Uber Mages

Mage class discussion.

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Uber Mages

Post by Elleandra » Thu Aug 02, 2007 1:27 pm

Well, after hearing all this 'hit hit hit hit' discussion I decided to try and fumble around a bit to see what end game raids are doing out there.

Though I didn't look for a long time, I found no mages with maxed hit. Most sit between 6 and 10 percent hit. This would raise you to about 89-93 percent against boss mobs, where 99 is the best you can be.

From my understanding, hit percentage is all or nothing on damage. I may be wrong, but if my normal fireball hit is 3000 and I hit for 2300, the spell hit is not responsible for my loss of 700 damage.

I've heard some say that 1% hit = 1% damage increase. This is clearly wrong, because your increase will obviously have diminishing returns. Using theoretical numbers, it looks like this.

You cast a 1000 damage spell 100 times. You hit 83% of the time, doing 83000 damage.

With each percentage of spell hit gained (and thus 1000 more damage per 100 casts) at this point you see increases in damage of:

1.205%, 1.190%, 1.176%, 1.163% ... to the last percentage increase of 1.020%

To use bigger chunks (say 5% hit gain) you see increases of:

6.024% (88% vs. 83%)
5.682% (93% vs. 88%)
5.102% (98% vs. 93%)

Immediately it seems that this is more efficient way to raise damage dealt against bosses, but against mobs that are not bosses (or level 73) the game changes.

My opinion on this matter is to aim for the ballpark of 10%. This will prevent you from hurting stats for the hit gain and still make you quite effective. As a plus, your 10% gain is fully effective against more enemies than a 16%. As of this moment, I'm around 7.1% without any gem swaps and even lacking any gems in my spellfire hood. The 10% level also prevents any waste on those casters who have big gains from talents.

So how does this stack vs. spell crit? Well, that's a trickier question that requires a careful review of your talents.

Here's the rub for my mage. I have an arcane tree talent that gives me a +50% damage on criticals. This increases my damage immediately to 175% on a critical. In addition, I have the talent ignite, which does even more damage on a crit (in the form of a dot.) With both of these talents I can consider myself to gain 215% damage on a critical vs. the base of 150%. The dot may has less value in the short term but even if I consider it at less than full strength it does make a difference.

Doing some more math, let's go back to our trust 83% hit example with a 1000 damage spell over 100 casts. Our base crit is about 5%. Intelligence meddles with this, but for now I'm going to slip past it's rather tricky effect and simply lump it in as raw crit bonus rather than trying to make a distinction between int and crit gear.

Our damage with 5% crit on 100 casts with 83% hit is (remember you cannot crit unless you hit, and on normal spell crits you do 50% more damage):

83000 + (83 x 5% x 1000 x .5) = 85,075
with my spec = 87,773

Raising crit by two chunks of 5% we have
83000 + (83 x 10% x 1000 x .5) = 87,150
with my spec = 92,545

83000 + (83 x 15% x 1000 x .5) = 89,225
with my spec = 97,317

The first gain of 5% grants only 2.439% more damage vs. base. With a fire/arcane mix like mine the gain is 5.751%. The second 5% of crit grants 2.381% and with my spec is 5.156%.

Now to bring a more comprehensive spell hit equation into the mix so it takes into account the gained access to critical spell strikes due to more hits.

Our real base looks like this for damage:

83000 dmg + (5% crit/strike x 83 strikes x .5 dmg/crit x 1000 dmg/strike) = 85,075 damage base (88,810 with my spec)

Gaining 5% hit raises the damage to:
90200 (+6.024%)

Okay, so what does all this mean? It's fairly straight forward, if math-heavy. If you base crit damage is not enhanced, a spell hit of about 16% or so (total, with talents) is a good idea. If you are like me and have crit enhancers, you have to examine the math much more carefully. I will craft another post getting into my own approach.
Last edited by Elleandra on Thu Aug 02, 2007 2:32 pm, edited 1 time in total.

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Post by Lealla » Thu Aug 02, 2007 1:40 pm

Elle, are you sure that talent doubles your critical strike damage? If it says "increases critical strike damage by 50%", that's applied against the base increase which is itself 50%, making the final critical strike damage bonus 75%. As an example, the Druid talent Vengeance increases spell critical strike damage by 100% at 5 points, which brings it from +50% (1.5x damage) to +100% (2x damage). Similar talents for other classes also work the same way. The wording is important.

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Post by Elleandra » Thu Aug 02, 2007 1:51 pm

Now, for me it works differently. Rather than break the exact priorities into 1% chunks (long and messy) I'm going to go with larger chunks of 5%. Using the numbers we have above I can see a few things right off the bat.

First, I'm already way over the early crit levels. I'm over 20% right off the bat and my spell hit is over 5% already as well. So let's focus on what you gain with the blocks of 20->25% crit vs. 5->10% hit. Our immediate guess is that spell hit to 10% is best move. The math will tell.

Our base level is:
88000 + (20% crit/strike x 88 strikes x 1150 dmg) = 108,240 damage

Then crit gain gives:
88000 + (25% crit/strike x 88 strikes x 1150 dmg) = 113,300 damage (4.675%)

93000 + (20% crit/strike x 93 strikes x 1150 dmg) = 114,390 damage (5.682%)

So getting spell hit to 10% is better than forcing crit up to 25%. This is not surprising. So what about the next spell hit gain from 10% to 15%?

93000 + (25% crit/strike x 93 strikes x 1150 dmg) = 119,737 damage (4.674%)

98000 + (20% crit/strike x 98 strikes x 1150 dmg) = 120,540 damage (5.376%)

This works as expected. The spell hit has an advantage right up to cap. This difference is enhanced more by the number of spell hit bonus it takes to make a full percentage gain, which is less than the amount of spell crit bonus need to get one percentage point. Crit is also enhanced by int (to a very small degree.)

In the end, we're talking about very small differences and since most DPS casters have a lot of crit bonuses it's very important to not just assume that hit will always beat crit. It looks like there's a sweet spot for crit enhance of about 20% and hit should universally be maxed in the end.

If you have crit damage that is completely off the charts (say 250% or 300%) crit may come first for a greater span of time. If I'm given some numbers I can crank out the math here for different builds. I just need to know the base hit and base crit and what information is desired.
Last edited by Elleandra on Thu Aug 02, 2007 2:44 pm, edited 1 time in total.

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Post by Elleandra » Thu Aug 02, 2007 1:52 pm

Lealla - I'm basing this on what others have posted concerning the arcane talent. They all stated that the additional 50% raised you to 200% damage on a crit. I will poke around for more information.

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Post by Elleandra » Thu Aug 02, 2007 2:06 pm

Checked around still more... Lealla, it looks like you are right. Time to redo my math!

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Post by Nagisa » Thu Aug 02, 2007 2:35 pm

.... something I stole from an old forum...

All About Stats

This section includes discussion of the various combat ratings and other stats that come on our gear, how they work, and what they're good for. And what they're not good for.

How Does +Damage Work?
Or, "what is a damage coefficient?"

Short Answer

Any spell with an untalented casting time of 3.5 seconds will receive the described amount of extra damage. Any spell with a shorter casting time will receive less, any spell with a longer casting time will receive more.

Long Answer

+Damage gear is usually described in tooltips with the phrase "Increases damage and healing done by magical spells and effects by up to X." There are other similar wordings used in some tooltips, but the effect is the same, and the description is misleading, as some spells actually receive more than the listed amount.

Every spell has what is called a "damage coefficient." This coefficient is based on the spell's casting time, with 3.5 seconds being the divisor. The untalented casting time of the spell is the dividend. Instant-cast spells, such as Fire Blast, are treated as 1.5 second spells (the length of the global cooldown). Thus:

Fireball: 3.5 / 3.5 = 1.000
Arcane Missiles: 5.0 / 3.5 = 1.429
Scorch: 1.5 / 3.5 = 0.429
Fire Blast: 1.5 / 3.5 = 0.429

We multiply the +damage total of your gear and buffs by this coefficient to determine how much benefit that specific spell receives from the +damage. Let's say you have +900 damage (using normal rounding):

Fireball: 3.5 / 3.5 * 900 = 900
Arcane Missiles: 5.0 / 3.5 * 900 = 1286
Scorch: 1.5 / 3.5 * 900 = 386

Some spells, such as Frostbolt, have a coefficient penalty based on an additional effect (0.95 for its snare, in the case of Frostbolt):

Frostbolt: 3.0 / 3.5 * 0.95 = 0.814

The Empowered Frostbolt, Fireball, and Arcane Missiles talents provide bonuses that are additive to the base coefficient:

Fireball: 3.5 / 3.5 + 0.15 = 1.150
Frostbolt: 3.0 / 3.5 * 0.95 + 0.1 = 0.914
Arcane Missiles: 5.0 / 3.5 + 0.45 = 1.879

The Improved Frostbolt and Fireball talents reduce the coefficient multiplicatively with a 0.9 modifier:

Fireball: (3.5 / 3.5 + 0.15) * 0.9 = 1.035
Frostbolt: (3.0 / 3.5 * 0.95 + 0.1) * 0.9 = 0.823

Note that this is unique to these talents; most talents and effects that reduce casting time do not create such a penalty. Spell Haste, for instance, has no effect on your benefit from +Damage gear, nor does using Presence of Mind to cast a spell instantly. Arcane Blast receives the value expected from its 2.5 second base casting time:

Arcane Blast: 2.5 / 3.5 = 0.714

There are some unique cases, such as Pyroblast, which have seemingly arbitrary coefficients. Pyroblast gains a total 171.43% benefit from damage gear (as expected from its casting time), but only somewhere between 100% and 120% is applied to the direct damage, with the remainder applied to the DOT.

AOE spells suffer a penalty as well; they gain approximately 1/3 the benefit that would be expected from their casting time. The exact coefficients were adjusted slightly for each spell in 2.0.

How Do the Various Combat Ratings and Stats Convert to Useful Numbers?
Or, "eschewing obfuscation."

Short Answer

All conversions apply only at level 70.

12.6 Spell Hit Rating = +1% chance to hit
22.1 Spell Crit Rating = +1% chance to crit
21.0 Spell Haste Rating = 1% haste
39.4 Resilience Rating = -1% chance to receive a crit, -2% damage taken from crits

1 Stamina = 10 health
1 Intellect = 15 mana and 0.013% chance to crit (0.276 Crit Rating)

1 Spirit = 0.125 mana/sec when not casting
1 Spirit = 0.019 mana/sec when casting with 3/3 Arcane Meditation
1 Spirit = 0.038 mana/sec when casting with Mage Armor
1 Spirit = 0.056 mana/sec when casting with Mage Armor and 3/3 Arcane Meditation
1 Spirit = 2.000 mana/sec when Evocating

How much Hit Rating do I need?
Or, "stop flushing 10% of your damage down the toilet."

Short Answer

Assuming you're fighting same- or +1-level mobs and players in PvP, and +3 level raid bosses, you need the following Hit Ratings to max your hit chance at 99%.

Fire/Frost mage, no Elemental Precision: 51 soloing or PvP, 202 vs. raid bosses
Fire/Frost mage, Elemental Precision: 13 soloing or PvP, 164 vs. raid bosses

Arcane mage, no Arcane Focus: 51 soloing or PvP, 202 vs. raid bosses
Arcane mage, 3/5 Arcane Focus: 0 soloing or PvP, 126 vs. raid bosses
Arcane mage, 5/5 Arcane Focus: 0 soloing or PvP, 76 vs. raid bosses

Long Answer

Your maximum hit rate is 99%. Your base hit rate depends on level of the target you're attacking compared to your own:

Same level: 96% vs. mobs and players
+1 level: 95% vs. mobs and players
+2 level: 94% vs. mobs and players
+3 level: 83% vs. mobs, 87% vs. players

Bosses are generally treated as +3 level targets, so you need to increase your hit chance by 16% to max it out at 99%. It takes 12.6 points of Hit Rating to increase your chance to hit by 1%. So subract any +Hit% you have from talents from 16, and multiply the rest by 12.6 to find your target Hit Rating.

How Much Should I Emphasize Hit/Crit/Damage?
Or, "why there isn't an easy answer to that."

Short Answer

No matter what your spec, unless your current gear is already dramatically unbalanced, Hit Rating > Damage > Crit Rating.

Long Answer

Here's a dramatically simplified explanation: first, it takes fewer points of Hit Rating (12.6) to get +1% hit than it takes points of Crit Rating (22.1) to get +1% crit. So even if 1% hit and 1% crit were equivalent (which they're not), a single point of Hit Rating is worth a larger fraction of that 1%.

Second, it's been tested and proven that spells use a two-roll system: one roll determines whether you hit the target or not, and if you hit, a second roll determines whether it's a crit or a regular hit. What this means is that the value of both Damage and Crit Rating is reduced by your miss rate.

Now, here's where it gets tricky: as I said, no matter your spec, and assuming your gear is reasonable, Hit Rating > Damage > Crit Rating. However, the actual relative values -- how much better is Hit Rating than a point of Damage -- depends on your spec and your current gear.

For a very, very rough rule of thumb, you could use the following values:

Deep Arcane spec: 1.0 Hit Rating ~= 1.5 Damage ~= 2.9 Crit Rating
Deep Fire spec: 1.0 Hit Rating ~= 1.4 Damage ~= 2.2 Crit Rating
Deep Frost spec: 1.0 Hit Rating ~= 1.4 Damage ~= 2.5 Crit Rating
33/28 Arc/Fire spec: 1.0 Hit Rating ~= 1.5 Damage ~= 2.0 Crit Rating
Arcane/Frost spec: 1.0 Hit Rating ~= 1.7 Damage ~= 2.0 Crit Rating

For a more exact determination for your own gear and spec, you can use Muphrid's formula:

(Muphrid's formula here when I can find a version that's not all unicode-munged.)

Additional resources for this question
Irontygress's Mage Calculator: http://forums.worldofwarcraft.com/threa ... =106863613

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Post by Elleandra » Thu Aug 02, 2007 3:09 pm

And later on we get to complicate this further with spell haste!

But that comes in about the time you hit BT..

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Post by Elleandra » Thu Aug 02, 2007 4:07 pm

So after all this mess, I think I'm going to go in and respec, but only tweak it very slightly. I will give up a 2% crit and 20% savings on crit spells to increase my hit by 3% with talents.

Do we know anyone who has the dawnstone spell hit cut?

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Post by Elleandra » Fri Aug 03, 2007 2:09 pm

If you thought it was bad before, you ain't seen nothing yet.

Elle's gonna respec! This time, there's going to be some dense mathematics!

So my current spec is deep arcane with fire (40/21)

http://www.worldofwarcraft.com/info/cla ... 0000000000

This spec has some flaws in it off the bat, so here is what I consider my correct base spec:

http://www.worldofwarcraft.com/info/cla ... 0000000000

The big change there is tossing out 20% refund on crit, +2% crit chance on fire, and gaining +3% hit on frost and fire. This is something I should have done right off the bat, I think. Anyway, the second link is our base.

So how do I balance these mathwise? There are a few different rotations you can use with this spec. Some are more challenging, some burn up mana faster, some do more dps. I'm no master of this, so I'm going to use my current style as the base metric for this and expand into some other rotations I've heard of to compare.

Currently in fights (ignoring other help I may get from fellow scorch tossers) I do this:

Scorch x 5, Fireball, Fireball, Fireblast, Scorch, Fireball, Fireball ...

There are more advanced choices, but rather than make this extremely painful I will focus on this fairly normal approach. Further, because fights are long, it is the repeated steps that I will use for calculations. The time span will be five minutes, because most boss fights (i.e., what we care about in this calculation) last longer than that and it allows for time to use 3 minute abilities and see their effects vs. the entire time span of one cooldown.

For calculations, I will use the average damage of max ranked spells.

Pyroblast = 1065 + 356 dot (12s)
Fireball = 815 + 84 dot (8s)
Scorch = 333
Fire Blast = 725
Arcane Blast = 700 (cast time from 2.5 to 2.17)

Some of these aren't in my base rotation, but they will be used at different points in the calculations. Yes, this will be very painful, so if you aren't into heavy numbers, please wait until I've finished for a summary of the results. For now, we have our basics down. If this goes well, I will open pandora's box and try my hand at frost calculations.

I imagine someone else may have done this, but I like making a mountain out of a molehill, so if there is another big post, please include a link so I can check it out!

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Post by Elleandra » Fri Aug 03, 2007 4:37 pm

Now, beyond base damage from spells there is equipment to consider. I'm going to use my current set-up as the metric. This set-up will be rounded for simplicity. Crit/hit/dmg bonus calculations can always be done off this base.

- Relevant Data -

Base (all without talents)
Spell Hit: 10%
Spell Dmg: +843 (fire/arcane + 24 for 7% int-based spellfire damage bonus)
Spell Crit: 20%
Crit Damage: 150%
Int: 380 (174 base + 206 gear)

Arcane Fire Build (talents noted)
Spell Hit: 13% fire (Elemental precision) / 16% arcane (capped)
Spell Dmg: +955 (fire/arcane + 24 for 7% int-based spellfire damage + arcane instability + mind mastery)
Spell Crit: 23% (ignores +15% intellect from arcane mind)
Crit Damage: 175% + 40% fire / 175% arcane
Int: 404 (174 base + 206gear + 24 talents)
Special Notes: Clear Cast on 10% of casts with +30% crit chance, Presence of Mind freecast, Arcane Power 30% more damage for 15 seconds, Improved Counterspell, Arcane Impact grants +4% crit on Arcane Explosion and Arcane Blast, Improved Scorch

Fire Arcane Build
Spell Hit: 13% fire (elemental precision) / 16% arcane (capped)
Spell Dmg: +843 (arcane + 24 for 7% int-based spellfire damage bonus)
Spell Dmg: +1% all / +11% fire
Spell Crit: +29%

<more later, out of time for the moment!>

Confusing Points of Interest:
Mind Mastery's +25% damage is only on base intellect even though it claims 'total' intellect
Does the bonus work the same with Arcane Fortitude?
Improved Fireball alters the fireball damage coefficient
Pure arcane might be viable if mana was endless

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Post by Obanswrath » Fri Aug 03, 2007 4:57 pm

holy math batman!!!!

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Post by Elleandra » Sun Aug 05, 2007 11:03 pm

After scouring the internet, after entombing myself in mathematics and coming to the very brink of despair, I have found it at last!


http://forums.worldofwarcraft.com/threa ... 1&pageNo=1

http://img412.imageshack.us/img412/1975 ... nt2lb6.jpg

Behold these works, ye mighty, and despair!

These people have gone through hell and come up with the answers! At long last I can say I am satisfied. Thinking of nothing but pure dps without other concerns, there is a definitive answer!

For those too lazy to look, it turns out that the 10/48/3 spec is the winner for almost all normal level 70 gear. Only the most gimped will prosper in my current spec (41/20/0) and there is no gear set that can possibly reach 33/28/0. For those who are impatient, the x and y axis are computed using ONLY gear bonuses. All other values are already factored in.

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Post by Elvenbane » Mon Aug 06, 2007 10:06 am

Is this the 10/48/3 everyone's talking about?
It's the thought that counts, not how many people die because of it.

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Post by Elleandra » Mon Aug 06, 2007 3:20 pm


The arcane invests 2 points in arcane subtlety and 3 points in arcane focus (these 3 are all that really matter, the other 2 points can go anywhere.)

I haven't spent all my points yet, actually, but I have all the mission criticals. I have not found a more useful investment of points then blast wave or dragon breath at this point, though!

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Post by Elvenbane » Mon Aug 06, 2007 10:48 pm

Was looking at your spec earlier Elle, Arcane Fortitude is a complete waste of a point imo, you'd be much better off finishing Arcane Impact.
It's the thought that counts, not how many people die because of it.

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