Theorycrafting the SV Glyphs

So today I thought it might be interesting to actually post about the entire theorycrafting process. Sort of a peek behind the curtain of my theorycrafting process with my current theorycrafting project: the survival glyphs.

Beware that this will be a wall of text. Seriouly, it’s gonna be massive. If all you’re interested in is the results, you can skip this entire post, which is about the process. And while interesting, it’s not terribly entertaining. Warning done.

Theorycrafting

Theorycrafting is basically just doing math. It involves testing to get actual in-game numbers, and then using our knowledge of the game to calculate the theoretical result of various in-game abilities. The goal of theorycrafting is to choose the best of several options: it is qualitative in nature.

There are a lot of different ways to theorycraft, from very broad vague guesses, to painstakingly precise spreadsheets. Here at the WHU we use something in the middle. We do the basic calculations to get a pretty good feel for where each ability takes us, and if something is clearly better, we probably don’t need to go a whole lot deeper.

Also, theorycrafting is hard.

The math usually isn’t hard, but establishing the equations can be. It’s very easy to forget things. For example: Lock & Load gives you two free explosive shots. Some people when theorycrafting would assume that it then increases your damage two explosive shots worth every time it procs. But that’s not true — because those explosive shots are taking the place of the steady shots you would otherwise be using (it’s not like you would have just sat there). So the actual increase in damage from the lock & load is the difference between the average explosive damage and the average steady damage. And then to get the average damage of each, you need to factor in the crit chance to get a true average.

So we try our best to take everything important into account. Normally after I theorycraft something significant, I run all of my numbers by someone else. I’m not so much worried about math errors, but about leaving out some important factor. For the sake of this post, you’re getting the raw, uncensored results. Let’s see if you can find any mistakes that I missed!

Our Assumptions

For theorycrafting purposes, we have to start with some basic assumptions. Now, we don’t optimize for trash — if you’re having problems killing most trash you got a lot more than optimization going wrong. We optimize for bosses.

Since Ulduar is now out, and the boss fights are longer than the brief Naxx boss fights, we’re going to go ahead and assume an average of a 5 minute boss fight (300 seconds). We’ll also assume that the boss will be below 20% health for 1 minute of the fight (for purposes of working with Kill Shot).

Finally, we aren’t going to worry about mana regen, since we find ourselves usually at full mana for any boss fight in 25-mans, and just fine for 10-mans. We’ll also assume that we can more or less optimize our shot cycle for the fight.

Note that these results will only apply to SV hunters. Different specs get different value out of the same glyphs.

Our Data

I went to the heroic lvl 83 target dummy in Ironforge (greatest city in Azeroth) and did a bunch of tests at my optimal shot cycle, and got the average results. Note that I had no glyphs at all when I did these tests, so we can get a truer measure of the benefit of the glyphs we’re looking at. I used the WHU recommended SV Talent Build.

Here is the data we’ll use in our theorycrafting:

Overall DPS: 2953
Explosive Shot: 40.7%
Auto Shot: 24.1%
Steady Shot: 14.9%
Black Arrow: 7.8%
Multi-Shot: 7.5%
Serpent Sting: 5.1%

Explosive Shot Average Hit: 1,383 (60.6%)
Explosvie Shot Average Crit: 3,435 (39.4%)
Net Explosive Average Damage: 2,191

Steady Shot Average Hit: 1,007 (66.7%)
Steady Shot Average Crit: 2,412 (33.3%)
Net Steady Average Damage: 1,475

Multi-Shot Average Hit: 1,498 (66.7%)
Multi-Shot Average Crit: 3,34 (33.3%)
Net Multi-Shot Average Damage: 2,142

Kill Shot (separate test) Average Hit: 3,929 (42.7%)
Kill Shot Average Crit: 9,094 (57.3%)

The Glyphs

Now, the very first thing we do is the sniff test. We can usually tell at a glance if a glyph is going to increase our dps or not. For example, Glyph of the Viper increases our mana regen when in Aspect of the Viper. Well, we find in raids that we’re usually at full mana because of the awesome mana returns available to raids. Thus this is going to be a useless glyph. For a MM hunter who actually runs out of mana in boss fights, we might take a closer look at this.

Also, minor glyphs generally do not help out dps in any way. So looking through all the major glyphs, the ones that we want to actually theorycraft out are: Hunter’s Mark, Explosive Shot, Multi-Shot, Hawk, Steady Shot, Serpent Sting, and Kill Shot. Now let’s do some theorycrafting!

Explosive Shot
This one is pretty simple. The glyph gives us a 4% increased crit chance. We know that a crit does 250% damage, and we know that Explosive Shot is about 40.7% of our overall dps. So let’s multiply our overall damage by 40.7% to see that on average explosive shot is contributing 1,201 dps.

Now, since increasing our crit chance will only be increasing the damage of the shots that aren’t already crits, which we know is about 60.6% of them, we see that we’re looking at 727dps that we’re affecting. A crit does 250% damage, which is an increase of 150%. Thus we take our 727dps * 4% (the crit increase) * 150% = 44 dps.

Note that the lower your crit chance is, the higher the percentage benefit of this glyph will be.

Glyph of Explosive Shot
44 dps
1.5% increase in dps

Kill Shot
Here we’re decreasing the cooldown of Kill Shot from 15 seconds to 9 seconds. Since our assumption is that we’ll have 1 minute of the boss under 20%, that means we’d normally get off 4 kill shots. With the glyph we’d get off 7, or 3 extra kill shots.

Now normally we’d still be shooting when we aren’t using Kill Shot, and optimally the Kill Shot would be replacing a Steady Shot. So first we need to know what our average Steady Shot damage is. We need the median damage from our crits and hits. Thus we use: average hit * hit chance + ave. crit * crit chance. So we see that 1,475 is our net average Steady Shot damage. Do the same with Kill Shot and we see that we are getting 6,888 damage from our average kill shot.

Now we know that those 3 extra kill shots will be replacing 3 steady shots (ideally). Thus we take the difference between the average kill shot damage and the average steady shot damage — 5,413, and multiply it by the 3 extra shots we get = 16,239. Divide that by the 300 seconds in our assumed boss fight to get a dps increase of 54.13 dps in an ideal situation.

Glyph of Kill Shot
54.13 dps increase
1.83% dps increase

Multi-Shot
I put this in here not to actually theorycraft it, but rather to point out why it’s not worth taking. This glyph reduces the cooldown of multi-shot from 10 seconds to 9 seconds. However, in the real world, you will get almost no benefit from this.

If we assume we’re near haste-capped, and we give multi-shot our absolute priority, we don’t actually gain an extra shot with a reduction of only 1 second in multi-shot.

But more importantly, multi-shot is the second lowest shot on our priority list (ahead of Steady Shot). In general we want to cast Black Arrow the second it’s available, then cast Kill Shot if we can, then cast Explosive Shot if we can, then refresh Serpent Sting if we need to. In the example above, even though multi-shot is free after 6 seconds, you’d be a fool to use it over Explosive Shot, which also just became available.

Thus a 1 second reduction in cooldown is doing nothing at all for us. Depending on your haste and latency there is certainly a window in which you can fire multi-shot earlier from the glyph, but multi-shot is so little of our overall dps (7.5%) and so often even if we can fire it sooner, there’s another shot we’d rather fire.

Glyph of Multi-Shot
NA
NA

Steady Shot
The easist one to theorycraft. 10% bonus to Steady Shot damage when Serpent Sting is up. Because we are conscientious hunter, we can assume Serpent Sting is always up. We know that Steady Shot makes up just 14.9% of our dps after patch 3.1, thus it contributing 440 dps. 10% of that is a 44 dps increase. (Steady Shot was a larger percentage of dps before Black Arrow).

Glyph of Steady Shot
44 dps increase
1.5% dps increase

Serpent Sting
This glyph increases the duration of Serpent Sting from 15 seconds to 21 seconds. This is nice because we always want this DoT up, and every time we have to push our Serpent Sting button we’re losing, at best, a Steady Shot.

Over our 5 min boss fight we’d normally have to apply Serpent Sting 20 times. With a 21 second duration we only have to apply it 15 times. That means we can get off another 5 Steady Shots. We’ve established that our net average Steady Shot damage is 1,475, so multiply by five for an extra 7,375 damage. Divide by our 300 seconds to get a 24.58 dps increase.

Glyph of Serpent Sting
24.58 dps
0.83% dps increase

Hunter’s Mark
Increases the ap bonus of Hunter’s Mark by 20%. For SV, this means a 60 attack power increase. This one is a little bit tricksy, because your attack power factors differently into all sorts of shots. Let’s try to go down them one by one and see what we get.

• Auto Shot is the easy one, since we know that every 14 ap is 1 dps. Thus 60 ap gives us 4.25 dps to our auto shot.
• Steady Shot uses this formula: weapon damage + ammo + RAP * 0.1 +252. We’ll ignore armor reductions for now to make life easy and assume that we’re getting the full benefit of the 60ap. The only thing that changes is the ap, which we see is multiplied by 10%, giving us a 6 damage increase to the shot. Since we know the Steady Shot average shot is 1,475, adding 6 damage is a 0.4% increase. Steady contributes 14.9% of our dps, or 440 dps. Multipy by 0.4% and we get a new dps increase of 1.76 dps.
• Explosive Shot (average) uses this formula: RAP *0.14 +425. Again, all that changes is the 60 RAP, so we multiply that by the 14% to get an 8.4 damage increase per shot. Exlosive average damage is 2,191, so our 8.4 extra damage is a 0.38% increase. Explosive is 40.7% of our dps, or 1,202 dps, thus our 0.38% increase is an extra 8.3 dps.
• Multi-Shot should get the standard AP/14 = 1dps boost from RAP. So 60 AP will yield 4.2 dps. I believe multi-shot speed is normalized to 2.8, thus giving us 11.76 damage boost to multi-shot. Multi-Shot average damage is 2,142, so 11.76 is a 0.54% boost. Multi-shot is 221 of our overall dps, so a 0.54% increase is 1.19 dps increase.
• Serpent Sting uses this formula: RAP *.2 + 1210. I have 4,600 RAP, so this would normally be 2,130 damage. The extra 60 ap makes it 2142 damage, or a 0.56% increase. Serpent Sting is 5.1% of our dps, or 150.6 dps. The 0.56% increase make the glyph a .84 dps increase.
• Finally Black Arrow uses this formula: RAP *0.1 + 2765. Normally this would be 3,225, but we know Trap Mastery increases that by 30% to 4,192 damage. Adding the 60 extra ap gets us 4,200 damage, or a 0.19% increase. Black Arrow is 7.8% of our dps, or 230.3 dps. The 0.19% increase is a whopping 0.43 dps increase.

Okay, now we just tally up the increases: a total of 16.77 dps increase. Note that not only is this low, but if you have a MM hunter with Imp Hunter’s Mark, they’ll be overwriting your Hunter’s Mark anyway.

Glyph of Hunter’s Mark
16.77 dps
0.56% increase

Hawk
This increases the haste bonus of Improved Aspect of the Hawk an additional 6%. Now, the delicate part of this is that in addition to speeding up our auto shot, this also reduces the cast time of our Steady Shot, but only if we aren’t already at the soft haste cap. So part of the dps increase is going to vary widely based on our haste. Fortunately the haste benefit to our steady shot is a very, very minor increase to our dps. First let’s take a look at IAotH for a moment:

Each shot has a 10% chance to proc the effect, which lasts 12 seconds. Now, on average we have about 2 shots landing every 1.5 seconds (specials are 1.5 sec apart, auto is just over 2 sec, but then our Exlosives tick twice more after they land, which can trigger the proc). Thus we have 10 shots in about 7.5 seconds, so on average IAotH should generally always be up once it procs the first time. Sure, occasionally there’ll be some little down gaps, but it’s mostly always up, so we can count the haste bonus always.

The easiest way to look at this is from the auto shot persepective. We know that this glyph will give us 6% haste to auto shot, which will increase our auto shot dps by 6%. Since suto shot is 24.1% of our dps, we know that’s 712 dps. Increasing it by 6% increases our dps by 42.72.

Since our benefit to steady shot from the haste is going to vary wildly based on our haste rating. In general if you’re haste capped or close to it, you’ll get nothing more. For most of us, we’ll get the full benefit, which is another 26 dps worth (dps * steady shot % * 6%).

Glyph of the Hawk
42.72 dps… possibly 26 dps more
1.44% – 2.3% increase

Another Sniff Test

Okay, so we’ve done our theorycrafting, cruched our numbers. But before we just see which increase is bigger, we do another sniff test, applying what we know are some of the real-world factors that could affect the results. Generally this will just help you choose between two things with a very similar dps boost.

For example, the Kill Shot glyph. We see that it offers a nice boost; however, we also know that we probably won’t see that entire effect. That assumes that we are able to cast kill shot the instant it becomes available; however, we know that realistically sometimes we’ll be on the global cooldown, or we’ll be a second or two late in clicking the button – which could result in one fewer kill shots being cast. Same for if the end of that boss fight lasts just 45 seconds instead of a minute. The longer the boss fight, the better the ability. On the other hand, we do like the fact that the glyph is helping us disproportionately at the end of the boss fight — which is often when you want the dps surge the most. This is a good thing.

On Hawk I am not haste capped, so I should be getting the full 2.3% boost from it. However I also know that probability being what it is, the proc won’t actually be in effect 100% of the time. There will be some brief down windows. However, the glyph is so good that it’s still our first choice. Note also that the glyph will only help you if you have at least one point in the Improved Aspect of the Hawk talent.

Our Recommendations

So based on this, we have four choices: Explosive Shot, Kill Shot, Steady Shot, and Hawk. Any three of those are going to be good choices.

We recommend Hawk without reservation as a must-have if you are not haste capped. Personally I’ll be taking Explosive Shot because that shot is such a high priority for SV, and since it’s an instant we’re jump-shotting it even if we’re running. So I know I’m always going to get the maximum use out of that. Finally you have to choose between Kill Shot and Steady Shot. We’re going to recommend Kill Shot because, frankly, it’s just better for your raid. You need that dps surge at the end of many boss fights.

The Fudge Factor

Keep in mind that theorycrafting involves a healthy fudge factor. The big one that no theorycrafting no matter how elaborate cannot be rid of is that theorycrafting assumes an absolutely perfect environment. No lag, no running out of fire, no mistakes. This is okay, because the goal with theorycrafting is not to guess what the actual number output would be – but rather to determine which of multiple options is the best. It is qualitative, and we hope that the real-world discrepencies are evenly distributed among possible options.

Then we have the fudge factor area in more simple theorycrafting like what we just did, where we aren’t taking everything into account. We are not estimating how much mana it uses and what the return will be. We aren’t taking armor into account. We aren’t determining the bonus effect of extra crits on proc abilities like Go for the Throat and Expose Weakness.

Our goal is just to get “close enough.” Close enough to be able to make a qualitative decision about which option is best. So anything we didn’t do that wouldn’t change the qualitative outcome is an acceptable margin of error.

Let me repeat that: anything left out that wouldn’t actually change the qualitative outcome of “which is better” is an acceptable margin of error in theorycrafting. So given that, let’s see if I made any mistakes