Gathering Data and Determining Coefficients, A Beginner's Guide

World of warcraft math and science

Lately, we've been talking a lot about showing your work, that is, showing how theorycrafters come to conclusions, etc.  So I thought it might be fun to take a minute to make this guide, to show how I spend the majority of my time in WoW betas or PTRs.

Tooltips are Wrong

Something that's incredibly amazing about World of Warcraft is the amount of data we have. Sometimes I forget that not every game has a completely separate industry set up around providing data about the game. Most popular games these days have walkthroughs and guides,  but nothing like the wowhead and wowdb databases.  There are people who's full time jobs are to sift through the information found in the game client, and present it to us.  That's awesome.

However, it also leads to problems if we get lazy and take that data without verifying it, because the information found in spelldata or in the tooltips for any ability is often wrong.  Whether from being input incorrectly from the beginning, or from a hotfix that didn't require a client-side update, what a spell actually does is often different than what it's tooltip/spelldata claims it does.

Furthermore, because we have no way of knowing which tooltips are correct and which aren't just by reading them, if we want accurate data, we need to resort to the good ol' scientific method to test and verify our data.

In-game Experiments

A very convenient part of testing in WoW is it's really quite easy.  Most variables that would have to be controlled for in a real life experiment simply don't exist inside the game. There are still a few variables we may need to consider, which we'll get into later.

For the sake of this blog post, we're going to look at something fairly simple, Black Arrow.  Black Arrow has the benefit of being scaled off of Attack Power (not weapon damage, which is a bit more complicated), and causing Shadow damage, which isn't affected by armor. We will still build something into our tests to verify that it's not being affected by armor and isn't scaling off of weapon damage, but that's just sort of a "just in case" measure.

What do you already know?

Let's start by going over what we know about Black Arrow.  According to the spell data available from datamining our wow clients (or reading the spell tooltips):

Black Arrow:
  • Does Shadow Damage
  • Does 260% of Attack Power over 26 seconds
  • Does 1 tick every 2 seconds.
  • Each tick does 20% of Attack Power
  • Has a 1 second GCD
  • Has 3 charges
  • Cast time is instant
  • Is dispellable by any Magic Dispell
  • Costs 40 focus
  • Has a 40 yard range
  • Requires a ranged weapon
  • Has an 18 second cooldown
Ok, so much of that isn't important to us at the moment.  The big changes from Black Arrow as we know it in Warlords of Draenor are:  it's now a marksmanship talent, instead of a Survival baseline ability; it now has 3 charges, with separate cooldowns; and it's duration was increased from 20 to 26 seconds, so it should give 13 ticks, instead of the 10 ticks it did during WoD.  

Of those properties we learned from spelldata, there are just a few that we want to test and verify. Does each tick do 20% of Attack Power as shadow damage, and does each cast indeed do 13 ticks? So now we just take a trip over to the target dummies to test it out.  

Recording Data

To set up our test, we want to plan in a few variables. The best way to start out, is to take off all of your gear, and head to Orgrimmar or whatever your favorite capital city is, and find a white quality weapon from one of the vendors there.  What you're looking for is a bow like the Worn Shortbow. This is ideal for testing because the WD range is 1-3 (so you don't have to worry about the huge variance that current level bows have), and it doesn't have any other stats, so there's less to control for.

Next, you'll head over to the training dummies.  The first problem we're going to run into is that training dummies have pretty much the same percent HP all the time.  That is, there are some that are always at 100% HP, and some that are always at 15%, etc.  There are some abilities that react to the HP % of your target, so that could be an issue we need to control for.  Blizzard gave us a great tool for this a few expansions ago, over in Shattrath.  If you go to Shattrath on the PTR or Beta versions of the game, there are killable target dummies.  These start at full health and take damage until they're at 0% health, at which point they die (only to respawn a few seconds later).  This lets you test your full rotation, with executes and over a set duration of time.  However, so far we have no reason to believe that Black Arrow is affected by our target's HP, so while we may double check against a killable target dummy eventually, at this point, it's not needed (plus when not wearing any gear, and using a white quality weapon, it would take quite a long time to actually kill one of those dummies).

The last thing you need to collect data is a spreadsheet set up.  I like to use Google Sheets, because I like to do my work from various different computers, but use whatever you want. If you then open your character pane, take all of the stats available to you that could possibly have an affect on your damage, and record it in a little table like so:

Legion Black ArrowTest 1
WD1 - 3
Crit 15.00%
Mastery 4.00%

world of warcraft theorycrafting hunters experiments
Don't forget to label everything; this will allow anyone with the desire the ability to repeat your experiment—a core element of the scientific method. And let's be realistic here: eventually, someone is going to question your results, and you want to be able to quickly prove yourself right, not waste time trying to figure out what you had meant to write down...

Back in  your WoW client, turn on combat logging by typing "/combatlog", then start firing your Black Arrows.  We want a significant number of data points, which can get a bit boring, so now is a good time to turn on Netflix and watch Buffy the Vampire Slayer in your other monitor.

Once you have about 30 or 40 casts (you don't really need thousands of data, but you do want a lot), hit feign death to end the fight in your log (one of the nice conveniences of testing as a hunter). Alternately, you can just type "/combatlog" twice to turn off logging and turn it back on.  Assuming you were wearing no gear for the first test, you'll next want to put on a piece of gear and record how that affects your stats.  You should have slightly more AP, and a couple of secondary stats.

You're going to repeat this process several times, putting on more and more gear so that you'll have more and more AP and other stats to test between. You can also, at this point, try testing different weapons.  Just be sure to end combat between each test, and write down your stats with each variation of gear you're wearing.

You can, in general, use any pieces of gear you have to create various stat levels.  However, what you don't want to put on is anything that will cause stats to vary during combat.  This includes many trinkets, or any weapon that has an enchant that procs.  You'll also want to avoid any sort of on-use items, though of course you can still wear them, just ensure you're not on-using them.

As I mentioned earlier, we believe Black Arrow to be doing Shadow Damage, which means it should not be affected by Armor, but we still want to check, just in case.  The easiest way to do this is to try your test against different types of training dummies.  The raid dummies (which are set 3 levels higher than the player level cap) will have more effective armor than the dungeon test dummies, which will have more effective armor than the PvP test dummies. If your results are the same for each type of dummy, you can feel assured that armor isn't a part of the equation.

Reading Data

After running this test at several different stat levels, it's time to start interpreting the data.  This is the fun part, I suppose.  We're quite fortunate to have several good logging sites these days.  You can use or, or even Matlab, if you're into that kind of thing.  I'm going to be using Warcraft Logs for this example, but really just use whatever logging site you prefer.  

If you're using Warcraftlogs, go to the your damage done tab, and hover your mouse over the ability you're testing, in this case black arrow.  You should get a little table that looks like this:

The information we're interested in is for the regular tick, not the crits (MM critical damage has a lot of factors, and we don't need to reverse engineer it, to determine the coefficient of Black Arrow, though that may be part of another test we'd want to do, at another time).  So I'll go back the spreadsheet where I've been recording my stat and such, find the applicable test (I label my tests in order, 1, 2, 3, etc., just because most logs show the fights in chronological order, so it's easy to match them up).

I like to then put this data into my spreadsheet like this:

Test 12016-02-08
Crit 25.36%
Mastery 11.73%
Black Arrow

The first thing I want to mention is the cell called "(m+M)/2".  I have to call it that, because I've yet to hear of any sort of terminology for that type of average (but if you know one, let me know in the comments).  What it means is the minimum result plus the maximum result, divided by two.  I'm not going to get into the reasoning for this in too much detail here, but the basic idea is, in a Normal (or Gaussian) distribution, taking the mean average will generally yield the most accurate result, occasionally you may use the median or mode for some data sets, I suppose.  However, our results in wow do not have a Gaussian distribution, they have a uniform distribution.  So you're more likely to find the true average by looking at the halfway point between your smallest and largest data points, than by taking a traditional average.  For more information on this, check out Hamlet's article on wow distributions.

The final four cells are where we put our formulas.  Because the spelldata we looked at earlier tells us that this ability is based on an AP coefficent, we're going to at least start by working off of that (it may be helpful to look at a possible Weapon damage coefficent later, if having an AP coefficient leads to inconsistencies).

I like to keep a cell open for all four of the min, max, average and (m+M)/2. To get an accurate result, you really only need to look at (m+M)/2, though.  I  just happen to find it helpful to look at all four if something doesn't work out right.  In the case of abilities modified by an AP percentage, there's generally a very small range, so in this example, as you'll see, each cell gives nearly identical results.

So in the bottom right four cells, I'm simply going to take the relative result (min, max, etc) and divide it by the AP I wrote down above.  If I had any versatility, I would need to multiply "1+v" (where v is the floating point for my versatility percentage) by my AP first, but in this case I have none, so it's not part of the equation, at the moment.

Doing this in all four cells gives me a result like this:

Black Arrow

What that's showing, is the coefficient is 26%, not the 20% we were expecting.  I won't display here all of the test results I got, but a couple looked like this:

Test 22016-02-08
Black Arrow

Test 32016-02-08
Black Arrow

Something we can also try at the point, is checking if there could be a weapon damage coefficient.  However, doing so quickly shows that you get wildly different coefficents with different weapon damage values, where as with trying for an AP coefficient, we get the same result regardless of the AP value or the WD value. So we can feel quite assured that we're dealing with an AP coefficient here. 

Declaring a Result

In this particular case, all of my tests gave me the result of an AP coefficient of 26%.    Our scientific definition of "correct" is an hypothesis that can accurately predicts results.  By this standard, with enough data points and variations of the test, I'm convinced that we've got the correct coefficient.

It's worth noting here, that there is a significant difference between 20% AP per tick and 26% AP per tick. It means the full value of the ability over its entire duration is 338% AP, instead of 260% AP. In a spec that may end up with too much focus, at least during certain points in the rotation, like when building stacks of vulnerability, this may end up being a worthwhile talent.  Regardless, we want to know how much damage it actually does, or there's no point trying to make comparisons with other abilities or talents.

Other Resources

If this is the type of thinking/experimenting you're interested in, check out these articles by people who've been doing theorycrafting way longer than I.

From Theck:

From Frostheim:

Legion Beta: Some Thoughts on the Marks Artifact Weapon

Thas'dorah, Legacy of the Windrunners

A proud heirloom of the Windrunner family, Thas'dorah was carved from a bough of the mother tree of Eversong Woods shortly after the elven kingdom of Quel'Thalas was founded. Handed down to the eldest of each generation, the bow was last wielded by the high elf Ranger Captain Alleria Windrunner. It disappeared along with its owner following the destruction of the orcs' homeworld, Draenor, and the subsequent formation of Outland.

  • Deadly Aim - Critical Strike damage increased by 10%, that is, critical strikes do 210% the damage of a normal hit. 
  • Precision - Focus Cost of Aimed Shot is reduced from 50 to 44.
  • Marked for Death - For 10 Seconds after casting Marked Shot, Aimed Shot has a 15% greater chance to crit.
  • Legacy of the Windrunners (on equip ability) - When you cast Aimed Shot, there is a chance for 6 extra Wind Arrows to coalesce and also shoot at your target.
  • Quick Shot - Trueshot's cooldown is reduced from 3 minutes to 2 minutes 30 seconds.
  • Rapid Killing - While Trueshot is active, your crit damage is increased by 50%, so that crits will do 250% the damage of a regular hit (260% for Aimed Shot).  
  • Whispers of the Past - While Trueshot is active, any target marked with Hunter's Mark will be hit by a passive ability (called Whispers of the Past in logs, or Wind Arrows in tooltips) that are currently doing roughly 2/3 weapon damage every 3 seconds.
  • Call of the Hunter - Marked Shot has a chance (currently unknown) to summon a regiment of fallen hunters that will shoot arrows at your targets (damage currently unknown).
  • Windrunner's Guidance - Marked Shot overall damage is increased by 10%.  
  • Marked for Death - For 10 Seconds after casting Marked Shot, Aimed Shot has a 15% greater chance to crit.
  • Critical Focus - Arcane Shot critical strikes generate 10 focus (double the amount from a normal hit).
  • Call the Targets - Multi-shot damage is increased by 10%, to 65.05% of weapon damage per target.
  • Mark of the Windrunner - Hunter's Mark can now apply to one additional target.
Bursting Shot: 
  • Gust of Wind - Reduces the focus cost of Bursting Shot by 10, from 50 to 40. 
Damage Reduction and Healing:
  • Healing Shell - While AotT is active, you heal for 24% of your max health over 8 seconds.
  • Survival of the Fittest - All damage taken is reduced by 10% (a la Iron Hawk).
New Abilities:
  • Bullseye - Special Attacks against a target below 20% HP give a stacking 3% crit buff for 6 seconds.
  • Windburst - a 3 sec. cast shot that deals relatively weak damage, but costs no focus.  

A Few Thoughts:

Having tried a few different iterations of the artifact weapon talents that are currently unlocked on Alpha, the first thing that really jumps out about the artifact talents is that none of them really change your rotation.  There are a couple that I'll make some notes on, though.

Windburst - 

This ability doesn't have a place in your rotation.  The only exception to that might be pre-casting on the pull, if the added speed can be helpful to melee running toward the boss. As it is, Windburst isn't doing the 500% weapon damage that it's tool tip claims it should be doing; instead, it's doing about 300% weapon damage, which is significantly less than an Aimed Shot, even with no stacks of Vulnerability. If, after tuning passes, Headshot is a very powerful ability that benefits significantly from use at full focus, we may end up pre-casting Windburst (which has no focus cost), followed immediately by a Headshot, so that we've used up all our focus and can then cast a lot of Arcane Shots in order to proc Hunter's Mark, without fear of focus capping (at least not for a few GCDs).

Bullseye - 

This is currently not an ability we can test on the Legion Alpha, as Artifact Weapons are capped at 10 talents.  So (as with everything I'm talking about here, 'cause alpha), it's possible none of this will be the least bit applicable by the time Legion goes live.  However, it's still fun to think about.

On first glance, Bullseye doesn't look too interesting: 3% crit for 6 seconds is fairly insignificant.  But what gets really interesting, to me at least, is that this doesn't include a cap for stacks.  On bosses with large health pools, where we're perhaps staying under 20% HP for a significant portion of the fight, we should be able to see 100% crit for a while.  What makes this potentially insane is the number of critical strike damage increases we now have: our mastery, Sniper Training; Deadly Aim, a 10% increase to Aimed Shot critical damage; and Rapid Killing, a  50% increase to all critical damage during Trueshot.  Lining up Trueshot with the end of a fight should be a recipe for some crazy damage spikes.

There is one question still up in the air, that will have a huge effect on how we play the game, and that is if Bullseye will be a debuff on our targets, or a buff to the hunter. Most MM hunter's are currently familiar with a practice called Kill Shot Sniping, where you pick off targets that are below 35% health, to cast your kill shots on while the boss is still out of the execute range. If Bullseye is a buff for the hunter, instead of a debuff for our targets, then it may be a way to gain some small crit buffs throughout the course of a fight.

Legacy of the Windrunners - 

Maybe it's just me, but it seems odd to me that we have these artifact weapons with big long talent trees on them, but each one also has an on-equip ability.  For BM hunters, you get to summon Hati (Skoll's brother), which is a fairly huge part of the spec in Legion.  For MM and SV both, we get these weird passive abilities that seem like afterthoughts.

For MM hunters, we get this proc of 6 shots, that seem to do about 100% weapon damage.  This happens about ever minute and a half, and not in a way you can rely on in the slightest.  The other part about this that bothers me, is you don't actually notice it.  In MoP, our legendaries had that big Xuen symbol that appeared and a spray of projectiles coming out from us.  In WoD, the ring made you get really big and then explode.  In Legion, you get a few extra auto-shots, and not very often.


The biggest complaint I have about the artifact weapons isn't about any of the abilities or mechanics being introduced, but is instead with the game design in general: our artifact weapon isn't making us more powerful. Instead, Blizzard is making everything less powerful to begin the expansion, then slowly giving us our power back as we level.  Of course, as with any game, increases in power are always an illusion, as the more powerful you get, the more powerful the bosses get. The goal then of the game designers should be to create a convincing illusion, so bosses are still hard and interesting, but we feel like we're getting more powerful.  In this respect, for Marksmanship, at least, the artifact weapon is a failure. I'm not saying they're aren't a some interesting abilities, and some fun interactions with the spec, but I don't feel like I'm using a powerful artifact; I feel like I've been nerfed, and am slowly regaining the power that I should have had as a baseline.  

Didn't they threaten to take away Distracting Shot last xpac, too?

A Sonnet to Distracting Shot

How do I love thee? Let me count the ways.
I love thee to the depth and breadth and height
My arrows can reach, though my pet line-of-sights,
For you, distracting shot, are ideal style of play.

I love thee in a dungeon when tanks do fail
to keep ads at bay, giving healers a fright.
I love thee freely, as pets love the fight.
I love thee purely, as hunters love a good ale.

I love thee with the passion put to use
In peeling off mobs ’till there is not one left.
I love thee with a love more than talents that I lose
Of all my lost buttons, I love thee most to press,
Smiles, tears, of all my life; and, if the old gods choose,
I shall but love thee still after blizzard puts you to death.

Legion Beta: the First Taste of the New Marks

Last weekend, I tried to dedicate a good chunk of time to practicing the new Marksmanship spec on the Legion Alpha.  Truth be told, there's really not a ton to do at the moment, other than leveling.  In WoD, I didn't get a beta invite until after max level was opened, so once I did get in, I spent pretty much 100% of my time in Shattrath, beating on the killable raid test dummies.  We don't yet have that luxury in the Legion Alpha, unfortunately.

That means, I'm spending a lot of my time leveling, and re-leveling, to try to get as much feel for the various artifact talents, and just get a grasp on the feel of the spec.

Marksmanship Playstyle 

As hunters, we've never really had to think about leveling.  I've heard rumors that when people are playing support classes, they have to think about what mobs they're pulling, how they're going to deal with any special mechanics, etc.  For us, for the last few expansions, at least, if by some odd chance we've found one of the few mobs that had a special ability that would kill our pets, then we would just use our ample tool kit to kite the mob until it died, leaving feign death as a last resort, if we made any mistakes.

For the most part, the feel of leveling is still the same for marksmanship hunters. Even in the starter gear they give the pre-made level 100 characters (so far you can't copy your characters to the alpha), I've yet to come across any individual mob that I needed to plan ahead for; the only significant difference is instead of mindlessly pet tanking, you're focus is placed on kiting.

Along with the removal of many of our most interesting utility abilities, Blizzard has (at least as far as I've found so far) removed the mechanics they might have negated.  That is, I've yet to come across a mob with an enrage buff that tranq shot would have removed.  Just to clarify, I'm still very upset about the dumbing down of the hunter class. I'm not trying to say it was a good decision on Blizzard's part.  I'm simply stating that we won't notice the loss of those abilities in the leveling process, as they've equally dumbed down the rare and elite mobs that you run into while leveling (again, perhaps I just haven't run into the interesting mobs yet).

What keeps MM interesting, from my perspective, at least, is that the mobs are set up very similarly to WoD. That is to say, they're everywhere. If you don't pick out your kiting path carefully, you'll likely end up pulling dozens, perhaps hundreds of mobs.  In fact, dealing with large packs of mobs was the most fun part. It took me a while to get back into the mindset of efficient kiting, but once I did, it seems there are lots of opportunities where you can take on a dozen or so mobs at once, focusing down the casters (who you no longer have the option of MD'ing to your pet) while kiting around the melee.

One of the fun parts about leveling as a hunter has always been going into a zone, tagging every mob in a 40 yard radius, and laughing at the silly support classes who tried to take the mobs on one at a time.  We fortunately still have that option in Legion, it's just a much higher risk (I actually doubt their will be any risk for anyone in raid gear, but if you're starting the xpac in WoD greens/blues, there will be).

General Thoughts on the Leveling Experience


In WoD, Blizzard removed the achievements for being the first ___ to reach max level.  The point was, as far as I can tell, to encourage people to enjoy the leveling experience instead of rushing through everything.  With Legion, they're adding even more incentive to being out in the world questing and exploring, through the means of empowering your artifact weapon.  Every rare I found dropped a token that gave you artifact power.  Several quests offered artifact relics as their rewards, which also adds the benefit of experiencing some of the artifact talents earlier than you would if unlocking those talents with artifact power.

I think this is a good thing overall.  Depending on how quickly the first raid opens after the release of Legion, it may be worthwhile to do the loremaster achieve on your first playthrough.

Hunter Class Hall

I'm so incredibly tired of Horde vs. Alliance story lines, while that remains a part of the legion experience, the introduction of class halls means we have a much greater calling than some petty faction.  Let's be real, for those of us playing the only legendary class currently available in WoW, our allegiance has been to our class for a long time.  While I can see the benefit of faction squabbles for people who play one of the support classes, since they don't have anything as glorious as Hunter to rally behind, it just never meant much to me.  

The point of that is, having a class hall is great. I don't want to put any story spoilers on here, but I'm very glad to be pledging allegiance to something other than the horde/alliance.
However, not letting horde/alliance talk to each other is a huge mistake. We should at least be able to speak with each other within Trueshot Lodge.  I'd be more than willing to work for this, also.  Perhaps there could be a game mechanic where you have to gather a certain number of tomes for each race and that would let you learn to understand them in the various class halls.  Or we could learn a special hunter code that allows us to communicate with our fellow hunters, but not any other class.  However the issue is addressed, it needs something.  It's silly to continue the language divide while sharing a class hall.  

Thrill of the Spreadsheet: SV PvP Stat Optimization

As we'll soon have no choice in gear/stat optimization in PvP, I thought it might be fun to go over some of the min/maxing type choices we have now, and why I use what I use.

Optimized for Burst

In opposition to PvE standards, what I'm looking for in PvP is not how to get the highest DPS over the course of the fight.  Instead, I'm looking for the highest burst potential, both reactive and planned. 

For SV hunters, this means taking advantage of your procs with your on-use abilities, the biggest, of course, being a Murder of Crows.  So I logged a few fights against a healer friend of mine, with him doing nothing but healing himself.  Of the times I tried, the best 20 second (the duration of crows) segment I had breaks down like this:

Explosive Shot29,996.256179,977.50
Black Arrow100,321.001100,321.00
Arcane Shot17,325.307121,277.10
Serpent Sting10,597.80663,586.80
Auto Shot7,422.90751,960.30
Pet Melee3,049.601133,545.60
Cobra Shot10,266.70220,533.40
Pet Bite3,479.20310,437.60
Frozen Ammo2,296.30716,074.10
Glaive Toss21,339.00121,339.00

To be clear, my total for these 20 second segments were within the range of 630k and 726k damage, this one certainly had some good RNG, and I timed my trap fairly well for the 2pc set bonus.  Also worth noting, this damage included having versatility enchants (which we'll look at later), but no weapon proc, and no trinket buff (proc or on-use). 

Determining Weapon Scopes

The first thing I looked at was what the effect would be of lining that up with a Mastery Scope proc, or a MS Scope proc.  Because it's hard enough to line up good RNG with my burst when not dealing with any scope/trinket procs, and because I was relying on my friend instead of a training dummy (as a side note, they should really make the PvP training dummies work like hitting a player), I decided to just math the effects of the scope procs.  

To do so, we need to see what each proc gives us.  Each provides 750 of their stat, for 12 seconds.  So the first thing I did was average out my damage sheet for a 12 second duration instead of 20 seconds. The scopes provide the following benefits:


Survival's attunement stat is Multistrike, so we get 5% more of that stat from the proc.  So we're looking at 8.11% more mastery, or 11.93% more multistrike.  Mastery is pretty simple to apply.  We'll take the damage done by an ability, divide it by our current mastery,  then multiply that number by our current mastery plus 8.11% (because the mastery from the scope works additively (not multiplicatively) with the mastery you already have, the result would be too high if you just multiply by 1.0811), for the abilities we have that are affected by our Mastery. For example, Explosive Shot did 29,996.25 damage normally, and my mastery is 39.70%, then I would do: 

(29,996.25/1.397)*(1.397+.0811) = 31,737.62

For Multistrike, we have a few more variations from how you would normally calculate its value. Instead of looking at the actual damage portion of Multistrike, I'll be working with the expected Value, statistically. In PvP, we only get one chance to Multistrike, instead of the two you get in PvE.  Also, because of SV's passive ability, Survivalist, Multistrikes do 20% more damage.  So our expected value with Multistrike will be "0.36*MS%".  Again, because the Multistrike from the proc adds with the Multistrike you already have, we'll have to take out the EV of the Multistrike from our gear, then multiply it back together, as we did with Mastery. As with all statistical analysis of this sort, this won't be true every time, but with a large enough sample size, our average will tend toward these results. To use Explosive Shot as an example again, with ES averaging 29,996.25 damage per cast, and my MS rating at 18.61%:

(29996.25/(1+0.36*0.1861))*(1+0.36*(0.1861+0.1193)) = 31203.64

As is obvious from just comparing the two scope's effect on Explosive Shots, Mastery gives you about about 1.7% more damage; however, mastery is only applied to some abilities, while MS is applied to all abilities. Comparing the damage from each scope, we get something like this:

AbilityBase DPCCasts/12secBDmg/12secsw/ Mast scopew/ MS scope
Explosive Shot29,996.254119,985.00126,950.49124,814.55
Black Arrow100,321.000.660,192.6063,686.9662,615.43
Arcane Shot17,325.30469,301.2073,324.3472,090.66
Serpent Sting10,597.80442,391.2044,852.1444,097.50
Auto Shot7,422.904.231,176.1831,176.1832,431.06
Pet Melee3,049.606.620,127.3620,127.3620,937.51
Cobra Shot10,266.70220,533.4021,725.4221,359.90
Pet Bite3,479.20310,437.6010,437.6010,857.73
Frozen Ammo2,296.304.29,644.4610,204.3510,032.66
Glaive Toss21,339.00121,339.0021,339.0022,197.92

So we actually ended up with the MS scope coming out slightly ahead of the Mastery scope. The reason this happens, is that a Murder of Crows is such a large amount of our burst.  So while most of the time, in your normal rotation, you have nearly 80-85% of your damage coming from abilities affected by Mastery,  while crows is up is down to 69.5%.  

While this is surprising enough to be interesting. I do have some caveats.  Even though the MS scope came out slightly ahead, it was very, very slightly: .04% more.   If we get just one more Explosive Shot during the duration of the scope's proc, the Mastery scope pulls back into the lead, by about .5% more.  Also, when the scope procs while Crows is on CD, then we start seeing the Mastery scope pull ahead by more than a percent.  

There's another significant consideration, because the two are so close, we actually start to see armor making a difference in which one is better. The slight edge that the MS scope has is that it works on all of your abilities. However, the extra abilities that it works on (compared to the Mastery scope) are all physical damage, and do reduced damage based on your opponents armor. I did my testing above against a monk (leather armor); if you switch the armor values for a clothe class, you'll see the value of the MS proc go up (not significantly, but a little bit), while the Mastery scope doesn't change.  On the other hand, if you put in the values for a mail or plate class, the value of the MS scope goes down.

Of course, we're talking about incredibly small differences here.  From playing with my spreadsheet a bit, to me it looks like the Mastery scope is the better choice. This is because with bad RNG, the MS scope is only very, very slightly better, but with good RNG, the Mastery scope can be significantly better than the MS scope.  

PvP Enchants

In the Hunter Discord channel, Dilly asked me to run the same scenario but for Mastery vs Versatility enchants.  The math works the same, but just to show what we're working with:

Mast chants27592.52.97%
Versa chants2751302.12%

Again we see that we get slightly more percent damage increase from Mastery, but Versatility applies to all of our abilities, whereas again, Mastery only applies to elemental damage.  Using the same 12 second burst window to compare, the values look like this: 

AbilityDPCCasts/12secDmg/12secsw/ VersaW/ Mast
Explosive Shot29996.254117,805.38119,985.00120,309.91
Black Arrow1003210.659,099.1660,192.6060,355.60
Arcane Shot17325.36102,063.44103,951.80104,233.29
Serpent Sting10597.8220,810.5721,195.6021,253.00
Auto Shot7422.94.230,609.8431,176.1830,609.84
Pet Melee3049.66.619,761.7320,127.3619,761.73
Cobra Shot10266.7220,160.4020,533.4020,589.00
Pet Bite3479.2310,247.9910,437.6010,247.99
Frozen Ammo2296.34.29,469.269,644.469,670.58
Glaive Toss21339120,951.3621,339.0020,951.36

Again, we're not talking about huge differences here, but Versatility enchants do come out slightly ahead, and they have the added benefit of giving you a little over a percent of passive damage reduction.