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# 3.0.8 Hunter Math

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### #1 Relwin

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Posted 17 December 2008 - 07:09 PM

This is the thread for all relevant calculations, spreadsheets, and DPS models that pertain to hunters under the upcoming 3.0.8 patch. Focus on combat logging, accurate modeling and comparison, documentation/examples of scaling changes, and critiques of posts/data related to those. WWS or Stasis logs are highly encouraged and should be paired with analysis of the data you are presenting.

Posts that do not pertain to the aforementioned topics and are strictly whining will be removed and posters infracted. Constantly shit up the thread with anecdotes/bitching/new ability suggestions and you'll get some time off courtesy of yours truly.

### #2 Tolmandary

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Posted 03 January 2009 - 06:45 PM

<Disclaimer> These are very basic calculations below but I think they adequately show what I am trying to. <Disclaimer>

This discussion clearly also applies to hunters prior to patch 3.0.8, however following the changes, squeezing out more personal rather than pet DPS looks to become more important, especially for BM specced hunters. A secondary question I'd like to discuss, although have no calculations to hand to do this, is if the 0.87% extra critical strike chance from a +40 crit scope outweighs the damage benefit of a +15 damage scope when the extra proc rate of Go for the Throat is taken into account, instinctively I would suggest no but it needs calculations to prove it.

So which scope is actually better for us now, +40 critical strike rating or +15 raw damage? To simplify the calculations I have assumed every hunter has the talent Mortal Shots for +30% to critical strike damage, but have excluded the extra meta gem bonus of +3%. I have included detailed calculations for the first combination of a mean 1000 damage per shot with 25% critical strike chance to show where I have made these conclusions. Additional combinations of 1000 or 1200 mean damage with 25% or 35% critical strike chance have been included. I have also personally looked at many more combinations of mean damage and crit but because the conclusions remain the same I have omitted those from this discussion.

Basic stats and damage:
25% crit rate
Average 1000 damage per shot
Damage over 100 shots: (1000 x 100) + (1300 x 25) = 132500

+40 Crit Scope:
You need 45.91 rating for 1% critical strike chance, therefore this scope applies +0.87% chance.
Damage over 100 shots: (1000 x 100) + (1300 x 25.87) = 133632

+15 Damage Scope:
Damage over 100 shots: (1015 x 100) + (1319.5 x 25) = 134487.5

So in this first situation, using a +15 damage scope gives us on average an extra 855.5 damage over 100 shots compared to a +40 crit scope, not a huge difference but it's there. So what happens as mean damage and/or critical strike chance are increased?

1200 basic mean shot damage, 25% crit:
+40 crit scope: (1200 x 100) + (1560 x 25.87) = 160357
+15 damage: (1215 x 100) + (1579.5 x 25) = 160988
Averages an additional 631 damage for a +15 scope over 100 shots.

1000 basic mean shot damage, 35% crit:
+40 crit scope: (1000 x 100) + (1300 x 35.87) = 146631
+15 damage: (1015 x 100) + (1319.5 x 35) = 147683
Averages an additional 1052 damage for a +15 scope over 100 shots.

1200 basic mean shot damage, 35% crit:
+40 crit scope: (1200 x 100) + (1560 x 35.87) = 175957
+15 damage: (1215 x 100) + (1579.5 x 35) = 176783
Averages an additional 826 damage for a +15 scope over 100 shots.

Conclusion: Using a +15 damage scope should result in on average more personal DPS output than using a +40 crit scope. However even though these are very much simplified calculations, the general message seems to be that increasing your critical strike rate benefits the use of a +15 scope, while increasing your mean shot damage reduces the difference between the two scopes. Given many talents and glyphs boost the strike chance of specific shots and that most raiding hunters will have over 35% critical strike chance the benefits of a +15 scope become even more evident.

### #3 TrevvyTrev

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Posted 03 January 2009 - 08:52 PM

Conclusion: Using a +15 damage scope should result in on average more personal DPS output than using a +40 crit scope. However even though these are very much simplified calculations, the general message seems to be that increasing your critical strike rate benefits the use of a +15 scope, while increasing your mean shot damage reduces the difference between the two scopes. Given many talents and glyphs boost the strike chance of specific shots and that most raiding hunters will have over 35% critical strike chance the benefits of a +15 scope become even more evident.

Unless I'm mistaken, it had been established before that the +damage scopes only affected autoshots. Unless this has changed, the crit scope would favor all of the special shots that can crit -- arcane, aimed, explosive, chimera, steady -- and your calculations would have to account for the percentage of overall damage that those shots entail. In essence the comparison is (extra damage from crit scope to auto shots) + (extra damage from crit scope to specials) versus (extra damage from +damage scopes to auto shots).

### #4 Tolmandary

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Posted 04 January 2009 - 09:28 AM

I'll do some research and see if it does only affect autoshot. Of course you're right if it does then these calculations are meaningless.

### #5 ankah

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Posted 04 January 2009 - 04:28 PM

Doesn't the weapon speed, and the damage spread also affect the outcome? slower weapons with higher end damage will offer greater critical damage, no?

### #6 Tolmandary

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Posted 05 January 2009 - 07:48 AM

Doesn't the weapon speed, and the damage spread also affect the outcome? slower weapons with higher end damage will offer greater critical damage, no?

Because damage from 100 shots was looked at not over time speed wouldn't have an effect. Slower weapons will changed the damage from some shots but again because average shot damage was considered it shouldn't affect the outcome. What will though is if +15 scopes only affect Autoshots, which does seem likely...... poor old test dummies!

### #7 ankah

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Posted 05 January 2009 - 05:34 PM

Because damage from 100 shots was looked at not over time speed wouldn't have an effect. Slower weapons will changed the damage from some shots but again because average shot damage was considered it shouldn't affect the outcome. What will though is if +15 scopes only affect Autoshots, which does seem likely...... poor old test dummies!

That is true, but what I am saying is, by giving out just the mean, you do not take the weapon into consideration, no?

In other words, if you compare 2 weapons with the same dps, but different speeds, the higher end will shoot less, and there for, use the +15 less times, but crit higher. On the flip side, by adding the +crit, that same slower weapon will crit produce that higher crit just as often, but the difference will became greater, no? That is what I have always thought was the reason for us to use the crit scopes as oppose to flat damage increase. If you have a faster weapon the +15 will clearly bring more benefit, and a slower weapon will utilize the +crit more effective. By using just the mean numbers, based on a total number of shots, you just mesh all the weapons.

Also, doesn't instant spell (arcane, aimed, chimera, Es) receive greater benefit from being able to crit more often, than cast spells (auto, SS)?

### #8 Mineria

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Posted 10 January 2009 - 01:15 AM

The +40 Haste Rating Scope should be taken into consideration as well.
For some gear and talent choices/upgrades a haste scope will add a higher Damage per Second output then a critical or damage scope.
An example is if you are talented Survival and got around 450 Haste Rating as I am, a Haste Scope gives me more damage added then the other choices.
Later on with other gear upgrades the +40 Crit Scope adds more.

### #9 KraxisSingular

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Posted 10 January 2009 - 02:41 AM

Because damage from 100 shots was looked at not over time speed wouldn't have an effect. Slower weapons will changed the damage from some shots but again because average shot damage was considered it shouldn't affect the outcome. What will though is if +15 scopes only affect Autoshots, which does seem likely...... poor old test dummies!

It doesn't affect Shot+damage shots like Multi or Aimed? They are basically Autoshots with a flat damagebonus.

### #10 Burakan

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Posted 16 January 2009 - 05:08 PM

Umm . . . it's early so I may be out to lunch here, but aren't you calculating crit damage wrong.

Crit damage talented is 2.3 x Damage, not 1.3. Regular crit is double damage, plus 30% from talent.

ie. Hunter with Average shot of 1000, and 25% crit rate:

(75 X 1000) + (25 x 2300) = Total Damage over 100 Shots

### #11 Fierra

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Posted 16 January 2009 - 06:11 PM

Umm . . . it's early so I may be out to lunch here, but aren't you calculating crit damage wrong.

Crit damage talented is 2.3 x Damage, not 1.3. Regular crit is double damage, plus 30% from talent.

ie. Hunter with Average shot of 1000, and 25% crit rate:

(75 X 1000) + (25 x 2300) = Total Damage over 100 Shots

Easier to calculate a set 100-1000 shots at normal damage ( *1.0), and then add in how many of those were supposed to crit (*1.3). So, to break it down.

1000 shots = average 100 damage.

250 shots = number that crit, doing 230 damage total.

(1000*100)+(250*130) = average damage

Since you're adding them separately, it lets you add just the additional crit damage, and change the formula from crit rating to crit rating more easily; you only have to change the multipliers in the second half.

### #12 Tolmandary

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Posted 18 January 2009 - 09:25 AM

Exactly as Fierra said, both methods for displaying crit damage have the same effect, the one I used as explained by Fierra allows for easier adjustment of crit chance. However after extensive testing it a moot point for my initial theoretical argument given the damage scopes do only affect autoshot.

### #13 Mineria

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Posted 30 January 2009 - 09:41 AM

Since so many add points into Improved Stings.
I made some calculations over Improved Aspect of the Hawk vs Serpent Sting dps.
Note that the Serpent Sting result is taken directly from a wws.
In addition these calculations are purely over Auto Shots gained, hunters with lower Haste will gain more Steady Shots on top in the encounters duration.

Talent build used: Talent Calculator - World of Warcraft

Ranged attack speed = 2.19

Encounter duration = 3,38min = 218 seconds

Damage from Serpent Sting = 120% = 32.334 dmg
Damage gained from 2/3 Improved Serpent Sting = (32.334/120)*20 = 5389 dmg

Amount of Auto Shot's fired = 51 hits + 52 crits = 103 shots

Average Auto Shot damage = 1419 dmg
Max Auto Shot critical damage = 3859 shots

Just added if anyone is interested.
Amount of other shots:
Explosive Shot = 105/3 = 35 shots
Aimed Shot = 16 shots
Kill Shot = 3 shots
Complete Amount off Shots = 130+35+72+16+3 = 256 shots

Improved Aspect of the Hawk

32.79 haste rating gives 1% haste

Aspect of the Hawk is an Animal Aspect that increases the hunter's ranged attack power by a fixed amount.
With the talent Improved Aspect of the Hawk, the Aspect also gives their Auto Shots a chance to increase their attack speed.

The Aspect adds 3% pr. point, which then is 32.79*3 = 98.37 Haste Rating
Glyph of Improved Aspect of the Hawk adds 6% which adds 196.74 Haste Rating

3% 98.37 Haste Rating brings me down to a ranged attack speed of 2.14 seconds
6% 196.74 Haste Rating brings me down to a ranged attack speed of 2.08 seconds
12% 295.11 Haste Rating brings me down to a ranged attack speed of 2.03 seconds

Heroism
Increases melee, ranged, and spell casting speed by 30% (983.7 Haste Rating) for all party and raid members. Lasts 40 sec.

Rapid Fire
Increases melee and ranged speed by 40% (1311.6 Haste Rating). Lasts 20 sec.
So without Heroism ((218-40)/2.19) = ~81 Auto Shots
And with Heroism 20/1.74 = ~11 Auto Shots
And with Heroism + Rapid Fire 20/1.36 = ~14 Auto Shots

Auto Shot speed with 4/5 Imp. AotH = 2.03 seconds
Auto Shot speed with 4/5 Imp. AotH and Heroism = 1.64 seconds
Auto Shot speed with 4/5 Imp. AotH, RF and Heroism = 1.3 seconds

Amount of Auto Shots that trigger Imp. Aoth = (103-9)*0.1 = ~9 shots
Total duration with Imp. Aoth = 9*12 = 108 seconds, which means we got roughly 50% uptime.

So without Heroism ((108-20)/2.03) + ((108-20)/2.19) = ~83 Auto Shots
With Heroism (10/1.64) + (10/1.74) = ~11 Auto Shots
And with Heroism and RF (10/1.3) + (10/1.36) = ~15 Auto Shots
Which gives us a total of 109 Auto Shots, and 190-103 = 6 Auto Shots gained.

Calculating with 50% hits and 50% crits:

Average Auto Shot damage gained = (1419*3)*0.99 = ~4214 dmg
Max Auto Shot critical damage = (3859*3)*0.99 = ~11461 dmg

Total amount of damage gained from Auto Shots = 15675 dmg

Difference between 2/3 Improved Stings and 4/5 Improved Aspect of the Hawk = 15675 - 5389 = 10286 dmg

2/5 Improved Aspect of the Hawk + Glyph adds more damage compared to 2/3 Improved Stings

DPS increase from additional Serpent Sting damage = 5389/218 = ~24dps
Improved Stings DPS gain pr. point = 24/2 = 12dps

Patchwerk has 13mill HP
13mill/218 = ~59633 DTS
Which means he will die approximate 1/6 second faster with the added dps.

DPS increase from additional Auto Shots = 10286/218.15 = ~47 dps
Improved Aspect of the Hawk DPS gain pr. point = 47/4 = 11.75 dps

### #14 Corbetti

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Posted 30 January 2009 - 11:45 AM

Thanks for answering my question before I asked it. I have struggled with the logic of taking improved stings, given it is a 10%-per-point boost to a mere ~4% of total damage based on most WWS parses I've looked at.

One thing you didn't mention is that the more points in IAotH, the greater its uptime i.e. each point is actually marginally better than the last (assuming already beyond haste soft cap). In contrast, Imp. Stings is linear.

### #15 Selmarix

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Posted 30 January 2009 - 12:17 PM

Comparing 2 talent points + glyph to only 2 talent points is not really fair. The usual decision is between those two variants:
1 or 2 points in Hawk + glyph and 2 points in Imp. Stings
3 or 4 points in Hawk + glyph and no points in Imp. Stings

### #16 Mineria

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Posted 30 January 2009 - 12:55 PM

One thing you didn't mention is that the more points in IAotH, the greater its uptime i.e. each point is actually marginally better than the last (assuming already beyond haste soft cap). In contrast, Imp. Stings is linear.

The only thing adding up concerning uptime is the increased amount of Auto Shots added.
Which with 6 additional Auto Shots gained adds approximate 0.6% chance for an extra proc.

Comparing 2 talent points + glyph to only 2 talent points is not really fair.

Comparing 1 talent point + glyph to 1 talent point would have been more fair?
And currently that is the only Glyph adding more dps, that you can add as SV beside Steady Shot + Serpent Sting.

Please take note of dps increase pr. point in the conclusion:

```Improved Stings DPS gain pr. point = 24/2 = 12dps

Improved Aspect of the Hawk DPS gain pr. point = 47/4 = 11.75 dps```

Which pretty much shows that you gain more from going 1/5 IAotH+Glyph and x/3 Improved Stings.
The exception would be bosses that resist Sting's.

Another thing worth keeping in mind is that under movement heavy fights like: Grobulus and Heigan, Serpent Sting might bring more.
But not worth skipping a 1 point in IAotH + Glyph to take 1 point into IStings.

For a "by gear" hit capped hunter, it might be worth going over if 5/5IAotH + Glyph brings more then 2/5 IAotH + Glyph +3/3 IStings.

Another thing to consider.
Master Tactician and Expose Weakness both proc from Auto Shot hits and crits.
So more Auto Shots will have some minor effect on uptime.

### #17 Fierra

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Posted 30 January 2009 - 01:13 PM

Another thing to consider.
Master Tactician and Expose Weakness both proc from Auto Shot hits and crits.
So more Auto Shots will have some minor effect on uptime.

Not a bad point, but also keep in mind; virtually all SV hunters have enough crit to give EW a 100% uptime before any haste procs, with the crit bonuses to our main shot, ES. Master Tac also procs all the time as well. IAotH shouldn't really be a consideration for these talent's uptime.

### #18 Mineria

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Posted 30 January 2009 - 01:28 PM

Not a bad point, but also keep in mind; virtually all SV hunters have enough crit to give EW a 100% uptime before any haste procs, with the crit bonuses to our main shot, ES. Master Tac also procs all the time as well. IAotH shouldn't really be a consideration for these talent's uptime.

True, but it depends on gear to.

I still remember the chock I got, going level 80 and seeing for how much my crit rate dropped pr. level.

So hunters with low haste and crit rating should see a greater benefit from IAotH then hunters in level 200-2xx epics.

### #19 Fierra

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Posted 30 January 2009 - 01:32 PM

True, but it depends on gear to.

I still remember the chock I got, going level 80 and seeing for how much my crit rate dropped pr. level.

So hunters with low haste and crit rating should see a greater benefit from IAotH then hunters in level 200-2xx epics.

On the contrary, hunters with BETTER gear should see a greater benefit; they'll have more AP, and thus will see more high-powered Autoshots. Hunters with lower gear tend to rely a little more on specials, which haste has no effect on anyway (besides Steady), so I would think that haste would be an even lower priority.

### #20 Mineria

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Posted 30 January 2009 - 02:17 PM

On the contrary, hunters with BETTER gear should see a greater benefit; they'll have more AP, and thus will see more high-powered Autoshots. Hunters with lower gear tend to rely a little more on specials, which haste has no effect on anyway (besides Steady), so I would think that haste would be an even lower priority.

I was more thinking in the way of getting lower Steady Shot speeds to tighten up the time used between special shots on top.

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