WoW Mathematics: Server Loading

Hosts of MMORPGs face several dilemmas regarding the servers they operate. One of these, by far a significant one, is the maximum capacity the servers are able to take. Too low a capacity and players will complain about latency and other performance problems, while too high a capacity and the investment in the hardware will not be cost-effective. This problem is exacerbated by the tendency of the load to change cyclically throughout the day.

Deciding on the servers' capabilities is not a simple matter of allowing for a specific number of players. As the mathematics that follows shows, the throughput load created by those players will change according to the tendency of players to cluster together in the game world.

Merchant's Guide to Orgrimmar

Orgrimmar is the orc capital city and the capital city of the Horde territories. Also the current political capital, the incumbent Warchief Garrosh Hellscream is based here. It is the hub of the Horde's extensive zeppelin network and sees the bulk of adventurer traffic among all Horde capitals.

This combination of factors give Orgrimmar a high potential for lucrative business. It is large enough to boast five trade districts, each characterised by the architecture of the races that dominate their populations.

Goblin Slums

The Goblin Slums consist the goblin district in Orgrimmar. Dwellings are cloth tarpaulins supported by either branches or metal beams. Rudimentary waste disposal and a crude oil extraction operation has left the pond slicked with run-off seeping into downstream Valley of Spirits. Fishers are advised not to consume fish, especially endemic Toxic Puddlefish, caught from these waters.

Looking for Equilibrium

When using the Dungeon Finder to find a group, damage-dealers (dps) endure long waiting times, while tanks and healers enjoy a much shorter time in the queue. Since the facility was introduced, this has remained the case.


One may wonder why the average waiting time for a dps has not decreased, but instead even increased, since then. Having economic insight, one may envision the three roles as three choices a dungeoneering player decides on as part of an economic decision, and also that the the three choices, on the large scale with several people, tend to economic equilibrium with each other.

Cost and benefit
When faced with a choice of activities to perform, a person makes an economic decision whenever they try to gain the most satisfaction by choosing the best activity for them. For each activity, they need to compare the costs incurred with the benefits gained. The excess of the benefit over the cost is their (accounting) profit from the activity:

Accounting profit = Benefits - Costs

How to Catch Crawfish

As part of the Cooking daily quest (daily) Crawfish Creole, the player is required to "catch [sic]" Muddy Crawfish. Due to the likelihood of a player's doing it with the day's Fishing daily, they may interpret the instruction incorrectly.

When a person obtains a fish using a fishing rod, they are said to 'catch' it. In the circumstances, the player may apply that same definition to the word as used in the quest text. Of course, doing so is erroneous.

To interpret the instructions correctly, the player must read it somewhat more literally. The literal meaning of 'catch' does not imply the use of a fishing rod, in which case, the player is encouraged to use their hands (as they would for a slow-moving ball in flight).

A baseball can (literally) be caught using a special mitt.

Technically, the Muddy Crawfish NPC is to be looted in order to obtain the namesake item for the quest. Mousing over the NPC model reveals that it can be looted. To catch it ingame, the player must enter looting range and right-click.

EDIT 14Nov11: Appended hard copy version.

Azeroth Mass Transit Network Map [Map]

With the portals in Dalaran and Shattrath removed as part of patch 4.0.3a, there will be much greater use of Azeroth's slower transportation network. The following map serves as a reference for mass transit services provided to citizens of the Alliance and Horde.

The style used in the map departs from traditional methods of accurately charting landmasses and routes; instead, it aims for simplicity. It has been inspired by the highly stylised representations of real-life transportation networks, characterised by straight lines, highly simplified geographic features and regularly spaced nodes.

Notices

• Auberdine: The recent Shattering has decimated Auberdine. All nautical activities have been moved to Rut'theran Village in Teldrassil. Darkshore can be reached by private taxi to Lor'danel.

The Faction with Deeve Spairs [Interview Transcript]

The world of Azeroth faces great upheaval, much of which political. Join me, Deeve Spairs, as we talk to representatives from both the Alliance and Horde, to shed some light on the pressing issues facing both factions and, most importantly, how our leaders will tackle the uncertain future ahead. Watch The Faction, only on Critically Analyse.

22nd day of 11(1) ES 33, hard embargo – immediate release
N.B. Spoilers for World of Warcraft: The Shattering: Prelude to Cataclysm after the jump

Participants

• Deeve Spairs [Deeve]
• Lady Jaina Proudmoore [Jaina]

STATE OF CATACLYSM [News Article]

Fire engulfs Orgrimmar, rebuilding costly due to scarce supplies
Political tensions mount after Thrall appoints Garrosh as acting Warchief prior to vision quest

[Pguinto-Frostmourne-US], 16th day of 11(1) ES 33, hard embargo - immediate release

N.B. Spoilers for Golden, C (2010) (World of Warcraft: The Shattering: Prelude to Cataclysm) and strategy guide for the Elemental Invasion after the jump

ORGRIMMAR - A devastating fire tore through Orgrimmar today after the recent dry spell throughout Durotar had escalated the [fire hazard] to alarming [levels]. People throughout the Horde territories worry about political, economic and ecological difficulties stemming from it.

Orgrimmar had suffered an invasion of fire elementals, which caused an inferno that reached calamitous proportions and burned down most of the predominantly wooden architecture. Shaman are still baffled as to the reason for the elements’ disgruntlement.

The fire may be related to the recently foiled [arson] attempts by the Doomsday Cult. They had attempted to use special devices and rituals to mass summon fire elementals to the city.

As part of the fire fighting effort, which literally required monsoonal amounts of water, able shaman arrived at the scene to commune with the fire elementals responsible for the blaze. Thrall, shaman and Warchief of the Horde, personally assisted in the effort.

Repairing the unprecedented damage sustained is challenging given the strain the city's coffers are under from drought and restricted trade with the Alliance.

Prior to the fire, citizens of all major cities had complained of minor ground tremors. It is widely believed that action by the earth elementals, or some other related phenomena, would cause a more major earthquake.

Pictures with Leaders

30th day of 10(1) ES 33

With the Shattering looming ever closer, I figured that now would be a good time to catch up with the Horde's leaders before their worlds are turned upside down. Here I record my travels and the conversations I had with them.

N.B. Spoilers for World of Warcraft: Cataclysm and Christie Golden's World of Warcraft: The Shattering: Prelude to Cataclysm after the jump

Garrosh Hellscream

• Well known for: Leading the Warsong Offensive in Northrend as Overlord; challenging Thrall's leadership via Mak'gora; losing his composure near Varian Wrynn; being the son of Grommash Hellscream, damner to the original Blood Curse
• Where I found him: (32.81,38.02) Grommash Hold of Orgrimmar, Durotar, Kalimdor, Azeroth.
• What he was doing: Being appointed temporary Warchief by Thrall in a rather plain ceremony

Five reasons to like Treants

World of Warcraft's portrayals of things are noticeably cartoony when compared to real life equivalents. Treants and druids in Tree of Life form are no different, being any combination of cute, adorable, cuddly, pitiable and likeable.

1. Stubbiness
The classic treant model resembles a wide (for its height) sapling with short legs. Not only would they be appealing to hug, they would find it somewhat difficult to run around. In fact, the druid Tree of Life form formerly suffered a movement impairment.

The new Tree of Life form features longer legs, but still retains its width (in fact, it is much wider!).

Full Outer Join

During mid-September, WowStead changed its hosting partner to Curse Inc.. In doing so, it needed to migrate vast amounts of data over to the new Web servers and, among other things, merge the databases of both websites together. This was necessary given that users will log in to WowStead using their Curse Account. Unfortunately, several problems arose from the process:

• WowStead users that do not have a Curse Account cannot log in to WowStead.
• WowStead users that do not have a Curse Account have lost access to their characters and subsequently need to reclaim them.
• In the vice versa of the above, users have access to their characters but do not own the account they were assigned.

While explanations of what went wrong are not readily forthcoming, a likely cause is the misuse of the methods adopted to merge the two databases together. Given the popularity of relational databases in storing website data, one can contemplate how the use of relational algebra can bring about such complications.

Ulduar Constellations [Windows 7 theme]

Ulduar may well be one of the most awe-inspiring and (quite literally) captivating places in Azeroth. This theme brings a few of its highlights (in particular, its many constellation-like sculptures) to your Windows 7 desktop.

As I do not have file hosting available to me for hosting the .themepack file, I will give instructions apply it manually. This theme offers the following appearance customisations:

• Desktop background
• Window colour
• Sounds
• Screensaver

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.

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.

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}.
  

Insanity: The Yogg-Saron Soundtrack

I am surprised as to the number of songs written and sung about the mental state, and how diverse in musical style that collection is. This inspired me to compile a selection of those songs into an alternative soundtrack for the Yogg-Saron encounter in Ulduar.

Since actually mixing a full track would require me to pay royalties (and my disk jockey (DJ) skills are rudimentary), I will simply describe it. I will first present the entire list, then attach some commentary after it for those interested in the reasons for my choices.

The playlist

• Phase 1: Flo Rida, Ke$ha 2009, 'Right Round', R.O.O.T.S., Atlantic Recording Corporation, track 5.
• Start of Phase 2: Lady Gaga 2008, 'LoveGame', The Fame, Interscope Records, track 2.