I'm going to split my thoughts on addressing this question over a couple of posts. This first post is essentially a stream-of-consciousness where I was trying to figure out how to structure my thinking on how to answer this question. The next post will be written to try to explain what conclusion I reached and how I reached it, so if you're not interested in the details it's safe to skip this post.
Max mana/hp matters in the tough fights where you're gonna end up almost oom/low-health at the end of the encounter. For a healer, it lets you sustain a healing chain longer. For a nuker, it lets you keep nuking non-stop for longer. So when deciding whether a slot should add X mana or Y health, the question becomes, what lets me sustain my max mana burn for longer? Neither mana nor health will let you burn mana faster.
So the question I'll try to answer is "using a manna robe, how do you maximize the time before hitting oom while burning mana at a constant rate."
If you're burning 500mana/minute, adding 500 mana gives you another minute of casting. Since manna robe converts 60hp->20m, 1500hp gives you another minute of casting. But this doesn't take into account passive mana regeneration, canni dancing, or passive hp regeneration. I'm going to refer to using manna robe as "canni", as it's similar to shaman cannibalization line.
To calculate how long you can burn, you need to know:
mana/minute burn rate: call it burn
total mana pool: call it pool
passive mana regeneration: call it passive
total hp available to canni: call it hp
canni burn rate in hp/minute: call it canni_burn
canni regen rate in mana/minute: call it canni_regen
simplest equation:
time = pool / burn, for example 3500 mana / (500 mana/minute) = 7 minutes. As a sidenote, the most important error-checking in calculations is dimensional analysis: mana divided by (mana/minute) gives you minutes, the right dimension you want to end up with. If you keep track of the units for each number, you can confirm that everything cancels out except the unit/dimension you're trying to calculate, time in this case.
Without manna robe:
total mana regen = time * passive
time = (pool + regen) / burn
time = (pool + time * passive) / burn
time = pool/burn + time * passive / burn
time - time * passive / burn = pool/burn
time * (1 - passive/burn) = pool/burn
time = (pool/burn) / (1 - passive/burn)
1 - passive/burn = (burn - passive) / burn
time = (pool/burn) * burn/(burn - passive)
time = pool/(burn - passive)
This makes sense. Effective burn rate equals actual burn rate minus mana regeneration
When adding manna robe, we can skip a lot of steps and just go to the last equation, adding canni regen:
time_to_oom = pool/(burn - passive - canni_regen)
or, if we define total_regen = passive + canni_regen, we have:
time_to_oom = pool/(burn - total_regen)
the other equation that matters is how long you can sustain canni:
time_to_low_health = hp / canni_burn
So, you want to ensure you have enough health to sustain canni until you hit oom.
Next, let's look at some of the regen rates. At 60, 21 mana/tick while medding gives you 210 mana/minute. 3.2 seconds per cast gives you 18.75 casts/minute, or 375 mana/minute with 1125 health/minute
With some rough numbers, we can start with a 3500 mana pool, 500 mana/minute burn rate, and maybe 2000 health to burn. That gives us 7 minutes before oom without manna robe, and perhaps two minutes of canni that can add 750mana, or another minute and a half of burn, getting us to 8.5 minutes. So clearly, we'll burn through all the health we feel safe burning before going oom.
Since that's the case, the encounter can be split into two sections. For the first few minutes we're going to canni down until we're at whatever low-hp threshold we're comfortable with. After that, we'll mostly med, adding a couple canni clicks as passive hp regen builds up.
The time spent canni-ing will be hp / canni_burn. During that period, the burn rate will be burn - passive - canni_regen. After that period and discounting passive hp regen, the burn rate will be burn - passive.
Passive hp regen will be 29 hp/tick or about one canni every other click.
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