WoW Mathematics: Steady-State Health Level

In the final phase of the Anub'arak encounter in the Trial of the Crusader (ToC), healers must heal through a variety of sources of damage, including Penetrating Cold and Leeching Swarm. While the former deals constant damage over time, the latter does more damage the higher players' health levels are! The raid might be interested in knowing the optimal health level the healer(s) can keep the players at.

At the steady-state health level, DPS of Anub'arak against the raid equals the HPS of the healers for the raid. From here, health levels do not tend to move either way; they are stable, and this determines whether the healers can provide enough healing.

Summary:

• Where h is the total HPS, r is the proportion of current health Leeching Swarm does as damage, p is the proportion of players affected by Penetrating Cold at cast and P is the tick size of Penetrating Cold, the steady-state health level H* is H* = ¹/_r(h - ³/₁₀pP). It is a good idea to incorporate a buffer against the randomness of the damage.
• For Heroic 10-man, the steady-state health level is H* = 5h - 450, and for Normal 25-man, it is H* ~ 10h - 228.
• As long as the steady-state health level is more than zero, the healing the healers provide is sufficient.

Random Ramblings to 28 August 2010

Carriage return
A typed character that commands the computer to move the cursor to the beginning of the line in a word processor. It is created using the Enter/Return key, which also sends another character that commands the computer to move the cursor to a new line. It is named after the lever on a typewriter, which performs both functions on a typewritten document.

Volumes of Tori and Pyramids

The volume of some solids can be found intuitively (e.g. for a right rectangular prism, V = lbh). However, some more exotic solids will require calculus for their volumes to be found.

Two such solids are the torus (donut) and rectangular pyramid. The former's volume can be found, possibly among others, using the technique of volume by rotation, and the latter's with volume by cross-section. These techniques will be used for deriving the formulae for the volumes of the respective solids. In summary:

• Volume of torus = 2cπ²r²
• Volume of rectangular pyramid = ¹/₃abh

The Stuff of Sensations

With the senses of sight and hearing, a person can see colour and hear sound, respectively. So many hues and timbres exist, yet both are composed of basic elements and can be constructed by combining them in special ways.

Colour

• Sensing body part: Eyes. The lens and cornea focus light to fall on a surface of rods and cones, the pattern of which is sent to the brain as electrical impulses.
• Element: Primary colour
• Medium: Colourants (usually ink) on a white surface, or light on a black surface
• Types of element: For colourants, cyan (reflected blue and green light), magenta (reflected red and blue light) and yellow (reflected green and red light) (practical implementations also use black), although the fine arts has traditionally used blue, red and yellow (which alone cannot theoretically produce black). For light, red (long-wavelength visible light), green (mid-wavelength visible light) and blue (short-wavelength visible light).

Halian Geometry

The Halion encounter in the Ruby Sanctum requires careful positioning and movement in order to conquer it. Certain principles of geometry can help greatly with this endeavour, so it helps to be acquainted with them! Even if they will not be used in actually formulating strategies (since strategies will conveniently be recommended here), it is good to see how they were derived.

Circles and their radii
A circle is a (plane) shape where all points on its perimeter (the circumference) are the same distance from a single point (the centre). A radius is any straight line drawn from the centre to the circumference. Because of the definition of a circle, all radii are of the same length.

Vision’s Incentive Systems: A Case Study

Every World of Warcraft raiding guild aspires to progress through raid content in a timely pace. Most members of the raiding corps focus on attaining gear and other goals, and so cannot be expected to directly satisfy the guild’s purpose. Thus, the guild must facilitate this indirectly by setting compatible goals, and then motivate raiding members to achieve them.

Human Resources (HR) departments of real-life companies handle these issues regularly, and the officerships of ingame guilds are no more exempt. I will introduce the theories associated with incentive systems, then apply them to analyse the incentive systems of my current guild, Vision of Frostmourne US.

Direct Costing (with Defects)

In the ideal world, every bit of material and labour allocated to a product is used, and no waste is generated. Unfortunately, materials can have defects and precious labour is spent on dealing with it. This means that more input than ideally required is actually used.

In developing standard costs for products, management accountants must take defects into account. To do so, they need to have a good grasp of division and multiplication.

If C is the theoretical amount of material or labour and r is its defect rate, the total amount of material/labour actually used (T) is:

T = ^C/_{1 - r}