Arcane Mage: Stats contribution

by Tachyon on Wed. 23. September 2009, 20:47

Filed under: arcane, spec, theorycrafting, analysis

In the previous article, we derived the formulas to calculate the DPS (Damage per Second) and DPM (Damage per Mana) for the two suggested new arcane rotations (covered in this article).

The formulas are based on the mage's spellpower, crit chance, hit chance and haste. In this article, we want to further split up those variables and show how they are calculated from your mage's stats (intellect, spirit, spellpower, crit/hit/haste rating), talents and glyphs (for arcane mages: Glyph of Molten Armor, Glyph of Arcane Blast, Glyph of Arcane Missiles).
Given those refined formulas, we can then investigate how much each stat contributes to the new spell rotations' DPS.

Stats conversion

Intellect
Intellect is increased by 15% by the Arcane Mind (5/5) talent:
effectiveIntellect := intellect * 1.15
Spirit
Spirit is increased by 10% by the Student of the Mind (3/3) talent:
effectiveSpirit := spirit * 1.1
Spellpower
Spellpower is increased by 15% of your intellect by the MindMastery 5/5 talent:
effectiveSpellpower := spellpower + effectiveIntellect * 0.15
Crit%
The base class crit chance for mages is 0.91%. Intellect will also increase your crit chance (by 1% every 166 2/3 int). The rest of your crit chance is determined by your crit rating (1% per 45.91 crit rating), whereas you get 55% of your spirit as additional crit rating if you use Molten Armor with its glyph (with 2pT9 bonus it would be even more). Crit% is capped at 100%, for obvious reasons.
crit% := min (1, 0.0091 + effectiveIntellect * 3 / 50000 + (critRating + spirit * 0.55) / 4591)
Hit%
Against boss targets (who are considered lvl 83), you have a 17% chance to miss with spells. Arcane Focus (3/3) increases your hit chance by 3%, and in any reasonable raiding scenario an additional 3% is contributed by a Shadow Priest (Misery debuff) or Balance Druid (Improved Faerie Fire debuff). Additional hit rating will grant you 1% hit per 26.23 rating, or 17% for 446 rating. Hit% is also capped at 100%.
hit%:= min(1, 0.83 + hitRating * 0.17 / 446 + 0.03 + 0.03)
Haste%
32.79 haste rating grants 1% haste, and from Netherwind Presence (3/3) you get an additional 6% haste.
haste%:= hasteRating / 3279 + 0.06

DPS per stat: Graphical analysis

To find out how much additional stats contribute to the DPS, we can start with a base set of stat values, calculate the base DPS for that stat combination using the DPS formulas, and calculate the relative DPS increase that results from increasing any of the stats individually. Details on the spell rotation used here can be found in this article.

For a basic poor mages' stat combination, I chose the following values:
500 intellect, 200 spirit, 1500 spellpower, 0 crit/hit/haste rating.

Chart: Relative DPS increase per additional stat value, A=0/B->Infinity rotation:


As you can see, hit rating proves to be the most important stat until the hit cap is reached; after that point it ceases to provide any more DPS.
We can now calculate the Spell Power Equivalent (SPE) value for each stat, which allows us to compare how much each stat is worth compared to 1 spellpower:

1 hit rating = 1.2280 spellpower
1 crit rating = 0.4917 spellpower
1 haste rating = 0.8250 spellpower
1 intellect = 0.3269 spellpower
1 spirit = 0.2975 spellpower

Those values vary depending on the given stat combination, but using the formulas above you should be able to do the math to find out the SPE values for your current gear.

Once you reach the hit cap, and your stats get better, the chart and SPE values will look a little different. As an example, here's the results for my current gear:
1170 intellect, 634 spirit, 2411 spellpower, 370 hit rating, 582 crit rating, 481 haste rating.

Chart: Relative DPS increase per additional stat value, A=0/B->Infinity rotation:


1 hit rating = 0.0000 spellpower
1 crit rating = 0.5659 spellpower
1 haste rating = 0.9828 spellpower
1 intellect = 0.3559 spellpower
1 spirit = 0.3424 spellpower

The chart for a A=4/B->Infinity rotation looks almost the same:

Chart: Relative DPS increase per additional stat value, A=4/B->Infinity rotation:


1 hit rating = 0.0000 spellpower
1 crit rating = 0.5663 spellpower
1 haste rating = 0.9983 spellpower
1 intellect = 0.3560 spellpower
1 spirit = 0.3426 spellpower

Here, additional hit rating is completely worthless, and haste rating has become worth as much as spellpower (in fact it will even become worth more that spellpower the better your overall stats are).

For more accurate results, you can try to take all raid buffs into account and inject them in the formulas, or use your raid buffed stats as an input.
The aim of the formulas is to give you a tool to do some quick analyses and comparisons, but keep in mind that they cannot be as accurate as a simulated scenario which also takes raid buff uptimes, trinkets, movement, lag, input delay and different encounter lengths into account.

Oh, and thanks to Google for their wonderful and well-documented Chart API, which I used for the charts here and intend to use from now on whenever suitable

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