Effective mp/5 from spirit?

Ok, so a while back, I posted about which was better, intellect or spirit. I eventually concluded that spirit was best for healers but not for dps. DPS generally stay in the FSR because they're casting as often as they can. While healers only need to cast when someone's hurt, they can benifit from spirit-based mana regen.

Now, with that said, which is better, spirit or mp/5?

Instead of comparing the mathematical forumlas, wowwiki describes the relationship between spirit and mp/5 in terms of enchants.

"For example the two top mana regeneration enchants for chest items yield either 15 spirit or 6 mp5 ([Enchant Chest - Major Spirit] and [Enchant Chest - Restore Mana Prime]) - this shows the factor of 2.5 very clearly."

They surmise with this, that 1 mp/5 = 2.5 spirit. I don't agree. I think that mp/5 is worth far more spirit. To demonstrate, I've done some calculations using excel again with the same input parameters as I did in the intellect vs spirit discussion. Assuming a character has 1000 intellect and 500 spirit, the following graph shows their equivalent mp/5, depending on their time spent outside the FSR.

Realistically, the value of 1 mp/5 compared to spirit depends largely upon time spent outside the FSR. Let's assume that a priest spends 25% of their time outside the FSR (which is fairly generous, since we decided that 13% was the break even point last time). At 25% outside the FSR, the effective mp/5 from spirit is 79. Now, if we divide the spirit required by the acquired mana regeneration, you get:

500/79 = 6.33 spirit = 1 mp/5

mp/5 is worth 6 times more than spirit, not the 2.5 that wowwiki suggests.

Now, say you think you're an exceptional healer, and get 50% outside the FSR:

500/132 = 3.79 spirit = 1 mp/5. That's still higher than wowwiki's 2.5 suggestion.

In fact, if we solve the equation 500/x = 2.5 (x = 200), and compare that mp/5 value to our graph, we find that we'd need to spend 75% of the time outside the FSR to achieve this mp5 to spirit ratio.

So, spirit is disproportionally availiable on gear. Take gems for example. The highest epic gem granting spirit give +20 spirit. While a +10 mp/5 gem is availiable. The mp/5 is worth +63 spirit according to our calculations, and doesn't have the FSR limitation.

I've now geared my priest so that it has 150 regular mp/5, with 965 spirit and 1182 intellect unbuffed which equates to 139 mp/5 at 25% FSR. A total of 289 effective mp/5. I'd love to swap out all my spirit for mp/5 if I could. At an exchange rate of 6.33 spirit per mp/5, I'd get 152 additional regular mp/5. The problem is that it's just not availiable in those quantities. Since gear is lacking in mp/5 equip bonuses, it is impossible to swap out all your spirit for mp/5. I could trade out some gems and upgrade a few pieces, but it's tough to come across, especially below raid-quality gear. Healing gear comes pre-loaded with spirit, just not at the exchange rate we'd expect. I assume this is to keep the difficulty level of the regular and heroic 5-mans.

Intellect or Spirit?

Five Second Rule (FSR)
"Whenever mana is expended for any purpose, mana regeneration is interrupted for five seconds. This is most often caused by casting spells, but diseases that drain mana will also interrupt mana regeneration. During this time, no spirit-based mana regeneration takes place unless the character has certain talents; there is also the fixed regeneration from mana/5 items, which is never interrupted for any reason." (www.wowwiki.com)

Due to the FSR, spirit will only help you regenerate mana if you spend a considerable amount of time doing nothing.

Mana regen is a difficult thing to gear for since it depends wildly on the tank you're healing. If the tank has low HP, you will most likely be needing to heal him constantly, and therefore receive very little regeneration. However, the opposite is also true. A well geared tank that takes less damage will allow the healer to rest between heals and therefore get some regen.

The actual mana regeneration from spirit equation is as follows for level 80 characters:

mp5 = 5 * (0.001 + sqrt(Intellect) * Spirit * 0.005575 ) * 0.60

I took this equation and graphed the results in excel with varying intellect and spirit values. I assume here that stacking intellect means that you have 500 spirit + varried intellect, and that stacking spirit means that you have 1000 int + varied spirit. Those are realistic values at level 80.

These graphs make sense. Since the mp5 varries with the square root of total intellect, the player receives diminishing returns for regen when stacking intellect. However, mp5 varies proportionally with spirit as to create a linear trend. Initially, this looks like it's obvious that stacking spirit is the wise choice.

However, this is not the entire picture. Sure, you'll end up with more regenerated mana, but what about your total mana pool?

Woah, not what you would have expected, eh? It looks like from this graph that stacking spirit actually ended up with far less mana than did stacking intellect. Well, that's because the graph was only for a 60-second fight, allowing only for 20 regen ticks at most. Furthermore, I assumed a FSR of 50%, meaning that you were casting half the time. Realistically, most boss fights are longer than that. While fighting Kael'Thelzud, the last boss in 10-Naxxramas, the fight lasted 15 minutes. Let's re-examine these graphs when a longer fight is assumed.

Now there's a drastic change. Even with a low amount of spirit, the regneration based on spirit scenario ended up with more total mana in the end because of the base amount of intellect that you'll have anyway. It compounds as spirit is stacked, resulting in a difference of 49k mana. That's a lot... more than 3 full mana bars than the stacked intellect case.

Ok, so you still don't think that's realistic. You don't think you'll reach 50% FSR. Yeah, that's probably not realistic. So let's look at 20%FSR. That's 12 seconds out of every minute, you don't cast. (Well, actually 17 because you have to wait 5 seconds before regen starts)

Here, we see that the two trends are almost parallel. So at every amount stacked in either case, the total mana availiable increases proportionally. However, the spirit case still ends up with the large of the two by about 10k mana. That's for a 15 minute fight, the less time, the worse the spirit case appears.

So the break even point is 13% FSR for 15 minutes while stacked at 2100 spirit 1000 int. Remember that the x-Axis is not time. The x-Axis is amount stacked. It's also important to realize that priests in the best guilds on my server only have 1300 intellect and 1100 spirit. They're not stacking one over the other, and it's highly unlikely that any priest would be able to stack 2100 intellect or 2100 spirit.