Divine Aegis Nerf

I am writing to make the case for stacking Divine Aegis, or some mechanic that allows for the wasted shield to be recovered.

First of all, divine Aegis is a creative version of the standard DPS talent "The bonus (healing) of your critical spells is increased by Y%".

To determine what Y% is, we take the size of a shield divided by the standard healing bonus of 50%. The numbers work out to be:
shield = 0.30 x (Heal x 1.5) = 0.45 x Heal
crit bonus = Heal x 0.5 = 0.50 x heal
so Y = 0.45/0.5 = 90%

The divine aegis talent could read "The bonus healing of your critical spells is increased by 90%, with a reduced chance of overhealing."

The inability for Divine Aegis shields to stack DRASTICALLY reduces the effectiveness of this talent. Unfortunately, this is more difficult to show with basic algebra. Lets take the example of Penance.

Case Study: Penance

Penance heals so fast, there is almost no chance of a DA bubble being used up mid-cast, so we'll assume that does not happen. For the overwriting of a DA shield to occur, two or more shields must proc during the cast.

Case 0, no shields proc P(no shields) = (1-crit) x (1-crit) x (1-crit)
Case 1, only one shield procs P(one shield) = crit x (1-crit) x (1-crit) x 3
-- The x3 is for the three bolts that can each crit.
Case 2, two shields: P(two shields) = crit x crit x (1-crit) x 3
-- The x3 is again for three combinations. Think of it as each bolt has the chance to not crit
Case 2, tree shields: P(three shields) = crit x crit x crit
-- Only one possible combination here.

For a reasonable crit level of 25%, this is what we get.
Case 0: P(no shields) = 0.42
Case 1: P(1 shield) = 0.42
Case 2: P(2 shields) = 0.14
Case 3: P(3 shields) = 0.02

Average number of shields = 0x0.42 + 1x0.42 + 2x0.14 + 3*0.02 = 0.74 shields per penance.
The Average number of WASTED shields = 1x0.14 + 2*0.02 = 0.18 shields per penance.

This means that the talent of DA is reduced in power by 0.18/0.74 = 24%

Case Study: Chain Casting FHeal

This is a more difficult problem, because we do not know how often the target is taking damage. If we say the tank is taking damage every three seconds, then chain casting FHeal the chance of getting a shield overwritten is equal to the chance of getting a crit.

For my 25% crit rating, this results in at least a 12% decrease in the effectiveness of Divine Aegis (two shields, only one goes through, happens when you get a crit on your next cast = 1/2*crit).

Case Study: GHeal-Penance

There are other situations that can lead to catastrophies. The primary would be casting a GHeal-Penance. If the GHeal crits, there is a large chance that the penance will also crit, causing a small shield to overwrite a large one.

In this situation, the shield is reduced by a factor of 3 (each penance tick is approximately 1/3 the size of a GHeal).

In fact, this situation is an extention of the Penance case studied above, as all of the healing (and thus all of the crits) occur in a two second window. The reduction in DA effectiveness for the GHeal is 0.58(chance of Penance Critting)*1/1.3(lost shield over total shielding if there were stacking) = 45% reduction in the power of Divine Aegis

Summary
The effect of this lack of stacking is to effectively put a timer on our critical bonus. For a 25% critical strike rating, it reduces the power of DA by:
penance - 24%
back-to-back FHeal - 12%
Gheal followed by Penance - 45%

This is a large nerf in the power of this ability. I believe its net loss to be approximately 20% on boss fights, making it a talent that could read:
"The bonus healing of your critical spells is increased by 72%, with a reduced chance of overhealing."

If we are balanced around this reduced power in DA, then this is not a problem. If the Blizzard models show the 90%, or worse 100% as being "close enough", then we are actually performing quite a bit worse than their models would indicate. Additionally, the power of Divine Aegis will scale negatively as our crit rating increases.