The truth about WOTLK Totem of Wrath

[BobGnarly]

So maybe you've seen me talking about how the new ToW is not a nerf, but in most cases actually a buff for multiboxing shaman. I assert that ToW, on its own, is much better in WOTLK, and even good enough to equal or exceed multiple live ToWs. Here's proof.

Understand that there are tons of variables in this situation. I am just going to choose some "reasonable" baselines to give some feel for the change. Just know that these numbers aren't absolutes.

Assume:
- level 80 shaman
- 1500 spell damage
- 25% chance to crit.
- Using level 79 lightning bolt "Casts a bolt of lightning at the target for 715 to 815 Nature damage." This spell has a 79.4% spell damage coefficient due to its cast time of 2.5s and modified up after the infamous "LB/CL elemental nerf" of 2007. See wowwiki.

To compare crit to damage, we first need to come up with some sort of equivalency between the two metrics. Let's consider the case of 100 casts.

ncrits = number of casts that are crits
crit_multiplier = how much a crit multiplies your damage = 2.0 for shaman assuming presence of lightning fury talent.
spell_dmg = amount of spell damage.
spell_coeff = spell damage coefficient - given as 79.4% above.
avg_dmg = average spell damage = ((715+815)/2) from above.

So, the formula to calculate the damage done by 100 casts would be:

(((avg_dmg + (spell_dmg * spell_coeff)) * ncrits) * crit_multiplier) + ((avg_dmg + (spell_dmg * spell_coeff)) * (100 - ncrits)) = dmg.
(((765 + (1500 * 0.794)) * 25) * 2) + ((765 + (1500 * 0.794)) * (100 - 25)) = 97800 + 146700 = 244500 damage done over 100 casts.

Now, consider another 100 casts, but with 1% more crit chance:

(((765 + (1500 * 0.794)) * 26) * 2) + ((765 + (1500 * 0.794)) * (100 - 26)) =
(1956 * 26 * 2) + (1956 * 74) = 101712 + 144744 = 246456 damage done over 100 casts.

Raising 1% crit gave us an extra 1956 damage over 100 casts (which sounds right intuitively since making one more cast a crit, and a crit is double damage, is something like just adding one more cast - which are each 1956 damage).

So how do we relate that to spell damage? Well, we need to figure out how much we'd need to raise our spell damage in the above equation to put us at the same net damage as the case where we raised the crit 1%. The easiest way to do that is solve for spell dmg and just plug in the numbers.

First, let: castdmg = avg_damage + (spell_dmg * spell_coeff)

Insert into our eq:

dmg = (castdmg * ncrits * crit_multiplier) + (castdmg * (100 - ncrits))

distribute castdmg:

dmg = (castdmg * ncrits * crit_multiplier) + (100 * castdmg) - (castdmg * ncrits)

factor out castdmg:

dmg = castdmg ((ncrits * crit_multiplier) + 100 - ncrits)

solve for castdmg:

castdmg = dmg / ((ncrits * crit_multiplier) + 100 - ncrits)

To check our math, plug the original back in:

castdmg = 244500 / ((25 * 2.0) + 100 - 25) = 1956
castdmg = 1956

Which we can tell is right, but for completness, plug it in to our substitution:

castdmg = avg_damage + (spell_dmg * spell_coeff)

solve for spell_dmg:

spell_dmg = (castdmg-avg_damage) / spell_coeff
spell_dmg = (1956 - 765) / .794 = 1500. Which is exactly right, so we have some confidence in my math.

OK, now what I want to do is solve this same equation, but rather than using the baseline "dmg", I use the "dmg" from the crit example. This will tell us how much spell damage I would need to see exactly the same damage as I saw from the crit increase, which is what we are after. So:

castdmg = dmg / ((ncrits * crit_multiplier) + 100 - ncrits)
castdmg = 246456 / ((25 * 2.0) + 100 - 25) = 246456 / 125 = 1971 damage.

solve for spell_dmg again:

spell_dmg = (1971 - 756) / .794 = 1530

So adding 1% crit is roughly the same as adding 30 spell damage in the above scenario.

Now, given this knowledge, let's make some comparisons (I am assuming you can get your enemy with 40 yards. If you can't, you can't cast on them anyway):

WOTLK totem = 280 spell dmg and 3% crit (or 90 dmg) = 370 dmg.
Live totem = 3% crit (or 90 dmg) = 90 dmg.

Not much of a comparison, huh?

In fact, four live totems will be 12% increase crit chance. 12*30 (30 dmg per crit) = 360 dmg.

Too Long: Hate Math version:

It would take 4 live totems to equal the one new ToW.

For those running 5 shaman teams, you might lose a little damage, but you do have one other totem slot for other use.

Four live ToWs are approximately equal to one post-wotlk totem, so those of us with the 1 paly 4 shaman team are going to be about equal.

Anything less than 4 shaman in a group will see a pretty substancial buff.

[Oatboat]

Holy Rusted Metal Batman!

I fail at algebra/math/geometry/calculator. Luckily there are people like you that i can sponge off of! Thanks for the hard work!
I'll turn it in for an A+ on my next paper.

[Rin]

You beat me to it. Great post :thumbsup:

[ithkus]

Nice post Bob, thanks. Are you the same BobGnarly that plays on Uther?

[Aradar]

You may want to rerun your numbers as they have nerfed the coefficient back to around .71 based on the nature debuffs now provided by druids/warlocks. However, they have admitted that this creates a problem for solo play and 5 mans where those other two classes are less likely to be in the group and are working on a solution.

Blue post admitting nerf.

Blue post saying they are working on the solo/small group aspect.

[Souca]

I like the math; it's refreshing to see people back up their arguments. That said, the math doesn't take into account any secondary effects of crit such as clearcasting and other procs. While I don't think it's a huge factor, I did want to point it out. It would also be interesting to see how much extra dps searing totems add when they can be dropped insterad of the extra ToW.

- Souca -

[Aradar]

I ran the numbers and as you said, currently each ToW is worth 90 damage, whereas in the current beta build considering the coefficient change, ToW is worth ~342 so it depends on how many you are currently dropping.

Souca also has a good point since there are so many other factors that go along with this, for example, assuming a holy trinity setup with 3 ToWs, you just lost 9% of your hit, not to mention the 3% in elemental precision lost or the 3% lost in nature's guidance. You're going to have to sacrifice enchants/gem slots to make up for that differance.

I applaud your effort and I think you make a good point but the factors go on and on...

[Ughmahedhurtz]

So, basically, just spec 40/21 on everyone but the one guy that specs for ToWrath...even for PVE. Schweet. Of course, I didn't bet the farm on shammies, so even if they'd deleted ToWrath from the tree it wouldn't have affected me that much.

[bodefeld]

I agree. It's also nice to have a few searing totems in the standard totem setup. (Have we got numbers as to how spellpower will scale into those?)

However, it was the 15% +spell hit I got from 5 ToW that catapulted my team to the spell hit cap (with the head enchantment). So even with cheap PvP gear I could seriously participate in the PvE content -- especially since the ~50% spell crit (after spec) along with clearcasting compensated well for the lack of mp5 on PvP gear.

But heck, I'm positive! How much have we got till wotlk? 4 weeks? Yummy!

[Aradar]

[quote='bodefeld',index.php?page=Thread&postID=1279 79#post127979]It's also nice to have a few searing totems in the standard totem setup. (Have we got numbers as to how spellpower will scale into those?)[/quote]

According to WoWWiki these are the [b][u][i]current[/i][/u][/b] Shaman spell coefficients:

Ability Name - Spell Damage/Healing Coefficient

[b]Healing Abilities [/b]

Chain Heal 125.0% (71.43% + 35.71% + 17.86% on each "jump", respectively)
Earth Shield 285.7%
Healing Stream Totem (per tick) 4.5%
Healing Wave 85.71%
Lesser Healing Wave 42.86%

[b]Offensive Abilities [/b]

Chain Lightning 125.0% (71.43% + 35.71% + 17.86% on each "jump", respectively)
Earth Shock 42.86%
Fire Nova Totem 21.4% (untested)
Flame ShockDD 15%
Flame ShockDoT 52%
Flametongue Weapon (per hit) 10%
Frost Shock 42.86%
Frostbrand Weapon (per hit) 10%
Lightning Bolt 79.4%
Lightning Shield 100%
Magma Totem 66.7% (untested)
Searing Totem 16.67% per shot and randomly +1 damage

For those with non shaman characters, here is the [url='http://www.wowwiki.com/Spell_damage_coefficient']page[/url].

Obviously these reflect the current system and not the incoming spellpower change which will add another twist, not to mention changes in spell coefficients themselves like I mentioned earlier with Lightning Bolt.