I should start this post with the warning that the maths here, although strictly linear (and therefore boring if you’re a mathematician) does get a bit heavy. If you’re not someone to slog through equations, there is a handy TL:DR at the end.
Condensation Totem is one of the new Restoration Shaman talents which was shown off in the Blizzcon beta of Warlords of Draenor. It’s interesting because as well as being an exciting new totem, and a water totem no less, it looks like it could be used (and abused) as quite the healing boost. This post is dedicated to showing you what the totem behaves like, in the context of Mists of Pandaria. I chose to do the maths for the Mists of Pandaria spells for the main reason that it helps to put the results into context for the population of raiders right now. Changing the results to Warlords of Draenor numbers, as I will show you, is as simple as changing the relevant coefficients on a spreadsheet.
The post is laid out like this;
- To Craft a Theory (Algebra!)
- But What It Means?? (Crazy Graphs and More Algebra)
- Enough Maths! Gief Numbers! (Useful Bit)
- Me, thinks. (What I Think)
- Too Long: Didn’t Read?
To Craft a Theory
To start the analysis, let’s take a quick look at what we actually want to know; if I have Condensation Totem up, which spell should I spam to get the most benefit from it?
That’s quite a question. This will absolutely depend on a lot of factors; not least being the realities of keeping people alive while trying to build up the buff. For the sake of this analysis, we’ll assume that you have 0% Mastery, 0% Crit, and all spells hit for their mean value exactly. That means that for a general spell, with base healing constant K, spellpower coeffiecient C, and assuming that our heals always overheal by fraction O, the spell heals for healing H, and you gain spellpower S on top of your base spellpower s:
In the equations above, the subscript denotes which number heal we are on since we had no buff – you can think of the “current” cast as cast number i. Combine the two equations, and we find that you have to start nesting the terms, like this;
So if I expand the terms for i in the range 1 to N, we have an equation which has N nested terms like the following;
And there I’ve only expanded to the third term! The equation goes on for a huge number of terms once you’ve healed once or twice, so it’s easier to write it in sum notation;
Which is nice and compact. You’ll notice that the equation has removed all reference to the gain in spellpower from the last spell, because now it takes account of all spells you’ve cast.
Right now is a good time to remind everyone that this equation assumes that the overhealing of each spell is identical. That won’t ever happen in practice, but it’s as close as we can easily do in theory. If you think that you need to take account of that, I suggest you talk to the nice people at Simcraft.
But What It Means??
An equation is all very well and good, but can we take anything from it? Well… we can do some maths… and we can also calculate some numbers. Let’s just start by picking some random numbers and seeing what this model looks like;
Which looks pretty interesting; there seems to be a limit on the amount of spellpower you can get from the mechanic! To investigate further, I had a play around with the numbers and found that for some sets of parameters, this happens;
The spellpower gain can exponentially increase and become infinite! AAAAAAAAA! So here is where we look at why it does that. I’m going to do a bit more maths, but this is the last time. If we use d’Alembert’s Ratio Test for Convergence, we can tell whether the equation we found earlier becomes infinite or not. That’s a good sanity check. To you, that just means; as I keep casting, does the spellpower gain get bigger or smaller? If it gets bigger, does it become infinite if I keep casting forever?
To find out, I calculate the value R. If R is larger than 1, then shit gets crazy. If R is smaller than 1, things stay sane;
This means that for things to get crazy (and for us to get glorious hilarious infinite healing) we need;
So ultimately you can calculate whether things will go insane or not! Taking the optimistic case that you do 100% overhealing, that equates to a spellpower coefficient of 400% – entirely unattainable.
Now! Time to look at some credible values based on real life healing right now.
Enough Maths! Gief Numbers!
OK fine. I went ahead and used this model to calculate the maximum spellpower that you can get out of Condensation Totem based on the model. For this bit, I took the overhealing fraction O to be 1 (i.e. you’re doing 100% overhealing because you want to get insane numberzz). Using a base spellpower of 45k (roughly what my toon has these days) and the spellpower coefficients from wowhead, I calculated the maximum spellpower you can get for each spell;
Yes, you’re reading that number for Chain Heal right. I checked the coefficients and the base values and the cells, that’s actually a real number.
So now we know that Condensation Totem will be powerful in the ideal case, and that Chain Heal will likely get you the most spell power in that case. So what happens to these as the amount of overhealing goes down? I looked at how the spellpower buff changes for different overheal %, O;
So you can see that as the overhealing goes down, the spellpower you gain goes down. Also importantly, the number of casts it takes to reach that maximum increases! I think that this is important, since it takes about 10 casts (20 seconds!) to reach an optimal value at 100% overhealing, but only 3-5 casts in more “realistic” scenarios. I also put on that graph Greater Healing Wave with 100% overheal, and it shows that any realistic use of Chain Heal will probably be able to be matched by Greater Healing Wave casts (your GHW healing is much more likely to be an overheal since you can design it do be so). GHW also ramps up faster, thus saving you time and/or mana over a realistic Chain Heal cast.
To round off the analysis, I wanted to show that losing a few % overhealing really makes a big impact to the buff that you gain, and in the process demonstrate that we’re probably never going to see such crazy numbers.
As you can see, the change in spellpower as overhealing increased is not linear! That means that squeezing every last bit of overheal out will give really big increases in the benefit that Condensation Totem returns.
I’m in two minds about Condensation totem.
On the one hand, this is a really cool mechanic, and it’s in the form of a water totem which requires clever use and is on a short cooldown. I could really get behind another regular-use totem to improve our healing – I think it would add to the flavour of the spec and really change the way we play. I want that.
On the other hand, it’s bananas. Condensation Totem isn’t sensible. It rewards over-reliance on purposefully exploiting its mechanics. It encourages overhealing, and I for one really really miss the triage play that was the paradigm in early Cataclysm.
I want Condensation Totem to be awesome, but I don’t want healing gameplay to head further in the direction of spam that it has already gone in since the start of Cataclysm.
Too Long, Didn’t Read?
So maths aside, what are the important points of this analysis?
- The amount of extra healing you get drops off as your percentage overhealing decreases, but it’s still worth using even when you’re only doing 10-20% overhealing – it’s a reasonable increase whenever you can get it.
- The buff should take only 3-5 casts to reach optimality, or about 10s of casting in a real situation. Also in more realistic situations, Greater Healing Wave will be the spell of choice to ramp this talent up.
- With current coefficients, spamming Chain Heal will gain you the most Spellpower.
- With current coefficients, you could gain up to 120k spellpower when used optimally, disregarding critical strikes and other spells like Healing Rain. That would be a ~170% increase for my character as he is right now. HOWEVER the likelihood of actually achieving this is very small indeed.
- For this reason, the talent will probably change quite a bit.