PvP or PvE?
PvE. The only PvP format where MM's are viable is AB. And there you pretty much need to play one particular N/D build to stand any chance of surviving opponents who are (usually) smart enough to prioritize killing you above all else. PvE is the only situation where you have much of a choice. This is about PvE.
Why must a MM have a self-heal in the first place?
If you have to ask, you probably shouldn't be playing a MM build in the first place... However, for the sake of those who can be taught, here's a brief summary of the reasons why: An unavoidable part of being an MM is sacrificing 25% of your health every 6 sec or so. Forcing your monks to handle that is (1) rude, if they happen to be a live person, and (2) dangerous because it diverts a lot of their energy and cast time from dealing with monster damage to babysitting you. Thus, you need to self-heal your sacrifice costs. Moreover, the above presumes the best case scenario that your monk is alive, hasn't rage-quit, isn't afk, isn't out of energy, and isn't just plain stupid. All of which are true from time to time. You really can't afford to turn into useless deadweight because your monk has poor e-management or insists on believing that life sheath or prot spirit works on your life sacrifices. Thus, you need a self-heal so that you can keep your army running regardless of how good or bad your monk is.
What makes a good self heal?
I'm looking at two major criteria here. They tend to force the conclusion to the point that discussing other criteria is not necessary here. The two major criteria are:
(1) Unconditionality.
A self-heal that relies on a condition beyond your control is no good. You simply cannot afford to have your army die because you couldn't get a foe under 50% hp on schedule, or none of your foes was enchanted, or there were no corpses to eat while moving between battles, or whatever. Some conditional heals make excellent secondary healing options, if you want to dedicate a second skills to that purpose. But all of them fail a priori as primary self-healing options.
(2) Maximum Supportable Max Health.
How high can you get your max health and still afford to heal back 25% of it every 6 sec or so, given your self-heal's e-cost, cast time, recharge time, mechanics, and amount healed?
Maximum supportable max health is a function of healing/time: Start with the presumption that you have at least 1 minion at max degen. Max degen is -20hp/sec. BotM heals for 122 at 16DM. 122hp/cast / 20/hp/sec = 6.1sec/cast. Presuming you are maintaining the 10 minion max, the sac for BotM is 25% max hp. Divide by 6.1 equals ~4.1%max_hp/sec. The more healing/time you get from your self-heal skill, the higher max hp you can afford to support.
Healing/time is in turn a function of healing/cast and cast/time. Healing/cast is apparent from skill descriptions. Cast/time is going to be capped by the lowest of the three following limitations: Cast time. A self-heal does you little good if it eats up so much of your cast time that there's no time left to summon or do other things. Assuming you cast BotM once every 6.1 sec, and one summon (with bloodstained insignia) every 6.1 sec (that's questionable, but I don't have a better figure), and then add in aftercast delays, and you're looking at 4.75 out of every 6.1 sec, or ~78% of your time, dedicated to BotM and summoning. To fit into that remaining ~22%, a skill with a 1sec cast cannot be cast more often than once every ~7.9sec, and a skill with a 2sec cast time cannot be cast more often than once every 12.4sec. If you add Masochism into the mix once every 30 sec, these numbers become ~10.7 for 1 sec casts and ~16.9 for 2sec casts. (Exact figures can be found at the end of this post.) Recycle time. (Obviously) You cannot cast a skill more frequently than it's activation time plus its recharge time. Energy cost. You cannot cast a skill more frequently than you have the energy to afford to do so. In the worst-case situation (either moving between battles or fighting a battle where you are struggling to make a kill), your energy income is going to be limited to 4 pips, or 4/3 e/sec. BotM is going to eat 5/6.1 e/sec, leaving you with 0.513661202 e/sec to pay for your self-heal. Here's where Masochism works the biggest change: Assuming a SR rank that returns 3 energy per sac, using masochism leaves you with a much more robust 0.838797814 e/sec to finance your self-healing. (Though, ultimately, you might prefer to go with a lower max life and put some of that energy towards more damage, you have the option of spending all of it on self-healing.)
Some assumptions about attribute points and such.
For the purposes of these numbers, I'm going to be making some assumptions. Some are stated above (ie 10 minions, at least 1 minion at max degen, BotM as your minion heal, etc.). To try to make the rest clear: I'm assuming 16 Death, 10+1 or 10+2 SR (exact value doesn't matter here), and 8 in your self-healing attribute (9 if it's a necromancer attribute). I'm assuming no special items other than a bloodstained insignia. If I add in special equipment, I'll make an express note of it.
Self-Healing Skills:
Aura of the Lich
[skill]Aura of the Lich[/skill]
Unconditional: Yes.
Maximum Supportable Max HP w/ or w/out Maso:1122.4 (pre-AotL) (limited by recycle time)
Notes: You must recast it on recharge to achieve this effect. (The heal effect occurs regardless of whether you recast, so you get the most healing by recasting whenever possible.) A 20% enchant mod has no effect whatsoever (except to delay the first heal you receive).
Heal Area/Karei's Healing Circle
[skill]Heal Area[/skill]/[skill]Karei's Healing Circle[/skill]
Unconditional: Yes.
Maximum Supportable Max HP w/ Maso:
When healing self + minions: 628.3 (limited by energy) (accomplished by using BotM once every 13.9534884 sec and Heal Area once every 9.77198697 sec.)
When healing self only: 225.1 (limited by energy)
Maximum Supportable Max HP w/out Maso:
When healing self + minions: 517.0 (limited by energy) (accomplish by using BotM once every 12.5625 sec and Heal Area once every 10.6914894 sec.)
When healing self only: 137.9 (limited by energy)
Notes: Heal Area only works so well because it can also heal minions, thereby reducing the energy and life sac you have to spend via BotM.
However, once a fight starts and the minions leave Heal Area's range, a secondary self-heal is absolutely necessary. Conditional heals are OK for a secondary, in-battle self-heal. (Vampiric horrors are highly recommended.)
In order to achieve the maximums for healing self + minions, you'd need to use, by definition, the least efficient distribution of your energy between BotM and HA possible (that still keeps the minions alive). As a practical matter, you would be much better off going with a lower max health, casting BotM more, casting HA less, and using the energy you'd save for other things.
My prior post were erroneous. I baselessly assumed that HA and BotM must be cast in a 1-to-1 ratio, and permitted that ratio to limit casting rates, rather than energy, recycle, or cast time. (Energy is the proper limiting factor in this case.)
Derivation: Since these figures were somewhat difficult to produce (and I mucked them up the first time), I've decided to give the derivation of the self+minions, no maso case for those who'd like to reproduce/ammend my figures at the bottom of the page.
Mystic Regeneration
[skill]Mystic Regeneration[/skill]
Unconditional: Yes.* Relies on your ability to keep other enchantments active, but that's (generally) trivial.
Maximum Supportable Max HP w/ Maso:
No Extra Enchantments: 292.9 (limited by speed of regen)
One Extra Enchantment: 439.2 (limited by speed of regen) (Assumes either Infuse Condition or Dark Bond (@ 3 blood) for the third enchantment.)
Two Extra Enchantments: 488 (limited by speed of regen) (Assumes Infuse Condition or Dark Bond (@ 3 blood) for the third and fourth enchantments.)
Maximum Supportable Max HP w/out Maso:
(Assumes Mystic Regen + Dark Bond + Infuse Condition.)
W/ 20% enchant mod: 349.7* (limited by energy) (see note below)
W/out 20% enchant mod: 259.5* (limited by energy) (see note below)
Notes: Using Masochism, a 20% enchant mod will not increase the max life you can support, but it will increase the amount of spare energy you'll have around.
The non-masochism figures assume that Mystic Regen is the skill that doesn't get recast on the recharge to stay within 4/3 e/sec. I believe that cheaper cost/sec of the other enchants and the fact that they too are needed for max regen makes this the optimal choice. However, if I was ever able to prove that, I've forgotten how. These figures might need revising if someone can disprove that assumption.
The usefulness of Dark Bond, Infuse Condition, or any other cheap, long-lasting substitute enchantments in the PvE environment is questionable. They make the build work, but at the cost of skill slots that could be dedicated to more useful skills.
Using Aura of the Lich in addition to Mystic Regen (and a third enchantment) is a popular build (probably due to its usefulness in AB), but it is, in fact, less energy efficient than simply devoting more energy to recasting AotL more frequently. Mystic Regen adds nothing unless you're already recasting AotL on the recharge.
Spirit Light
[skill]Spirit Light[/skill]
Unconditional: Yes.* Though you need a spirit for optimal results.
Maximum Supportable Max HP w/ Maso: 382.6 (limited by cast time)
(If we disregard the cast time limit (b/c it's based on my arbitrary estimate summon frequency), we'd get 415.8* (limited by energy) and no time to cast summons.)
Maximum Supportable Max HP w/out Maso: 219.1* (limited by energy)
Notes: Assumes either Pain or Bloodsong recast every 33 sec. Using a more expensive spirit like vampirism lowers the maso value to 324.2 (limited by energy).
Blood Renewal
[skill]Blood Renewal[/skill]
Unconditional: Yes.
Maximum Supportable Max HP w/ or w/out Maso: 328.2 (limited by recycle time)
(Adding a 20% enchant mod increases it to 337.0.)
Notes: Not the super-fantastic self-heal it's made out to be. Multiple 25% sacs in succession can get dangerous.
Leader's Comfort
[skill]Leader's Comfort[/skill]
Unconditional: Yes.* (The condition is trivial since having the minions you need to heal meets it.)
Maximum Supportable Max HP w/out Maso: 274.9 (limited by cast time)
(If we just toss the cast time limitation (since I arbitrarily pegged that figure) we get 342, limited by recycle time.)
Maximum Supportable Max HP w/ Maso: 202.4 (limited by cast time)
(342 (limited by recycle time) if we ignore the cast time limit.)
Notes: Unpopular, despite mathematical superiority to some other popular options.
Generous Was Tsungrai
[skill]Generous Was Tsungrai[/skill]
Unconditional: Yes.
Maximum Supportable Max HP w/ or w/out Maso: 259.3 (limited by recycle time)
Notes: Also it sticks you with an ashpot that yo-yo's your energy, toggles your staff mods on and off, and mucks up your minion control by preventing you from wanding. Ridiculously overrated.
Healing Breeze
[skill]Healing Breeze[/skill]
Unconditional: Yes.
Maximum Supportable Max HP w/ Maso: 245.6 (limited by energy)
(286.5 if you shirked points out of SR to get to 9 healing.)
Maximum Supportable Max HP w/out Maso: 150.4 (limited by energy)
(175.5 at 9 healing.)
Notes: Even if energy weren't a problem, it would be capped at 292.8, b/c that's as fast as 6 regen can go.
This entry in my prior posts was erroneous. I assumed the speed of regen was the limiting factor without noticing that energy actually capped it lower.
[EDIT: Healing Breeze was changed so that it lasts for 15 sec and gives 7 regen at rank 8. New figures are:
Maximum Supportable Max HP w/ Maso: 341.6 (limited by the speed of regen)
Maximum Supportable Max HP w/out Maso: 263.2 (limited by energy)
(315.84 (limite dby energy) with a 20% enchant mod.)
Notes: Not really so bad now. Maybe even borderline viable.]
Spirit Transfer
[skill]Spirit Transfer[/skill]
Unconditional: Yes.* If you bring the spirit yourself and keep it alive...
Maximum Supportable Max HP w/ Maso: 243.1 (limited by energy)
Maximum Supportable Max HP w/out Maso: 128.1 (limited by energy)
Notes: Assumes either Pain or Bloodsong recast every 33 sec. Results are worse with more expensive spirits, shorter-lasting spirits, and actually moving.
Mend Body and Soul
[skill]Mend Body and Soul[/skill]
Unconditional: Yes.
Maximum Supportable Max HP w/ Maso: 219.1 (limited by cast time)
(If we disregard the cast time limit, then 238.2 (limited by energy) and no time to cast summons).
Maximum Supportable Max HP w/out Maso: 125.5
Notes: Surprisingly bad.
Healing Signet
[skill]Healing Signet[/skill]
Unconditional: Yes.
Maximum Supportable Max HP w/out Maso: 196.4 (limited by cast time)
(If we ignore the cast time limitation, you could say 406.7 (limited by recycle), leaving yourself virtually no time to summon.)
Maximum Supportable Max HP w/ Maso: 144.6 (limited by cast time)
(Again, 406.7 if we ignore cast time.)
Notes: Though no one seems to use this, using dual fast-cast gear to save cast time on BotM and summons might make it viable...
Ghostmirror Light
[skill]Ghostmirror Light[/skill]
Unconditional: Yes.* Well, you need to have at least 1 living other ally and keep a spirit around.
Maximum Supportable Max HP w/ Maso: 169.7 (limited by cast time)
(If we disregard the cast time limit, then 184.5 (limited by energy).)
Maximum Supportable Max HP w/out Maso: 97.2 (limited by energy)
Notes: Really, really sucks. Assumes either Pain or Bloodsong recast every 33 sec. Results are worse with more expensive spirits, shorter-lasting spirits, and actually moving. Included in the list only because some moron on GWonline suggested it seriously as a MM self-heal.
Orison of Healing
[skill]Orison of Healing[/skill]
Unconditional: Yes.
Maximum Supportable Max HP w/ Maso: 145.0 (limited by cast time)
(If we disregard the cast time limit, then 192.4 (limited by energy).)
Maximum Supportable Max HP w/out Maso: 117.8 (limited by energy)
Notes: Sucks.
Signet of Lost Souls
[skill]Signet of Lost Souls[/skill]
Unconditional: No. Fails as primary heal.
Notes: Nice secondary heal, e-management
Taste of Pain
[skill]Taste of Pain[/skill]
Unconditional: No. Fails as primary heal.
Notes: Nice secondary heal.
Consume Corpse
[skill]Consume Corpse[/skill]
Unconditional: No. Fails as primary heal.
Notes: Nice secondary heal, e-management. Teleport effect is less suicidal than one would expect. (In fact, it can be used to tele-kite sometimes.)
Soul Feast
[skill]Soul Feast[/skill]
Unconditional: No. Fails as primary heal.
Notes: Probably inferior to Consume Corpse for MM secondary heal purposes.
Taste of Death
[skill]Taste of Death[/skill]
Unconditional: No. Fails as primary heal.
Notes: Useful as an emergency heal.
Arcane Echo + Flesh Golem + Taste of Death is simply retarded. Don't get me started...
Unholy Feast
[skill]Unholy Feast[/skill]
Unconditional: No. Fails as primary heal.
Notes: Proximity to monsters is unwise for MM in any case.
Dark Bond
[skill]Dark Bond[/skill]
Notes: NOT a heal. Does NOTHING to offset life sac.
Conclusions:
Before Masochism came along, AotL and Heal Area were the only self-heals that could support a life total I consider safe to run (>= 400ish). With Masochism added, Mystic Regen now also supports a decent life total, if you can come up with a third enchantment that's worth using.
And that's about all there is to it. The rest don't merit serious consideration. (Though I give non-serious consideration to Spirit Light, Leader's Comfort, and Heal Sig.
)From here, there's some room to debate which of these three skills is the “best” choice. To breifly sketch the largest pros/cons: AotL gives the best healing, by far, for the least energy, by far, but it uses up your elite slot and puts you in danger from life steal and degen and makes you look very appetizing to monsters. Heal Area does the best job of moving minions between battles, allows you to move faster, and can serve as an emergency backline heal, but it requires a secondary heal for battle and runs the tightest against your energy limits. Mystic Regen (plus Maso) allows a decent life total and foolproof e-management (Renewing your enchants as they expire never runs you over your energy allotment.) but it requires you to put a least one extra skillslot to sub-optimal use for an extra enchantment and opens you up to enchant stripping more than the other two. Ultimately, each option probably works better than the others in certain builds and worse in other builds.
Future Amendments:
I'm pretty tired of crunching numbers on this, so it's highly unlikely that I'll change or add anything on my own initiative. At least not any time soon... However, if you find an error or omission, please bring it to my attention. I'd especially like to hear a convincing proof/disproof for the optimal way to run non-maso mystic regen. If you think you've got an unlisted self-healing option that's seriously worth mentioning, do the math yourself, then please bring it to my attention. I'll check the math and make an addendum if I agree it deserves mention. However, if anyone suggests Arcane Echo + Flesh Golem + Taste of Death, I will shoot them.
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Some useful constants, if you're going to expand upon this math:
1 sec cast limit w/out maso: 7.90740741 sec
2 sec cast limit w/out maso: 12.4259259 sec
1 sec cast limit w/ maso: 10.7376362 sec
2 sec cast limit w/ maso: 16.8734283 sec
available e/sec w/out maso: 0.513661202 e
time needed for 5e w/out maso: 9.73404256 sec
time needed for 10e w/out maso: 19.4680851 sec
available e/sec w/ maso: 0.838797814 e
time needed for 5e w/ maso: 5.96091205 sec
time needed for 10e w/ maso: 11.9218241 sec
heal/sec --> max_hp multipler: 24.4
Derivation of no maso, healing self + minions case for Heal Area:
To find the casting rates for BotM and HA, start with the premise that the highest max hp will come from casting HA as frequently as possible and BotM as infrequently as possible. This is limited by the need to get >= 20minion_heal/sec. And we know that BotM provides more minion_heal/e than HA, so the point of lowest acceptable minion_heal/sec is going to correspond to the point lowest acceptable minion_heal/e (and later the point of lowest acceptable BotM frequency/highest acceptable HA frequency). So, convert that to 15minion_heal/e. Now, 15minion_heal/e = (%_e_dedicated to_HA * 110minion_heal/10e) + ((1- %_e_dedicated to_HA) * 122minion_heal/5e). Solve. Multiply by 4/3 to get e_per_sec_dedicated_to_HA. Divide the 10e casting cost by that value to get the cast rate for HA. Repeat for BotM. Double check that recycle time and cast time don't impose a lower limit. (They don't.) Verify arithmetic by double checking that casting at rates uses exactly 4/3e/sec and yields exactly 20minion_heal/sec. Now go compute max health using (1/4 * Max_HP) / BotM_rate = 110self_heal / HA_rate.
<(Oops.) Though, ultimately, I don't think it makes much difference; most of your points seem applicable to either comparison.
