Tuesday, January 26, 2010

Soft Caps

It seems like it has been awhile since I've talked about theorycrafting on this blog, so let's begin a discussion on raiding soft caps. I chose this topic because I've seen a rampant number of posts over on TMR that just reek of misunderstanding. Posts along the lines of "Oh noes! My haste is 403 and I have this uber wep but it will put my haste to 480! Should I shard it!?"

Yes, Virginia, there are all sorts of folks misunderstanding what a soft cap means. So let's just takes a second to break down the difference between a soft cap and a hard cap.

Hard Cap

Hard caps represent a value of a stat after which increasing that stat yields zero gain. A perfect example is hit. For a Horde Druid (I always see people talking about Alliance druids...) the hit cap is 10% or 263 hit rating. At this point, you will not miss a spell cast against a boss level mob. The druid with 263 hit rating is going to garner exactly the same benefit as the druid with 363 hit rating. That extra 100 hit rating does absolutely nothing for the character. This effect is known as a hard cap. Other examples of hard caps come with expertise, armor penetration, and critical rating, among others.

Soft Cap

Soft caps represent a value of a stat after which the value of that stat relative to other beneficial stats changes significantly. Yes, this is a mouthful. Haste is an ideal example here. While casting Wrath, we often run into the problem of "clipping the GCD" while casting. This means that our Wrath casts in less time than the GCD takes (this is set at 1 second). When Nature's Grace is up, this happens at 400 haste. Any haste after 400 yields no benefit for a Wrath cast that is affected by Nature's Grace. However, any Wrath that is not affected by Nature's Grace, as well as all of your Starfires still scale with haste. So any value after 400 still has some benefit, albeit less than before 400 haste. This sudden change in value is called a soft cap. Other examples of soft caps come with expertise, armor penetration, and critical rating. Yes, I used the same examples and yes I did that on purpose.

Balance Druid Soft Caps


So now we will be discussing the Balance Druid specific soft caps and the relative loss of stat value that follows the soft cap. Hopefully this will demystify why any stat past its soft cap can still benefit you.

Haste

Since our cast time is bounded on the bottom by the one second hard GCD, we will look first at a haste cap that brings any Wrath affected by Nature's Grace down to one second.
((Base Cast Time / Desired Cast Time) - 1) * 32.79 * 100 = Haste Rating needed
((1.5 / 1.0) - 1) * 32.79 * 100 = 1639.5
(Haste Rating / 32.79) = % Spell Haste
(1639.5 / 32.79) = 50%

So we need to gain 50% haste or 1640 haste rating (since we can't get half a rating) in order to bring our Wrath cast time down to one second. Now lets examine the help we get from our buffs and our raid (keep in mind that while haste rating is additive, haste percentage modifiers are multiplicative).
Celestial Focus: 3%
Improved Moonkin Aura: 3%
Wrath of Air: 5%
Natures Grace: 20%
1.5 / (1.03 * 1.03 * 1.05 * 1.2) = 1.122138 or 12.21%
Remaining Haste Rating: 12.21 * 32.79 = 400.37


To predict Nature's Grace uptime we will use (1-(1- Critical Strike Chance)^Number of Casts) where 3 will be the number of casts that we will use, since that is the number of casts that can be started within one Nature's Grace proc. For simplicity, let's use a theoretical druid with 50% crit raid buffed. Then my uptime for Wrath will be:
1 - (1 - .50)^ 3 = 0.875 or 87.5% uptime while casting Wrath

Remember that we are only looking at the Wrath portion of our rotation, so I am able to say that 12.5% of my Wrath casts will be unaffected by Nature's Grace. Likewise, I am able to say that any haste after 400 is 12.5% as effective as any point of haste rating before 400 for Wrath.

So how much haste does it take to make Wrath a 1 second cast without Nature's Grace. Let's call this number the "less-soft-cap". Bear in mind as we calculate this cap that it is much less of a change than the previous soft cap, representing a very small change in the value of haste.
1.5 / (1.03 * 1.03 * 1.05) = 1.346566 or 34.66%
Remaining Haste Rating: 34.66 * 32.79 = 1136.5

As we can see, this is a large amount of haste rating. This is generally considered an unmaintainable number under normal circumstances via gear. Yes, you probably could reach this value with procs, but that only represents a very small segment of time. Based on these observations, we currently ignore the less-soft-cap, however, we could say something along the lines of "Between 400 and 1137 haste, haste rating is roughly worth ((1 - Nature's Grace Uptime) * 100) percent of its sub 400 value for Wrath. Naturally, these values fluctuate from gear level to gear level, but they should maintain relatively constant. Also remember that these values do not include the large gains that Starfire still garners from haste.

Crit

It is impossible to crit more than 100% of the time. This creates a hard cap for critical strike rating. However, the unique mechanic of Eclipse, coupled with the high Eclipse uptime, yields a soft cap for crit rating. Lunar Eclipse is present often enough to consider it when considering a soft cap. It does not approach the Nature's Grace uptime, but it is still fairly high.

Crit percent is much more difficult to calculate because it relies on two variables: crit rating and intellect. In order to make our lives easier, let's assume that the druid in question has 1500 intellect. We will use the following formula to calculate our crit rating needed to hit the crit soft cap:
Crit Rating = 1575.5 - Int/3
1575.5 - 1500/3 = 1075.5 crit rating

This translates to 43% on your character sheet with all raid buffs. Any crit past this percentage will be "ignored" during a Lunar Eclipse. However, we still fire Starfires outside of a Lunar Eclipse. We also fire every single Wrath outside of a Lunar Eclipse. Essentially, over 50% of our rotation is outside of a Lunar Eclipse, meaning that the additional crit is still contributing over 50% of the time.

TL:DR

While soft caps indicate a change in the value of a stat, they do not mean that the stat has lost value. Roughly, we could estimate the value of each stat at 50% of its pre-cap value (this is an underestimation). Even after this reduction, both haste and crit are better than spirit. So don't avoid haste, or crit, after the soft caps. Don't freak out if you go over 400 haste. In ICC it will happen. Just keep going for the sp/crit/haste pieces anywhere you're not putting a hit piece.

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