## Wednesday, March 12, 2008

### Counting on Probability

Ninjasuperspy, in a comment to the post about Spell Crit and Mp5, posted:
I've always viewed Crit vs. MP5 as the difference between Avoidence versus Mitigation for tanking. Sure, crit will refund mana in big chunks just like parry or dodge will avoid 100% of an attack. However you cannot count on it. MP5 like Stamina or Armor is always on, dependable regen.

This is not quite right. The Avoidance versus Mitigation debate has had the side-effect of promoting some incorrect beliefs about probability. The reality is that:

You cannot count on probability in the short term.
You can count on probability in the long term.

The reason you can count on the long term is something called the Law of Large Numbers. It's the same principle that casinos and insurance rely on. The key here is determining what is long term, and what is short term.

Tanking heavy-hitting bosses is inherently short-term. For some bosses, as few as three or four hits in a row will kill the tank. When the number of events is that low, you cannot count on probability to keep you alive, and probabilistic or Avoidance stats like dodge rating are less useful than stamina or armor.

However, if it takes a larger number of hits to kill you, probability becomes more and more reliable. For example, I tank the murloc adds on Tidewalker. Each add doesn't hit very hard, but there are many of them. It would probably take 10-15 full hits to kill me. In this situation, Avoidance stats are actually very useful.

For mana regeneration on healing crits, you are considering a large number of spells over a 10 minute fight or so. That's upwards of 100 spells cast, which is definitely a long term issue. So you can count on Illumination to return a reasonable amount of mana.

On the other hand, because it only takes one or two spells to heal the tank up to full again, you cannot count on spell crit to increase the power of your heals. Yes, over the course of the entire fight your average heal will be higher, but relying on the next heal to crit is a bad idea.

See the difference? Mana regen over an entire fight is a long term issue, but returning a tank to full health after a big hit is a short term issue. Spell crit helps with the first part, but should not be counted on for the second part.

1. Also one of the factos which is completely forgotten about on the avoidance vs effective health / mitigation theory, is rage / mana regen.

For myself, I'm usually a big fan of the avoidance theorys as far as tanking goes. However as I gear up more, I'm finding myself more in favour of the effective health theorys and so am stacking more armor / block value / stam as opposed to dodge / parry.

This has nothing at all to actually do with reducing the amount of damage I take in a dependable way. But rather to increase the amount of overall damage I take but in a more sustainable method. Reasoning behind this.... I'm finding that I am burning my mana too quickly on threat generation while tanking trash or kara bosses.

Generally no one can catch me on threat vs these mobs / bosses anyway, however that's not the point.

2. This is a very interesting perspective on mana regeneration while raid healing. Being a resto druid, I have never had the dillema of waiting for a crit to get mana back, but having played a tank and a mage who gets mana back from crits, I totally understand your perspective.

Elk
Runningelk.blogspot.com

3. I completely agree.

Mana from crit heals is guaranteed over a long fight. Paladins cast nearly constantly and will see their real crit percentage on most boss fights (like, for example, rogues/hunters/fury warriors seeing their real crit and hit percentage reflected on a boss fight due to the large number of attacks they make). And long fights are when mana is an issue.

Like you said, when 3 hits can kill a tank, one cannot rely on healing crits to keep him alive. This is why healing crit is seen as a mana-return stat more than an effective healing stat (effective healing has no meaning when your tank is dead, and you usually cast counting on a non-crit, when the heal crits, odds are alot of the healing power is wasted and not counted as effective healing).

All that said, the best raiding pally healer I even played with (up to TK) valued crit/+healing/int over mp5. Which is basically the old-school raiding pally perspective. But he may have just been good.

4. Part of this also depends on playstyle. I spam FoL a lot during boss fights, so while crits give me a little extra power, it's not enough to write home about, so I need to stack MP5. With paladins getting a 6% boost to their HL crit chance via talents, paladins who favor various versions of HL can get even more from crit heals (via more powerful healing and more mana regenerated). Get enough T6 pieces and you'll see even bigger returns.

This still doesn't negate the long-term/short-term benefits of MP5 versus spell crit, but it does alter the cutoff of where "short-term" ends and "long-term" begins. For me, "long-term" means something like FLK or Al'ar, where I'm casting heals for a long, long time. For people who like HL of many ranks, "long-term" starts earlier, like say VR or Solarian-length fights.

5. Anybody who doesn't believe that crit chance is dependable in the long term should take a look at their WWS log for a long boss fight.

In every WWS log I've looked at, my actual and theoretical (from the Blizzard character interface) crit rates matched perfectly.

6. The large issue that is usually avoided is that effective health is also subject to the Law of Large Numbers as it is the variance in the amount of damage done vs. the size of heals received that makes something as small as 100 hp or 100 armor matter.

What gets lost in the debate is that when you factor both together and calculate the average DPS that is being done against you, effective health theory is more accurate in predicting better equipment choices. It has nothing to do with effective health actually being more stable.

7. I'd buy that. To be honest, I've never been in a boss battle that lasted longer than 3 minutes (I apparently left out the "not yet" in front of "in Kara" the other day) so I wasn't thinking like that. I did stand in IF the other day spamming heals on myself, and dang if you aren't completely correct.

I learn something new every day. I'll get the hang of this eventually.