aggregate you provide through gear and hand adjustments.

Total DPS computed is +0.48 for HICS, +0.43 for mine. I believe this is due to rounding errors in my calculations. I tend to use floor functions for some things to match tooltip values. It might be worth seeing where I can remove them.

Doing the same things for +1 RAP is +0.24 HICS, +0.24 mine. Bingo there.

So you see a few rounding errors in my spreadsheet, which for very minor changes (like 1 Agility or 1 RAP) can be magnified based on how you use them (especially ratioing them against one another). I still feel my spreadsheet works well when comparing different gear/talent/shot rotation combinations. But it's not as exact as HICS on the very fine level.

Cheeky of Havoc