User blog:Amphitere/Amphitere's Skilling

In April, 2013, I decided to tackle the problem of the wiki not having a single, comprehensive list of enhancing percentages when skilling. None of the formulae given take all variables into account and thus do not work for any single-card skill enhance of any card. So I began to collect data in order to reverse-engineer a single, all-encompassing formula which can be used to calculate the percent chance shown.

Introduction
Since it was obvious multiple card enhances showed a percent that was simply the sum of each individual card used, only single-card skilling enhance percentages were necessary to calculate. So I started collecting data to fill in a table and asked guild members to feed me a few high skill level data points I did not have the cards to obtain myself. As time went on, data accumulated and patterns emerged. A brute force attack on the problem taking all variables into account at once seemed to me the easiest way to accomplish the task, although looking back, I probably could have saved time if I piece-wised the problem.

A month later, came the “eureka!” day in which a formula was generated which seemed to work when applied to any known data point I had so far collected. The formula turned out to be ridiculously complicated, however, and is unwieldy at best, incomprehensible at worst. There are simply too many variables which need to be taken into account, making use of the formula much more of a hinderance than a benefit.

To get around this, I used the formula to extrapolate every single-card skill enhance possibility and simply filled in the rest of the data points. The resulting table can be presented in many ways to allow for all variables to be shown. I shared the results to my guild in a few different table formats for their help and have kept it secret otherwise.

For the past three months, I never saw (nor did my guild report) a discrepancy between calculated values and game values, so I assume my formula is the same one the game utilizes. The tables have been most beneficial to my guild and I whenever skilling, so I have finally decided to release my results to the public. The two layouts I found most beneficial I have converted into wiki-representable tables to which I have made links.

Definitions
The tables use a common language. The two most important concepts are:
 * Enhancee: the card you are attempting to skill up
 * Enhancer: the card burned in the skilling process

Color Coding
The two words are almost identical and each has certain characteristics that are variables in the formula. To further complicate matters, these characteristics are usually identically named (eg. Enhancee rarity/Enhancer rarity). Thus, in an attempt to make the tables easier to read, everything is color-coded as follows:
 * White text on dark background: enhancee characteristics
 * Yellow text on red background: enhancer characteristics

Variables
For the tables to show every possibility of single-card skill enhances, they must show every possibility of every variable characteristic. The variables which affect the percent chance when skilling are as follows:
 * Enhancee rarity: 6 possibilities
 * Enhancee current skill level: 9 possibilities
 * Enhancer rarity: 6 possibilities
 * Enhancer skill level: 10 possibilities

Since each of the variables is not dependent on any of the other variables, a simple multiplication (6 &times; 9 &times; 6 &times; 10) reveals 3240 possible single-card enhance pairs, each having a different percent chance to bump the skill level up. As a result, the calculated percents have necessarily been split up into many tables; a single, all-encompassing table would be too difficult to read.

Table Formats
A table is simply a heirarchically-formatted visual representation of all values in a set of data. Every variable accounted for adds (or is) a level in the hierarchy in the same way each variable adds (or is) a dimension in a graphical representation. Given 4 variables, there is 24 = 16 possible ways to format the data into tables (actually, because each variable is independent, x and y can be assigned somewhat arbitrarily, adding another level: 25 = 32 possible formats).

In order to minimize the number of tables, the top-level in the heirarchy should have the fewest possibilities, making it a choice between enhancee rarity or enhancer rarity. I have chosen the former because it is more constant, so less table shuffling. That leaves the other three levels to be placed wherever. I've converted two of the layouts into html/css, click on the links below or below to view the tables: - - Enjoy the skilling process!

Top of Page &#x2014; Amphitere