Welcome to another article by elemental shaman specialist Matt Sampson, otherwise known as Binkenstein. By day, he's a geek; by night, he's also a geek, but with spreadsheets. He's the shaman behind TotemSpot and has decided to return to something he's really good at: math.
This time around, I thought I'd cover a question of increasing frequency: how will elemental scaling work in Cataclysm? After the rollercoaster ride of changes through Wrath of the Lich King, most shaman are a little worried about how things are looking. Since we're still in the early days of the beta, and since we can't get to level 85 yet, it's a bit difficult to do any in-game testing or experimentation.
However, that's never stopped me before. Rather than building a complex model on things we don't yet know the mechanics for, what we can do is look at how Lightning Bolt is going to work. Since LB comprises 70-80 percent of our damage, it's a useful measure of how damage increases with spellpower and critical/haste rating. So for some baselines, we're going to assume all the raid buffs are present, that the spells can't miss or resist, and that we've got 2.2k intellect, 15 percent haste, and 25 percent critical strike chance. I'm also going to assume a 5 percent mastery value, for when the mastery bonuses come into effect.
We then need to split things up into how they affect the spell. First we look at spellpower bonuses, damage bonuses based on passive talents, buffs and debuffs, which all need to be handled separately. Then we top everything off with critical damage multipliers, factor in Elemental Overload, and top it all off with haste.
I don't yet know how high the bonus is for Flametongue, so I'm going go with the currently listed Wowhead value of 235. A 2,200 intellect with a 5 percent bonus gives 2,310, and since the intellect-to-spellpower conversion is 1:1 (after the first 10 points), we get 2,605 spellpower total (,2300 + 235 * 1.3). We then add the 10 percent spellpower buff from Totemic Wrath to get 2,866 spellpower. The intellect-to-spellpower conversion so far is 1.155 (1 * 1.05 * 1.1).
That translates into 2,620 extra damage (0.714 coefficient with a 0.2 bonus from the Shamanism passive bonus). This then gets increased to 2,777 with the 6 percent bonus from Concussion. The intellect-to-damage conversion is now 1.119 (1.155 * 0.914 * 1.06).
The next step is to look at damage buffs, which is where we get into the first tricky part. Clearcasting will give a 10 percent bonus when up, Elemental Mastery gives 15 percent, and there is the 3 percent raid-wide damage buff as well. All of these stack additively, so we'll get a 28 percent bonus total, but the first two are not present all the time. This means we need to take the uptime figures into account.
The uptime for Clearcasting is easier to work out for Cataclysm than in Wrath because there are no spell-specific critical strike bonuses. First off, we know that the Lava Burst cooldown is 8 seconds. With 15 percent haste, the bolt cast time is 1.66 seconds (2 / 1.15 / 1.05, the last value is the 5 percent raid haste buff) so we can cast five in that 8-second window. To ensure the third burst is cast as quickly as possible, the fifth bolt in the second set is dropped for another Flame Shock (although since the Flame Shock DoT will be shorter with haste, the rotation won't quite be like this, but it gives a rough estimate which is what we are going for here). This gives us a total of two bursts, one shock and nine bolts, for a total of 12 spells.
Next, we work out the average number of critical strikes in that sequence. We have two 100 percent chances from burst, and 10 35 percent chances from the other spells (base 25% + 5% debuff + 5% buff). Ten times 35 percent gives 3.5, so we'd expect to see 5.5 criticals for every 12 spells cast. Since Clearcasting is a two-charge buff, we can double that to 11 charges for every 12 casts.
However, you can and will get two criticals back to back, which will cause the loss of an expected charge. To work out the chance of that happening, we need to split it into two parts. Firstly, the chance of one of the spells either side of the burst cast being a critical is 35 percent, which means we have 4 35 percent chances of a charge loss. Secondly, the chance of a double critical for the other spells is 0.35^2 (or 35% times 35%) or 12.25 percent. That applies to the other eight spell pairs, giving us 4 * 0.35 + 8 * 0.35^2 or 2.38 charges.
This gives us 11 - 2.38 charges, or 8.62 charges for every 12 spells, an uptime of 71.83 percent. It's important to remember that this uptime is on a spell count basis, not the time basis that you would see on World of Logs (not to mention that the combat log timestamps are not very accurate). This uptime means we'd see a 7.183 percent damage increase from clearcasting, on average.
Elemental Mastery up-times are a different kettle of fish. For simplicity, I'm going to ignore the haste portion and any other temporary haste buffs. The average rotation described above will take 7 * 1.66 + 8 seconds (as the 4 bolt + shock set clocks in at 7.88 seconds, we round it up to 8 for the next burst cooldown), giving us a length of 19.62 seconds. With 11 bolt casts in that time, we get 0.56 hits every second. This means that every 1.79 seconds we reduce the cooldown by 3 seconds.
We need a little bit of algebra for the next part of the calculation. We need to work out when 3 minutes minus three times X second equals 1.79X. The left side of the equation is fairly easy: 180 – 3X. The right side will be Y times X, where Y is our bolt frequency, and this value gives our average cooldown length. Using the above examples, we can calculate X as 37.58 (180-3X=XY converts to 180=4.79X, so 180/4.79 = 37.58). Since X is the number of casts required to reduce the cooldown to zero, X times Y gives us 67.26 seconds. This means our average EM uptime is 22.3 percent, and gives an average damage bonus of 3.35 percent. Don't be worried if this looks complicated, as it too me a while to figure it out too.
Damage multiplers, part two
Now that we have our buff uptimes, we can add them together to get the overall damage bonus. 3.35 plus 7.183 plus 3 gives 13.533 percent extra damage. Going back to our earlier int to damage figure of 1.119, we are now at 1.27. Total bonus damage is now 3,255.
OK, so that's the passive bonuses and buffs sorted; now it's on to the debuffs. Well, debuff really, as Curse of the Elements and Earth & Moon don't stack and only provide an 8 percent damage bonus. 1.27 times 1.08 is 1.3716. This brings us up to 3,515 damage.
With the damage bonuses sorted, we can move on to the critical damage bonuses. These can be a little confusing at times, to the point where even I don't remember how they work all the time. The trouble comes from how the meta gem bonus interacts with talent bonuses. A normal spell criticals multiplied by 1.5 for the 50 percent bonus. The multiplier from Elemental Fury increases the 50 percent bonus by 100 percent, which means that it gets increased from 50 percent to 100 percent (i.e., multiplied by two). The odd part is that the 3 percent bonus from the Chaotic Shadowspirit Diamond does not increase the EF bonus, nor the 50 percent damage bonus itself. What it actually does is multiply the whole 150 percent base critical value by 1.03 to get a 154.5 percent critical instead. The 54.5 percent bonus is then multiplied by two to give a 109 percent bonus, which is added to the base value gives us the 209 percent value, and that's how a 3 percent bonus gets turned into a 9 percent increase. The equation itself is 1+ ((1.5 * 1.03)-1) * (1 + 1) -- and as you can see, it's a little complicated.
How does that increase our damage? With our 35 percent critical rate, that (somewhat obviously) means that 35 percent of our spells will critical with an extra 109 percent damage. This equates to an average damage increase of 38.15 percent, which means the intellect-to-damage ratio is now 1:1.895, and our total damage bonus is 4,856. Each additional percentage of critical strike chance will increase the bonus damage by 1.09%, or 38.13 damage.
The next thing to consider is Elemental Overload. This is our mastery ability and obviously is affected by the new mastery rating. This is our old Lightning Overload talent, but reworked slightly. It gives a base 20 percent chance (plus a percentage bonus from mastery rating) to cast a duplicate of the spell you just cast, but only 60 percent of the normal damage. Assuming an extra 5 percent from mastery rating, a 25 percent proc chance gives a 15 percent bonus to any damage (0.25 * 0.6 = 0.15). This increases the expected damage per bolt cast to 5,409, and the intellect ratio to 2.18 damage per point.
That just leaves haste to take into account. This means our ratio becomes intellect to DPS, and is now 0.872, with a bonus of 2,164 DPS. The first thing to do is subtract off the 0.5 seconds from Eye of the Storm (which combines the old Eye of the Storm and Lightning Mastery into a single passive tree bonus) to get 2 seconds, 1.09 and 2,705.
One important thing about haste is how it stacks. Your ratings will always add together to give one total rating value, which is then converted into a percentage, and this multiplies with percentage-based haste buffs. The difference is that the haste buff stacking calculation is done by taking the existing cast time, and then sequentially dividing by each percentage figure. This means that instead of going 30% plus 5% plus 15% gives 50% haste, we need to go 1/1.3/1/05/1.15 to get 0.637, which is then inverted to give the overall haste bonus of 56 percent (1/0.637=1.5698).
Right now you are probably thinking, "That means I should be stacking haste buffs, right?" ... but you'd be wrong. Take a typical situation with our 15 percent haste, 5 percent aura, the 15 percent from Elemental Mastery and 30 percent from Heroism. If you compare the haste totals for the rating, aura, and either EM, Heroism, or both, you'll get 80 percent from everything, 39 percent from Elemental Mastery and 57 percent for Heroism. This means that you get more out of splitting the percentage haste buffs than combining them, although it goes without saying that an unused cooldown gains you no extra damage.
So the 15 percent base haste plus 5 percent aura gives us a base 20.75 percent haste. Adding in the Elemental Mastery uptime adjusted figure of 3.335 gives a total of 24.795%. This gives us a cast time of 1.60 seconds, which means our bonus DPS figure is 3,375, and the intellect-to-DPS figure is 1.360. Each percentage of haste will increase the bonus DPS figure by 26.4.
So what does this all mean? To answer that, I had to bring in a little outside help. Our very own Eli Khoury from the Blood Pact column here at WoW.com helped me out with some information about Shadow Bolt, but unfortunately, there isn't really any such thing as a direct damage warlock any more, so that didn't go anywhere. The next port of call was Gazimoff from Mana Obscura for an example fire mage build. From what he said, I put together a parallel example of how Fireball scales, again making a few assumptions to make things easier to work with. (I didn't want to produce a massive spreadsheet to handle all the different calculations for me... yet.)
The actual results were a little surprising, to be honest. While fire gets an extra 13 percent haste and 3 percent crit, because the base cast time of Fireball has dropped down to 2.5 seconds, it has lowered the spellpower coefficient from 100 percent to 71.4 percent. Further to this, there are no empowerment talents like they used to have (or like our Shamanism tree bonus). The end result was that the intellect scaling was in our favor by 1.36 to 1.266. Not much in it, but it is a promising result. Similarly, the bonus damage over the calculations was 3,375 for LB, but only 2,590 for FB. The 25 percent fire damage bonus for the tree is not as overpowered as people initially thought.
It is important to remember that this comparison is just between two spells and ignores several mechanics on both sides, but the overall impression from this is a good one. I can also make the spreadsheet I used available, but as it was only intended to be a rough working document to make sure I got the numbers working correctly, it will be a little messy and definitely not user-friendly.
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