Linear regression proved fruitless when studying the trivial, so a variant of the regression system was used to determine that the trivial is likely to be 341 В± 1 point, or approximately 342. Page 3 of 36 3. Introduction 3. 1. Background Have you ever wondered how the world works? The science of physics seeks to explain the nature of the world around us, but reality can be dauntingly employ even for experienced physicists, let alone a typical layperson. Computer games will sometimes seek to simulate the physics of reality, and in some cases, games can even create a new reality with its own laws of nature.
Games can be fanatically accurate – Microsoft’s Flight Simulator line of games can be used to supplement training to become a flight pilot, and the Microspore Falcon line of games is as close as you can get to flying an F-1 5 Falcon fighter jet without joining the Air Force. Other games reduce the physics of reality to a more manageable set of rules that can be modeled and recessed by a home computer, and easily understood by a player. Some games will seek to simulate an entire world (or a portion of a world, such as a city).
The player takes the role of one person, or occasionally a small group of people working together, who seek adventures within the world. When the focus Of the game is centered upon the progression and growth Of your character as he or she progresses through the game and upon the interaction of your character with other characters within the game world, the game is classified as a role-playing game. Within the context of a game, everything is calculated deterministically. The game uses established formulae and known values to calculate certain events.
Those events may contain a random element (such as the chance of a bullet hitting or missing the target), but ultimately, standardized formulae create consistent results. However, to the player, the results appear to be random. Since they cannot see the individual steps of the calculations, only the final results, the game appears to be random. Players can use this data in an attempt to work backwards and determine the underlying formulae and constants that run the game – in other words, players can unravel the physics hat hold the world together. . 2. What is Everest? Everest is a computer game that is played online, over the Internet. It is usually classified as a “massively multilayer online role-playing game” or MORPH. Everest allows the player to take part in a large fantasy world with hundreds or even thousands of other players from all over the world (hence, massively multilayer). The player creates a character that becomes his avatar in the virtual world.
Each player controls his own character, while other characters, animals, monsters, and so on are controlled by the computer server that runs the world. Everest simulates the fictional world of Narrator, its moons, and the ethereal planes surrounding Narrator (which serve as homes for Narrator’s various gods). Players start in the game by hunting creatures that threaten the player’s home city (ranging from vermin that plague the city like rats and bats to opposing races that seek to exterminate the city’s inhabitants), then progressing to more complicated quests and adventures.
As characters page 4 of 36 progress, they become stronger (represented in the game as “gaining a level”); characters start at level 1 and can eventually become level 70 (as of this writing). They also have opportunities to gain new equipment and “alternate advancement’ abilities that increase their power relative to other characters of the same level. Eventually, players can challenge the very gods in combat. Everest was first released to the general public in March 1999. 3. 3. What are Terrestrials? One of the alternate methods Of play in Everest is the ability to craft items, called “terrestrials. There are seven terrestrials that are available to everyone: smiting tailoring fletching (making bows and arrows), pottery, baking, brewing, and accelerating. Four additional terrestrials are restricted to certain aces or classes; these are poison-making, tinkering (the highly unpredictable art of making magical contraptions), alchemy (potion making), and research (the creation of new magic spells). The player will typically start a trademarks attempt (called a “combine”) by deciding which item he or she wishes to make.
Then the player has to collect the necessary components. Some components are sold by vendors in unlimited quantities; others have to be collected from defeated enemies or through the completion of quests; yet other components have to be crafted using terrestrials (this is referred to as “subcommands”). Once a player has collected all the necessary items, he places them in a “combine container” – this is a tailoring kit for tailored items, a forge for smithies items, an oven for food, and so on -? and clicks the “Combine” button.
The game then runs a complicated formula that determines whether the player is able to complete the combine successfully (yielding the desired item), or whether the player fails the combine (usually resulting in a loss of the components). To the player, the process appears instantaneous, and the only reported result is whether the player succeeded or failed the attempt. 3. 4. History of Terrestrials within Everest When Everest was first released, terrestrials were not a significant part of the game. Over time, the developers of Everest added new items that players could make and new abilities that made transgressing easier.
As terrestrials became more prominent, players started to investigate the mysterious mechanics behind their chosen profession. The investigation basically boiled down into attempts to guess or predict the chance to succeed at making items and the chance to increase your skill. Initial estimates and guesstimates were made for these formulae; and as changes were made to he game, these were updated or refined. In addition, the makers of Everest would hold a periodic gathering called a Fan Fairer at which players of the game could meet and interact with the developers.
At these Fan Fairies, deerstalkers would often ask for confirmation or verification of guesses or estimates by the player community. 3. 5. What are Trophies? Each trademarks except research has an item called a trophy. This item is intended as a prize for achieving high skill within the matching trademarks. It costs a significant amount page 5 of 36 of in-game money (platinum pieces, or plat for short; gold, silver, and copper ices are sub-denominations, with each piece being worth ten of the next- smaller denomination) and time to acquire the components, and it has a very high complexity level to make successfully.
Players do not know the exact difficulty level. Page 6 of 36 4. Description of the problem 4. 1. Objective The objective of this paper is to determine the difficulty level (called the “trivial”) of the trademarks trophies and the cap on the chance to succeed at a trophy combine, if any. It is important to players to have accurate information regarding their trademarks combines. This information is used by players to estimate their costs for making items or for increasing their skill. Inaccurate or missing information makes this harder.
In addition, there is always a sense of elegance associated with having complete information. 4. 2. What factors affect success rates? There are five factors that affect a player’s chance to succeed a particular combine. These are as follows: The item’s trivial The players skill Any skill-modifying items the player may use “Mastery/’ abilities Upper and lower caps on the chance to succeed 4. 2. 1 . Changes in 2004 Between September 2004 and March 2005, the developers of the game implemented a number of substantial changes to the mechanics that underlay terrestrials.
Three particular changes are of relevance to this study. Each will be discussed more thoroughly under the appropriate section below. First, the cap on unmodified player skill was raised from 250 to 300, and the cap on modified skill Was removed entirely. Second, the cap of 250 on item difficulty was removed. Third, the developers gained the ability to impose a cap on the chance to succeed for any particular combine, regardless of player skill. (For simplicity, these changes will be referred to as the 2004 changes. ) 4. . 2. Item Trivial and Difficulties Each item a player can make has an associated complexity level called the “trivial” (for reasons that will soon become apparent). Some items are easy to make, meaning they have a low trivial; while others are much harder, meaning they have a high trivial. In general, items that are more useful or more powerful will have a higher trivial; thus, it is more difficult to make these items successfully. Trivial values typically range from 15 to 404 (the highest trivial currently confirmed).
When the game was first released, the trivial values of each item you could make were not known. Instead, they had to be discovered by players. Once a player’s skill exceeded the trivial of the item, the game would give the message “This item is trivial for you to make?’ when the player successfully made the item – hence the origin of the term “trivial. ” This message was later changed to a clearer one (“You can no longer advance page 7 of 36 your skill by making this item”), but the term “trivial” is still used to describe the complexity level Of a trailside item.
For example, if you successfully made an item with skill 200 and did not get a trivial message, then succeeded on the same item with skill 201 and received message that you could no longer advance your skill by making this item, then you could conclude that the item had a “trivial” of 201 – this is the highest value to which you could raise your skill by making this item. Players collated this information and shared it with each other. The majority of such information was gathered at a Web site called CEQ Trader’s Corner (www. Standers. Com).
Around February 2004, the game’s interface was changed so that players could see the actual trivial of the combine they are attempting. However, not all items were visible in this manner; the trivial of teems not listed remained a mystery to players. The trophies are the most prominent of these mystery items. As discussed under the Derivation of Formulae section, each trivial is stored internally within the game as a number called the “difficulty. ” Ordinarily, players would never have direct interaction with item difficulties; instead, the game would invisibly convert the difficulty to a corresponding trivial.
The highest difficulty known at that time was 250, which corresponded to a trivial of 335. Not coincidentally, this difficulty yielded a success rate very close to 50% at the then-maximum skill of 252 (discussed below). After the changes in 2004, new items appeared in the game that had trivia’s far in excess of 335. As of this writing, the highest confirmed trivial is 404, which corresponds to a difficulty of 302. 4. 2. 3. Player Skill In Everest, players increase their skill in each trademarks by attempting combines whose trivial is above their current skill level.
On each such attempt, the player has a chance of getting a “skill-up” and increasing their skill in the corresponding trademarks by one point. For example, if a player has a skill of 200 and attempts a combine with trivial 252, that player has a chance o get a skill-up, regardless Of whether the player successfully makes the item or not. Initially, a player’s unmodified skill within a particular trademarks could not exceed 250. Players assumed that skill was stored as a one-byte unsigned integer, giving a possible range of O to 255. The changes in 2004 allowed players to raise their unmodified skill to 300.
Player skill levels in each trademarks can currently range from O to 300. 42. 4. Skill-Modifying Items Certain items in the game grant a bonus to the players skill in one particular trademarks, expressed as a percentage. For the purposes of the chance to succeed or fail, the players skill is increased by this percentage. For example, if a player has a base skill Of 200 and a Page 8 of 36 5% skill-modifying item, the player’s effective skill would be 210. Known solidifying items range from 1% to 1 5%; by far the most common are 5%. Modified skills are always rounded down to the nearest integer.
When the cap on unmodified player skill was 250, a modifier would raise this skill to a cap of 252. For example, if you had a skill of 200 and a 5% modifier, your effective skill would be 210. However, if your skill was 250 and you used 5% modifier, your effective skill was not 262 as you might have expected. The cap would limit your effective skill to 252. Skill values of 253-255 were presumably reserved values with special meanings in the game. The cap on unmodified skill was removed entirely with the changes in 2004; players could now get the full benefit of any modifier they had.
For example, the highest known modifier is 15%. A person with this modifier and a raw skill of 300 would have an effective skill of 345. The formerly-reserved values from 253-255 no longer hold any special meaning; they represent just another skill level. 42. 5. Mastery abilities As discussed previously, players can choose to work on their alternate advancement abilities in lieu of normal progression in the game. One line of alternate advancement abilities reduces the chance to fail in a particular trademarks by a set percentage. This is not the same as increasing the chance to succeed by that percentage.
The specifics of how Mastery affects the chance to succeed or fail are discussed under “Simplified Formulae” below. The individual abilities are called Tailoring Mastery, Pottery Mastery, and so on. They all function identically, save for which trademarks they affect. For this document, they will all be referred to generically as Mastery abilities. The first rank of each Mastery’ ability reduces the chance to fail a combine in a particular trademarks by 10%. The second rank increases that to 25%, and the third and final rank reduces the chance to fail by 50%.
These are referred to as Mastery O, Mastery 1, Mastery 2, and Mastery 3. 4. 2. 6. Caps The chance to succeed is capped at 5% at the low end and 95% at the high end. This overrides even the reductions of mastery abilities. The low cap means that regardless of your skill or the item’s trivial, you always have at east a 1 in 20 chance of succeeding any combine attempt. The upper cap of 95% is raised by 1% for each 40 points your skill is above the trivial. For example, if an item has trivial 200 and your skill is 240, your maximum chance to succeed is 96%. At skill 280, this chance is 97%.
At skill 279, your chance is 96% the cap is only raised for whole increments of 40 points. In addition, certain items have an individual item cap that overrides the default upper cap. Normally, this cap is significantly lower than the default maximum of 95%. For example, Page 9 of 36 an item might have a cap of 60%. So, even if your skill and other factors loud predict a success rate of, say, 75%, the individual item cap of 60% would override. However, if your predicted success rate is 50%, then the cap would do nothing – it is a maximum on the chance to succeed, not a set value.
Individual item cap values are not precisely known by players. 4. 3. What Is the Issue? Players have very little firm information regarding the trophies. All that is known for certain is that the trophies are not trivial at a player skill of 300. The trivial for the poison making trophy (which is not one of the terrestrials included in this analysis) is visible in the in-game interface, and has a value of 35. This would be in line with the age of the trophies; they were introduced at a time when this was the maximum trivial.
However, the observed success rates at very high skill levels do not match what would be expected given the formulae. An item with trivial 335 should succeed the vast majority of the time if the person attempting the combine has a high skill (over 280 or so), and should reach the maximum success rate of 95% at a modified skill of 295 (or skill 289, with Mastery 3). Therefore, we must conclude that either the trivial value of the trophies being studied differs from the poison-making ropey, or else the game’s developers must have implemented a cap on the chance to succeed at a trophy combine. . 4. Discussion of the Formulae 4. 4. 1 Derivation of Formulae Around 2002, a number of players collaborated on the CEQ Trader’s Corner message boards to generate a tremendous amount of data regarding player skills and success rates. Then, some statistically-knowledgeable players used that data to derive a best-guess estimate of the formulae. Some of the assumptions that underlay these estimates were that skill and difficulty were stored as one-byte unsigned integers (hence the limits of 250 or thereabouts).