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}

WoW Mathematics: Breach of Contract

Ever signed a contract later regretted? Unfortunately, they are all too common during the Blood-Queen Lana'thel encounter, as she regularly binds raid members into Pacts of the Darkfallen. The law in Icecrown Citadel cares not of requirements of intention and genuine consent, so surely it will not mind a breach? What is the most expedient and mathematically sensible way to do so?

Summary:

• To remove Pact of the Darkfallen the quickest way possible in the 10-man Blood-Queen Lana'thel Encounter, the raid members should run to the midpoint of the interval they form.
• To remove Pact of the Darkfallen in the quickest way possible in the 25-man Blood-Queen Lana'thel encounter:
• If the raid members trace an acute triangle, they should run to its circumcentre.
• If the raid members trace a right-angled or obtuse triangle, they should run to the midpoint of the longest side.

Compress Your Waveform

Many World of Warcraft raiding guilds use Ventrilo (Vent) to allow raid members to communicate more easily. However, it may be frustrating to find a large variation in volume between others' voices. Fortunately, Vent has a function to alleviate that.

The Compressor module can be used for reducing the such. It works by changing the shape of the envelope, or outline, of the waveform. It can be activated by going to Setup | Voice | SFX and adding Compressor under Sound Effects. To be able to configure these settings without a recommended configuration, one needs to know some of the basics of sound synthesis, in particular the ADSR envelope.

Random Ramblings to 24 April 2010

Cascading failure
A failure of a system where one component's failure causes a chain-reaction failure of other components. A system bearing a load is susceptible to this type of failure, where an overloaded component shifts its load to other components upon its individual failure. In an electrical grid, a cascading failure occurs when a transformer's failure requires the other transformers to bear the electrical load, increasing the chance that one of those transformers will also fail due to overloading.

Where the components are fully interconnected and handle a fixed load, the per-component load trend is a rectangular hyperbola. This signifies that the per-component load increases at an increasing rate as components fail. As a result, the chance of any individual component's failing also increases at an increasing rate.

A graph illustrating a cascading failure in a World of Warcraft boss encounter. The trend is a rectangular hyperbola.

WoW Mathematics: Sharing the (DPS) load

In any (conventional) boss encounter, a certain number of damage dealers (dps) need to whittle down the boss' health to zero over a certain time period. Barring any extraordinary tinkering by Blizzard, the health level remains constant between attempts.

This fixed DPS burden needs to be shared between all dps. I will examine the DPS burden per dps and how it changes with the number of dps that happen to die during the encounter.

Summary:

• Given a total DPS burden (total raid DPS) of D and a total number of dps of d, the average DPS burden per dps B, where x players are dead, is B = ^D/_{d - x}.