[4xShammy Arena] ToW Theorycrafting

[Boylston]

I thought I'd open up a thread to do some theorycrafting (and real world discussion) about the choice between Totem of Wrath and Nature's Swiftness for a 4xElemental Shaman team. Here are (I think) the key tradeoffs:

Choosing Totem of Wrath over Nature's Swiftness:
+ Extra spell crit (to-hit seems largely unimportant) of 12%
- No nature's swiftness for Chain Lightning (or a heal)
- Totem of Wrath shares fire totem slot with the popular Fire Nova Totem (so its use once engaged with a melee might be limited)
+ Don't have to respec for Arenas if you like to PvE with ToW

The conventional wisdom is that Nature's Swiftness is too good to let go for Totem of Wrath, with PvP Resilience often being thrown out there as a counter to spell crit. This may be true, but I'd like to kick off the discussion with the strawman argument that ToW may be even more useful than people think due to resilience.

But first, some statistics!

I'm going to use Bernoulli Trials here to look at "binomial events". That is to say, when you cast a spell you either score a critical hit (with some probability, say P=0.20) or a normal hit (the other 80% of the hits, ignoring misses for a variety of reasons). When you play your 4 shammies and cast 4 lightning bolts, the important thing for PvP is how much burst damage you do when they land. What we really care about is the likelihood that we will have single, multiple, or NO crits out of that spell volley. Bernoulli trials can tell us some useful information about this unique question.

For example: Members of a 4xShammy team each have a crit percentage of 20%. If they all cast lightning bolt, there is...
a 59% chance that at least one of them crits. (Number of crits between 1 and 4)
a corresponding 41% chance that no one crits
an 18% chance that you get 2+ crits
and a very, very unlikely shot at everyone critting (about 1 in 625 volleys)

From a PvP perspective, again, these multi-crit chances are very interesting to us because they allow the target to take much more damage and possibly die in just 2 global cooldowns. So, let's try some interesting scenarios and compare them against each other.

Scenario 1:
Reasonably well geared PvP shaman group (20% crit) fighting other reasonably well geared opponents (400 resilience, say -10% crit chance)
OR
Not so uber geared shaman team (15% crit) fighting not so well geared opponents (200 resilience, -5% crit)
Net crit chance: 10%

Scenario 2:
Same as above, but with 4xToW added (+12% crit)
Net crit chance: 22%


Scenario 1 (no-ToW):
Chance of no-crits on 4xSpellcast: 66%
Chance of 1+ crit: 34%
Chance of 2+ crits: 5%

Scenario 2 (ToW):
Chance of no-crits on 4xSpellcast: 37%
Chance of 1+ crit: 63%
Chance of 2+ crits: 21%

To make it more interesting, extend the spell volley to 8 spells (say a LB+CL opening attack)...
Scenario 1: Chance of 3+ total crits: 3.8%
Scenario 2: Chance of 3+ total crits: 24.8%

You may be thinking/asking about Lightning Overload (the talent, not my blog ). Since LO has a 20% chance to proc, you can use the first example to think about what you'll expect to see for LO procs. 59% chance that at least 1 shammy gets a proc, 18% chance that two or more get a proc. I haven't done this yet, but it would be possible to build out an event tree to capture LO procs and their corresponding crit chances.

At any rate, with just a little bit of theorycrafting, it would seem that stacked ToWs would provide a nice increase to the chance that you'll get good burst damage on each spell salvo. The 2+crit events happen at a 1 in 5 rate as opposed to a 1 in 20 for the hypothetical examples above.

At the end of the day, I think the NS+EM+CL button offers many benefits over ToW, but it might not have as much of a commanding advantage over the ToW stacker as we once thought. For a player who is mixing PvE and PvP challenges, ToW may provide a good return on your investment and not require constantly respeccing. ToW may also be superior for BG players who are operating in a defensive or "totem fortress" configuration where they have long periods of time with many opponents (i.e. multiple salvos).

For fun, if you consider a very different case, say, Ellay's guys + 4xToW vs. "scrubs" in the BG with 150 resilience, his crit percentage would be about 29.25% (21+12-3.75). For an "Ellay vs. n00bs Salvo", that's:
Chance of no-crits on 4xSpellcast: 25% (47% w/o ToWs)
Chance of 1+ crit: 75% (53% w/o ToWs)
Chance of 2+ crits: 34% (14% w/o ToWs)
Chance of 3-4 crits: 8% (1.8% w/o ToWs)



(Bernoulli Trials tool at http://people.hofstra.edu/Stefan_Wan...bernoulli.html )

[aetherg]

I think that's the first time I've ever heard someone say 'binomial events' on a video game message board . Muliboxers are a well-educated group!

One thing you're not factoring in is the fact that resilience not only lowers the chance to crit, but the crit damage as well. Your crits will lose up to 25% of their damage. In most cases you'll see a 20% reduction, since that's the level of resilience that the average PvPer has reached.

And I think the main benefit of NS is not its damage, but the fact that it's instant. When you go TOW, you may do more damage per spell, but you have to stand still to cast. Going NS lets you fit that damage into a shorter period of time, as well as doing it while moving.

[Boylston]

I should say that I fully appreciate the benefits of NS, especially the on-the-move aspect of it (and the fact that shamans have basically no anti-pushback abilities). It will be what I respec to after the rest of my 4xShaman team dings L70 (I plan to spend a lot of painful deaths in the arena). However, I think I might seriously reconsider if I was going to do primarily fight in BGs. I also think it's a tougher choice than most of us would have guessed-- even with some crit damage reduction, I can see a lot of scenarios where someone dies in 2 GCDs as opposed to 3...


Short story: I'm not trying to advocate ToW over NS. I'm just showing the negative trade-offs for choosing NS, which is significant decrease in the crits/salvo that you'll see. I also think the math supports it being a good battleground or casual arena spec for someone who might be loving ToW for PvE/gold farming in instances.

[Quasi]

From everything I've read, the high end of arenas revolve around stategies more than anything else. With that said, I beleive Ellay's strat. largely depends on NS + EM + CL = one player is dead, instantly. He drops somebody right off the bat, or severely damages three, making there healer work while he selects somebody else to drop.

With 4x ToW, sure, he could pump out a lot more damage, but the element of BOOM - YOU ARE DEAD is gone.

You know, before this thread, I'd never really considered ToW.

I think with Bloodlust, Lightning Overload, and the change to haste reducing your GCD, it would appear that ToW is superior.

[Ellay]

NS wins games. Not much else to be said. I've had games where the only way I could drop the opposing team was by NS, would drop a target, wait 3 minutes, drop another, wait 3 minutes drop another.

[Boylston]

[quote='Fursphere',index.php?page=Thread&postID=331 72#post33172]From everything I've read, the high end of arenas revolve around stategies more than anything else. With that said, I beleive Ellay's strat. largely depends on NS + EM + CL = one player is dead, instantly. He drops somebody right off the bat, or severely damages three, making there healer work while he selects somebody else to drop.

With 4x ToW, sure, he could pump out a lot more damage, but the element of[b] BOOM - YOU ARE DEAD [/b]is gone.[/quote]To be precise, the combo of Trinkets + EM + CL is very brutal. If you run Monte Carlo simulations on your expected damage with various spell combinations (again, math/statistics, I know), you'll find that the MINIMUM damage you can deal with a Lightning Bolt+Chain Lightning combo goes up through the roof when you add the trinkets and Elemental Mastery to the CL cast. Nature's swiftness allows this spell combo to happen 1.5sec sooner and with no spell pushback problems.

It is Elemental Mastery guaranteeing critical hits with a lot of +SpellDmg that is the big thing to getting the first kill. Granted, it's nice to have it instant... Here's a different kind of math.

1000 runs of LB+CL+ an earth shock followup (Assumed normal non-crit hits of LB=1350, CL=1450, ES=550 and 15% effective crit rate):

[b]No EM used for Chain Lightning:[/b]
[font='Courier New, Courier, mono']Average LB+CL Total 12,958
Average LB+CL+ES Total 15,491
Minimum LB+CL Total 11,200
Minimum LB+CL+ES Total 13,400

[/font]EM popped for Chain Lightning:
Average LB+CL Total 17,786
Average LB+CL+ES Total 20,320
Minimum LB+CL Total 17,000
Minimum LB+CL+ES Total 19,200

(I won't post the full numbers, but for this example throwing ToW into the mix would increase the average LB+CL and LB+CL+ES combos by about 1800-2000 points without EM used and 600-750 for the EM+CL case.)

In any event, the magic of the OMGWTFBBQ! kills is 4xEM+CL. Nature's swiftness allows that to happen on insta-cast, but even a 41/0/20 Shaman has EM at their disposal for a huge chunk of damage in ~4sec.

[Boylston]

NS wins games. Not much else to be said. I've had games where the only way I could drop the opposing team was by NS, would drop a target, wait 3 minutes, drop another, wait 3 minutes drop another.

Fair enough.

Do you think you could play a team of 600 +SpellDmg geared shammies (say, 250 resilience) with Totem of Wrath and sustain... 1700 rating? 1800 rating?

I'm guessing your team now does about 12,000-13,500 damage with a NS+EM+Trinket+CL combo? Is that about right?

[Boylston]

NS wins games. Not much else to be said. I've had games where the only way I could drop the opposing team was by NS, would drop a target, wait 3 minutes, drop another, wait 3 minutes drop another.

Fair enough.

Do you think you could play a team of 600 +SpellDmg geared shammies (say, 250 resilience) with Totem of Wrath and sustain... 1700 rating? 1800 rating?

I'm guessing your team now does about 12,000-13,500 damage with a NS+EM+Trinket+CL combo? Is that about right?

I guess what I'm saying is "Throw out the goals of hitting 2000+ Arena Rating". Can you still be "good" or even "great" at PvP and not have NS...?

[Boylston]

Boylston -

I think I just figured out part of the equation you're not factoring in = Lightning Overload. 20% chance to instant cast a 50% damage spell that can crit at no mana cost. i don't know if EM makes the LO crit as well... probably not.

But, if the winds were in your favor, thats a possible of EIGHT instant cast spells hitting up to three targets, and four of those can crit (actually its 12 if you are in range for a follow up shock attack). In my own personal experience W/O NS in world PvP, so many times I've been trying to blast someone where they either go out of casting range or "not in front of you" .1 secs before the spell casts - Very fustrating. A good PvPer will see when you start casting (1.5 secs seems fast, but its not) and either get out of LOS, or get out of range. Its really a Shaman's only weakness.

You are correct in saying that the Monte Carlo-like analysis that I did above doesn't yet have LO procs. Again, if you read the very first post, you can see that LO will proc on at least one shammy 59% of the time-- it's common and not insignificant. I am 95% sure that EM does NOT guarantee a subsequent LO proc. But LO is the same for all shammies who put 40 points in Elemental, as is EM. The real tradeoff is ToW vs. NS.

To make it concise, a summary of the discussion thus far is:

1.) EM+Trinkets+Orc Racial+Chain Lightning = Guaranteed Large Damage Spike - Well geared, this is going to 1-shot a lot of people
2.) NS+(EM+Trinkets+Orc Racial+CL) = Instant Cast Guaranteed Large Damage Spike
3.) NS+(EM+Trinkets+Orc Racial+CL)+LO-Proc(s) = Insult to injury (59% of the time)

4a.) ToW+PewPewRotation = Better DPS and burst potential than PewPewing without ToW, even in PvP with resilience mitigating some +Crit (I think this bolded part is what the math shows)
4b.) ToW = Always available, not tied to a cooldown, but disappears if you drop a Fire Nova Totem


So, a 41/0/20 gets the advantages of 1.), 4.), while the 40/0/21 gets 1.), 2.) and 3.).


Ellay contends that the defining advantage of the 4xShaman combo in the uppermost ranks of the 5v5 arena is that he can transform 1.) into 2.). Instant cast >> any possible ToW advantage. I tend to agree with him, especially since you can tell by his comments that he's fighting teams who know what he's capable of and keep out of his LoS/range as much as possible in hopes that he'll disco/drop/fall asleep before the battle is over. He HAS to play a cat and mouse game where he goes in and pops 1-2 instant cast spells in order to kill one. As he's mentioned, often times the dodge-ball game continues while they try to rez the unlucky bastard who ate the first NS+EM+CL barrage. They play into his hand to some extent by allowing 3min to pass and resetting this brutal ability.

ToW appears (from the math, anyhow) to be a really decent choice for PvP if you are not tightly constraining it to fit Ellay's 1900+ rated 5v5 matches. It's probably a decent choice for a Battleground hound in AV who is going to play "mobile totem fortress" and pew pew the heck out of people with the support of other players. It's better sustained DPS and has the nice side effect of providing a LOT more double+ crit volleys of whatever spell you're throwing at them. That kind of player will STILL have the EM+CL burst capability, just with a 1.5sec cast time. (I know it's not as nice as instant, but it's still short). It's probably not also so far behind a NS build that you'd want to blow 400g respecing back and forth if your arena goals are far more modest. In theory, you could play four 0/10/51 Resto shammies as ranged casters in an arena, but I think we'd all agree you'd be horribly prepared for success in that spec. The original reason for exploring the math behind ToW is that I would have assumed that ToW provided almost no benefit for PvP due to resilience-- turns out that gut feeling is probably wrong.

Personalizing it, I'm not sure that I will immediately go to a 40/0/21 arena spec when my guys hit L70-- I have a lot of cash farming and BG honor farming to do before they are going to do anything other than suck in the arenas. If I can maintain a 1500 rating with the team for the first 6 weeks, I'd be tickled pink (and accumulating arena points). Keeping a ToW build for that interim period may not be best for arena, but it's probably going to perform much better than I originally thought.

[Boylston]

Absolutely, ToW shines in Artillery Mode, as you call it.

My three little guys have it (well, Boylston does too when he's not Resto for certain raid events), and I only use it in two situations:

a.) I'm in an instance and relatively immobile while I pew-pew stuff down
b.) I need to kill a mob for a quest +3/4 levels above me

In outlands, most of the time I don't drop any totems while I'm out and about. What's the difference between killing the mobs in 2 spell volleys or REALLY killing them in 2 spell volleys? I will occasionally drop ToWs and some streams if I'm in a target-rich locale, but most of my time is spent running between very quick kills while questing.

When I use it however, it makes a significant difference. I wouldn't want to grind instances without it!!