Succeeding at giving way

A rolling mass of stone and earth is loose around the room, devouring anything, living or inanimate, in its path. Turning a corner, you breath a sigh of relief, having gained distance from the voracious being known as Oregorger. You are safe for now.

Unexpectedly, as if in an instant, the unstoppable goren zips to the intersection you just passed. Dazed by the collision against the wooden picket fence, it halts for a bit, although you know it will be mere seconds before it makes off again, almost certainly in your direction.

Run away: Turn to page 87
Try to run behind it: Turn to page 155
Turn the next corner: Turn to page 172

In the second phase of the Oregorger encounter in Blackrock Foundry, the namesake boss drops whatever it is doing and enters a Rolling Fury. At first it may seem random, but the motion observes a few very simple rules:

Succeeding at not getting motion sickness

It is commonly accepted that normal computer use will not physically harm humans. While flashing images for epilepsy sufferers is a well-known exception, another can be found in the Hans'gar and Franzok encounter in the Blackrock Foundry.

This encounter is characteristic in that most of the floor area is moveable conveyor belts, filling much of the screen (and, by extension, the field of view) with apparent motion, even though none is felt sitting at the keyboard. In the more queasy of players, this can result in motion sickness, producing dizziness, nausea and maybe even vomiting. Given how crippling this is to raid performance, how are you supposed to handle it?

The Lightwell method

Look deep into my eyes... if you can find them.

Since nausea can arise when you see movement but do not feel it, the most obvious solution is to look at something on the screen that is not moving. The user interface (UI) elements, such as actionbars and nameplates, are options, although they might be too far into the peripheral field to focus on. Some environmental alternatives include:

Yor'sahj's Law (of Deep Corruption)

Of all of the blobs of blood Yor’sahj the Unsleeping may call from Shu’ma, none are more confusing than the Shadowed Globule. Its unique buff (debuff to the raid), Deep Corruption, means that:

Receiving healing or absorption effects will trigger a detonation at 5 stacks.

So, which healing and absorption effects generate Deep Corruption? Apparently, this is a matter of law that requires some interpretation.

Summary
Abilities that generate Deep Corruption are:

• Single heals
• Heals-over-time (HoTs)
• AoE heals
• Aura AoE heals
• Ground AoE heals.

Abilities that do not generate Deep Corruption are:

• Non-heals
• Non-healer abilities
• Trinkets and the like
• Summoned totems
• Abilities with secondary effects for as far as the secondary effect(s) is/are concerned.

Non-heal rule

An ability without any healing or absorption effects does not generate Deep Corruption.

Lemon Dungeoneers

In 1970, economist George Akerlof released a journal article about the used car market. In it, he drew the distinction between cherries (good cars) and lemons (faulty cars), and predicted how those selling cherries would be driven out of the market (and conversely how the proportion of lemons would increase).

There is often comment by World of Warcraft players how they would, at times, join a sub-par pickup group (PuG) and resultingly endure an excruciating dungeon run. The 'market' for dungeoneering 'labour' may well degenerate similarly, for the fellow dungeoneers likely do not know how skilled each other is.

The thing about asymmetric information
In the lemon market as described by Akerlof, it is asymmetric information that drives cherries out of the market. In such a market, the buyer does not know much about the quality of the seller's product so as to form a price. In the used car market example, the used car has many parts hidden away from view, so the buyer cannot completely know whether the car is free from defects. As a result, they make a best guess that the car is of 'average' quality and so will be willing to pay an 'average' price.

Raid Checklists [Checklist]

Like an airplane, a raid is made up of several parts that need to work together for the whole thing itself to work. Those parts need to be set correctly in order for that to happen.

Because of the daunting number of controls to set, airline pilots need to use checklists to ensure that every switch, dial and button are in the correct states for whatever the plane will be doing, whether taking off, cruising or landing. Similarly, several aspects of a raid need to be in specific states for the raid experience to be as smooth as possible. The following checklists mimic the pre-flight checklists used in airline aviation, listing the states of the various aspects of a typical raid.

There are checklists for:

• Preparing for the raid (pre-raid checklist)
• Preparing for a boss attempt (pre-boss checklist)
• Handling a raid wipe (wipe checklist)
• Concluding a raid (post-raid checklist)

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.

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.

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.

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}.
  

Reused Boss Mechanics

All boss encounters as respective wholes are unique, although there are several cases of encounters sharing mechanics. From a computer programming perspective, it is good practice when mechanics that work are adopted again and incorporated in a future encounter.

A veteran player might notice this over the time they have been playing. In fact, while they have progressed through World of Warcraft's many raids, they may have noticed the following commonalities...

The Healer's Skills Record

In my adolescence, I went to swimming lessons. I would learn various swimming skills and the instructor would keep track of my progress. At the end of the program, I received a certificate, overleaf a checklist of the skills being assessed. Ticked were the skills I managed to master, and unticked were the ones I still need to work on.

The listed skills were also sorted according to difficulty. In the above example, from easiest to hardest, the categories are Red, Yellow, Green and Blue. There was also a note that continual practice was needed to maintain mastery of the skills learnt.

Like swimming, the responsibility of providing healing to a group requires the mastery of several skills. Like swimming, some skills are more difficult than others. And like swimming, being a good healer requires continuous practice, not only to maintain current proficiency, but also improve on it. In the spirit of the above example, I have prepared a checklist of the many skills a healer needs in order to heal well. It assesses the following general criteria:

WoW Mathematics: Destructive Shadow interference

During the Blood Prince Council encounter in Icecrown Citadel, players may find a number of Dark Nuclei floating around. These are vital for the tank tanking Prince Keleseth, for they each offer a stacking Shadow damage reduction. Against conventional wisdom, this damage reduction stacks multiplicatively, so full immunity cannot be achieved from a stack of three (as is the case with additive stacking).

Aim: To calculate the damage taken from Empowered Shadow Lance at a particular level of Shadow Resonance.

Summary:

• With Shadow Resonance of an order of a stack of n, the Keleseth tank will take 80,000(0.65)ⁿ damage from an Empowered Shadow Lance.

Optimising the Blizzard Default UI

Some people play World of Warcraft using user interface (UI) mods. These AddOns change how unitframes, actionbars, the chat frame, scrolling combat text and screen fonts are displayed on the screen, usually by making them more streamline and compact. They do away with the clunkiness of the ornamentation that is in the default UI.

However, these addons are usually highly intertwined with the WoW program code, and often stop working as intended when the game client is changed with a content patch. Players usually become very accustomed to playing the game using a narrow set of controls, and become very frustrated when they have to do without their UI mods, spoiling their virgin dungeon or raid experience.

Some other people would rather avoid such disappointment and leave their UI mostly unadulterated. Of course, others may find a joy or challenge in playing the game in the way Blizzard intended them to play it, with an elaborate and ornate UI complementing the vibe of the playing field. For whichever reason people play the game through the Blizzard default UI, there are still ways to make handling the character easier under it.

Riding Out the Swarm

The Heroic Anub'arak encounter places great strain on a 10-man raid attempting it. Teams with a relatively weak dps team may choose to bring two healers into it, placing a great burden on the healing team during Phase 3.

Phase 3 is notorious for Leeching Swarm that Anub'arak keeps up during this time. This is coupled with a heavily ticking Penetrating Cold debuff cast on three random players. Due to high-hitting melee attacks and Freezing Slash, one healer usually must focus 100% on healing the main tank, leaving the other healer handling the raid and the offtank. That raid healer has a hard job, though a few tips and tricks may make it much easier.

Father rescues son from Icecrown Citadel

The Deathbringer Saurfang encounter provides for a very tantalising and moving lore moment. Not only is the more recent death knight dilemma explored, but also it draws from history as far back as the First War.

A father (Varok Saurfang, also known as High Overlord Saurfang ingame) talks to the reanimation of his son (Dranosh Saurfang, the Younger), the latter of which is obstructing the former's passage. A commentary on the more detailed Horde version of the dialogue is offered in a Q&A format.

High Overlord Saurfang yells: Kor'kron, move out! Champions, watch your backs! The Scourge have been...
Deathbringer Saurfang yells: Join me, father. Join me and we will crush this world in the name of the Scourge. For the glory of the Lich King!

Names of Raid Target Icons

Each of the eight raid target icons (also raid icons or lucky charms) are referred to with common (and usually standard) names. However, for some of them, the names used in mathematics are different.

A few definitions

• Shape: An object occupying space, distinguished by its perimeter (outer boundary).
• Plane figure: A shape occupying a two-dimensional plane.
• Quadrilateral: A plane figure with four straight sides
• Parallelogram: A quadrilateral with opposite sides parallel to each other respectively.
• Rectangle: A parallelogram with at least one vertex (corner) a right angle.

A simple gear score

There exists several ways to rate the items a player has equipped (examples include gear scores from Be Imba, Armory Light and the GearScore addon. Each method places varying importances on different characteristics of the gear. While changes in single gear scores can track the player's gear progression, different gear scores cannot be compared with each other, or to any other benchmark.

There is another, simpler way to rate the quality of gear. Every item has an item level (ilvl), which Blizzard calculates from from the statistics (stats) they assign to it. Generally, the more stats there are on the item, the higher the ilvl. Why not base a gear score on a stat sanctioned by Blizzard?

The Time-Value of Health

This blog post builds on the concepts suggested in 'Not All Hitpoints are Created Equal', helping to adjust healing for the health level of the recipient.

Experts in finance speak of the time-value of money. Under this concept, the value of a certain quantity of dollars (or other currency) will decrease as time passes. Many attribute this to the fact that people want money now rather than later. Therefore, to keep this time-value the same, interest must be paid on top of this quantity of dollars.

Hitpoints restored by healing also seem to have this time-value, since a heal of the same size will be more valued the sooner it is received (considering that people wish to keep their health at a maximum). How should such heal weighting be done?

Succeeding at not being trampled

FailBot has been retired, but EnsidiaFails has taken over! What remains the same is the humiliation that arises if a boss ability, if avoidable, is not handled properly.

In the Trial of the Crusader, the Northrend Beast Icehowl casts Massive Crash, which can send players scattered throughout the instance. If players do not move out in time to avoid the following Trample, the situation can become very messy (in both senses of the word!).

There's Something About Lady RNG

Computerised environments intrinsically lack randomness, so a random number generator (RNG) must be used where an unpredictable result is required. In effect, the RNG works on randomly generated data provided to generate a seemingly random number. Since this piece of programming code decides your fate and destiny in WoW in several cases (just like how Fortuna (Lady Luck) decides your fate and destiny in real life), it helps to know a bit about probability!

The golden rule of probability
Probability is that branch of mathematics that deals with random phenomena to (among other things) determine how likely it will act in a certain way. It is important to know that, for truly random phenomena:

Random does not necessarily mean even or fair!