Xaxas
04-22-2008, 10:43 PM
After some thought and a few questions about my decisions in both enchants and stat choices, I decided it time to write up a full comparison of all stats and enchants and what makes them good or bad to a typical raiding mage.
Now the first thing that needs to be set down is what stats to collect to increase DPS and what stats we want.
Here is the accepted hierarchy of stats:
Spell Hit > Spell Haste > Spell Damage > Spell Crit
Spell Hit: Chance to hit is calculated as the difference between the level of the caster and the target. Bosses are the average level of the the raid plus 3. For a target of 3 levels higher than the caster, that calculates to a 17% chance to be resisted. Only 16% of this is able to be overcome by spell hit. Now for some numbers on why this stat is important.
Assume an average boss fight with 60 fireballs cast and an overall 2000 damage average per fireball:
Case 1: No Spell Hit
60 * 2000 * .83 (or 83% chance to hit) = 99,600 Damage
Case 2: Full Spell Hit
60 * 2000 * .99 (or 99% chance to hit) = 118,800 Damage
So using the following equation:
99,600 * x = 118,800
x = 1.198
Thus, we can see that a capped out mage is putting out 119.8% of the non-hit capped mage with equal stats. This also works with the addition of crits as a crit is calculated before the spell hit is calculated, so a fireball may be a crit, but is resisted. Since most (if not all raiding mages) have the Elemental Precision, the hit cap for fire (and frost) is 13%. According to Blizzard's CM Eyonix, 1% of spell hit requires ~12.6 Spell Hit Rating. Thus, 164 Spell Hit Rating is required to reach 13%. So with a DPS increase of 19.8%, the DPS increase per point of spell hit can be calculated as:
.198/164 = 0.12% increase in DPS per point of spell hit. Seems small, but keep reading.
Spell Haste: Now the way spell haste works is that each percent of spell haste you gain, you would gain one extra spell cast within the same period of time for 100 casts. In numbers, that means:
100 fireballs = 300 seconds to cast with no spell haste
101 fireballs = 300 seconds to cast with 1% spell haste
So if 100 fireballs counts as 100% DPS and 101 fireballs count as 101% DPS, 1% Spell Haste counts as a 1% increase in DPS. That’s fairly simple to follow so far. Now, also according to Eyonix, it takes ~15.8 Spell Haste rating to gain 1% Spell Haste. So using the same equation as the spell hit:
.01/15.8 = 0.06% increase in DPS per point of spell haste. Half the DPS increase for the same point of hit on an item.
Spell Damage: Now this one gets a little complicated. Spell Damages are based on casting times which gives a calculated coefficient to the amount of spell damage a spell receives. The equation looks like this:
x/3.5 * Character's Spell Damage = Spell Damage Bonus the Spell Receives from Spell Damage, where x is the unmodified cast time of the spell.
So for fireball with an unmodified cast time of 3.5 seconds the coefficient looks like this:
3.5/3.5 = 1; thus fireball receives 100% Spell Damage Bonuses. Now, assuming a Deep Fire Build, fireball receives an additional 15% Spell Damage for a grand total of 115% Spell Damage received.
Fireball’s average base damage is calculated as (713 + 904)/2 = 808.5 (Also assuming 5/5 Fire Power, but that was picked up on the way to Empowered Fireball); So, let’s do some numbers.
Case 1: No Spell Damage
808.5/3sec = 269.5 DPS
Case 2: 500 Spell Damage
[808.5 + (500 * 1.15)]/3sec = 461.2 DPS
Case 3: 100 Spell Damage
[808.5 + (1000 * 1.15)]/3sec = 652.8 DPS
Using this trend, this can be graphed as the function of y = (1.15x + 808.5)/3 for all spell damages giving us a linear relationship. By taking the derivative of the function, we can find the increase in DPS per point of spell damage.
y = (1.15x + 808.5)/3
dy/dx = 1.15/3 = .38 DPS per point of spell damage (notice it isn’t a percent, just a number)
Take note that the above numbers are assuming 100% spell hit and no spell haste. Less spell hit reduces the effectiveness of spell damage and spell haste increases the effect.
Spell Crit: The fun part about being a mage is the ability to critically strike with our spells. Spells inflict a base 150% damage of the normal strike damage. Now there is two ways to increase critical strike chance outside of talents, intellect and spell crit rating. The conversions for these two stats are as follows:
Intellect: 80 points per 1% crit or 0.0125% crit per 1 point of intellect
Spell Crit Rating: ~22.1 spell crit rating per 1% crit or 0.045% crit per 1 point of spell crit.
We will be focusing on the effects of spell crit as intellect doesn’t provide enough crit to be considered. Blizzard’s default crit chance for a mage with the proper intellect is 5% so this will be our base.
Using the mage with the capped hit from Case 2 in the spell hit discussion during the same boss fight, we will look at the effects of crit on DPS.
Case 1: 5% crit, no spell crit rating
118,800 – (118,800 * .05) + (118,800 * .05 * 1.5) = 121,770 Damage
Case 2: 10% crit, 111 spell crit rating
118,800 - (118,800 * .1) + (118,800 * .1 * 1.5) = 124,740 Damage
121,770 * x = 124,740
x = 102.4
Now this shows a base increase of 2.4% DPS for 5% crit chance over an average boss fight. Ignite continues to add an extra 40% crit damage bonus. I may or may not add the numbers for this.
Bottom Line:
Spell Hit: 0.12% DPS increase per point
Spell Haste: 0.06% DPS increase per point
Spell Damage: .38 DPS increase per point
Spell Crit: Still working on this one.
Opinions
I wanted to put this in a different section to make sure the mathematical argument holds its own place while I still have a place to add my opinion of stats based on many months worth of raiding with my mage at level 70.
Spell hit is the BEST stat to stack until the cap. The existence of a cap also helps with a goal to shoot for while collecting gear and allowing to one work into other areas of the stat collection. It is also very cheap for itemization, so we are still able to get a lot of other things along with spell hit rating.
I am not so much a fan of spell haste though. With my experience with raiding as a mage, mana consumption is high and mana regeneration is low. A shadow priest is rare gift and blessing of wisdom or mana spring totem can only hold off mana usage for so long. Even with early usage of Mana Emeralds and Mana Potions and using them as the cooldown is over, mana still is a problem. Haste causes a mage to consume mana at an even faster rate than normal. Yes, haste is a DPS increase but hitting harder can be just as effective as hitting faster. Spell haste is also a very expensive stat on gear and it doesn’t show up in significant quantities until T6 level gear and beyond.
Spell damage is exactly what we all expect it to be. Makes you hit harder at no extra cost to the mage. Standard itemization cost.
Spell crit is a nice stat in my opinion for the obvious instantaneous DPS increase and the mana return from Master of Elements. Hit a lot harder for an actually cheaper spell. It’s moderate in itemization values but does require quite a bit for only a chance at more spell crits.
Combat Rating Conversions Page: http://forums.worldofwarcraft.com/thread.html?topicId=36573662&sid=1
Intellect to Crit Conversions Page: http://www.wowwiki.com/Attributes#Intellect
Now the first thing that needs to be set down is what stats to collect to increase DPS and what stats we want.
Here is the accepted hierarchy of stats:
Spell Hit > Spell Haste > Spell Damage > Spell Crit
Spell Hit: Chance to hit is calculated as the difference between the level of the caster and the target. Bosses are the average level of the the raid plus 3. For a target of 3 levels higher than the caster, that calculates to a 17% chance to be resisted. Only 16% of this is able to be overcome by spell hit. Now for some numbers on why this stat is important.
Assume an average boss fight with 60 fireballs cast and an overall 2000 damage average per fireball:
Case 1: No Spell Hit
60 * 2000 * .83 (or 83% chance to hit) = 99,600 Damage
Case 2: Full Spell Hit
60 * 2000 * .99 (or 99% chance to hit) = 118,800 Damage
So using the following equation:
99,600 * x = 118,800
x = 1.198
Thus, we can see that a capped out mage is putting out 119.8% of the non-hit capped mage with equal stats. This also works with the addition of crits as a crit is calculated before the spell hit is calculated, so a fireball may be a crit, but is resisted. Since most (if not all raiding mages) have the Elemental Precision, the hit cap for fire (and frost) is 13%. According to Blizzard's CM Eyonix, 1% of spell hit requires ~12.6 Spell Hit Rating. Thus, 164 Spell Hit Rating is required to reach 13%. So with a DPS increase of 19.8%, the DPS increase per point of spell hit can be calculated as:
.198/164 = 0.12% increase in DPS per point of spell hit. Seems small, but keep reading.
Spell Haste: Now the way spell haste works is that each percent of spell haste you gain, you would gain one extra spell cast within the same period of time for 100 casts. In numbers, that means:
100 fireballs = 300 seconds to cast with no spell haste
101 fireballs = 300 seconds to cast with 1% spell haste
So if 100 fireballs counts as 100% DPS and 101 fireballs count as 101% DPS, 1% Spell Haste counts as a 1% increase in DPS. That’s fairly simple to follow so far. Now, also according to Eyonix, it takes ~15.8 Spell Haste rating to gain 1% Spell Haste. So using the same equation as the spell hit:
.01/15.8 = 0.06% increase in DPS per point of spell haste. Half the DPS increase for the same point of hit on an item.
Spell Damage: Now this one gets a little complicated. Spell Damages are based on casting times which gives a calculated coefficient to the amount of spell damage a spell receives. The equation looks like this:
x/3.5 * Character's Spell Damage = Spell Damage Bonus the Spell Receives from Spell Damage, where x is the unmodified cast time of the spell.
So for fireball with an unmodified cast time of 3.5 seconds the coefficient looks like this:
3.5/3.5 = 1; thus fireball receives 100% Spell Damage Bonuses. Now, assuming a Deep Fire Build, fireball receives an additional 15% Spell Damage for a grand total of 115% Spell Damage received.
Fireball’s average base damage is calculated as (713 + 904)/2 = 808.5 (Also assuming 5/5 Fire Power, but that was picked up on the way to Empowered Fireball); So, let’s do some numbers.
Case 1: No Spell Damage
808.5/3sec = 269.5 DPS
Case 2: 500 Spell Damage
[808.5 + (500 * 1.15)]/3sec = 461.2 DPS
Case 3: 100 Spell Damage
[808.5 + (1000 * 1.15)]/3sec = 652.8 DPS
Using this trend, this can be graphed as the function of y = (1.15x + 808.5)/3 for all spell damages giving us a linear relationship. By taking the derivative of the function, we can find the increase in DPS per point of spell damage.
y = (1.15x + 808.5)/3
dy/dx = 1.15/3 = .38 DPS per point of spell damage (notice it isn’t a percent, just a number)
Take note that the above numbers are assuming 100% spell hit and no spell haste. Less spell hit reduces the effectiveness of spell damage and spell haste increases the effect.
Spell Crit: The fun part about being a mage is the ability to critically strike with our spells. Spells inflict a base 150% damage of the normal strike damage. Now there is two ways to increase critical strike chance outside of talents, intellect and spell crit rating. The conversions for these two stats are as follows:
Intellect: 80 points per 1% crit or 0.0125% crit per 1 point of intellect
Spell Crit Rating: ~22.1 spell crit rating per 1% crit or 0.045% crit per 1 point of spell crit.
We will be focusing on the effects of spell crit as intellect doesn’t provide enough crit to be considered. Blizzard’s default crit chance for a mage with the proper intellect is 5% so this will be our base.
Using the mage with the capped hit from Case 2 in the spell hit discussion during the same boss fight, we will look at the effects of crit on DPS.
Case 1: 5% crit, no spell crit rating
118,800 – (118,800 * .05) + (118,800 * .05 * 1.5) = 121,770 Damage
Case 2: 10% crit, 111 spell crit rating
118,800 - (118,800 * .1) + (118,800 * .1 * 1.5) = 124,740 Damage
121,770 * x = 124,740
x = 102.4
Now this shows a base increase of 2.4% DPS for 5% crit chance over an average boss fight. Ignite continues to add an extra 40% crit damage bonus. I may or may not add the numbers for this.
Bottom Line:
Spell Hit: 0.12% DPS increase per point
Spell Haste: 0.06% DPS increase per point
Spell Damage: .38 DPS increase per point
Spell Crit: Still working on this one.
Opinions
I wanted to put this in a different section to make sure the mathematical argument holds its own place while I still have a place to add my opinion of stats based on many months worth of raiding with my mage at level 70.
Spell hit is the BEST stat to stack until the cap. The existence of a cap also helps with a goal to shoot for while collecting gear and allowing to one work into other areas of the stat collection. It is also very cheap for itemization, so we are still able to get a lot of other things along with spell hit rating.
I am not so much a fan of spell haste though. With my experience with raiding as a mage, mana consumption is high and mana regeneration is low. A shadow priest is rare gift and blessing of wisdom or mana spring totem can only hold off mana usage for so long. Even with early usage of Mana Emeralds and Mana Potions and using them as the cooldown is over, mana still is a problem. Haste causes a mage to consume mana at an even faster rate than normal. Yes, haste is a DPS increase but hitting harder can be just as effective as hitting faster. Spell haste is also a very expensive stat on gear and it doesn’t show up in significant quantities until T6 level gear and beyond.
Spell damage is exactly what we all expect it to be. Makes you hit harder at no extra cost to the mage. Standard itemization cost.
Spell crit is a nice stat in my opinion for the obvious instantaneous DPS increase and the mana return from Master of Elements. Hit a lot harder for an actually cheaper spell. It’s moderate in itemization values but does require quite a bit for only a chance at more spell crits.
Combat Rating Conversions Page: http://forums.worldofwarcraft.com/thread.html?topicId=36573662&sid=1
Intellect to Crit Conversions Page: http://www.wowwiki.com/Attributes#Intellect