FoE Advanced: Guild Expedition Meter

Purpose

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This post is intended to determine the Expedition Points (EP) required for each level of the Guild Expedition (GE) Meter, and the number of crowns obtained every time the GE Meter reaches a new level.

CONCLUSIONS

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EP PER GE METER LEVEL

• The points required for each level of the GE Meter are scaled based on the total potential points the guild can earn as a whole. The rough breakdown is that Level 18 approximately corresponds to every member only completing GE Level 3, and Level 25 corresponds to every member completing GE Level 4. A detailed breakdown is presented in the following table and plot:

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• Given the points breakdown based on player age, the following is an example impact that each player has on the GE Meter Level, compared to the equal contribution each player makes to completing the GE Championship (See FoE Basics: Guild Expedition):

In the above example, each player contributes an equal 2.8% to the Guild Championship, but the single PME player is responsible for 7.6% of the overall EP the guild can earn. Given the graph above, that represents more than an entire GE Meter Level. If all players but the PME player participated in GE, the championship could be won, but the guild would miss out on an entire GE Meter Level crown reward. This would result in the loss of hundreds of potential crowns for the guild above due to the inactivity of a single player.

CROWNS PER GE METER LEVEL

• The amount of crowns earned per GE Meter Level is the same for each level and is based on the ages of the guild members capable of participating in GE at the start. The following table summarizes the numbers which best fit the recorded data, but use of rounded numbers yields sufficiently close results for most purposes:

• An 80 player guild of exclusively IA players could theoretically earn a baseline of ~86 crowns per GE Meter Level [1.08 crowns / IA Player * 80 IA Players], and have a total possible baseline earning of ~2,150 crowns for completing all 25 GE Meter Levels [86 crowns / GE Meter Level * 25 GE Meter Levels]. (Note: it is quite likely that the IA crowns per meter per player is a flat 1)
• An 80 player guild of exclusively CE players could theoretically earn a baseline of ~4,250 crowns per GE Meter Level [53.12 crowns / CE Player * 80 CE Players], and have a total possible baseline earning of ~106,250 crowns for completing all 25 GE Meter Levels [4,250 crowns / GE Meter Level * 25 GE Meter Levels]. This represents approximately 5,000% more baseline crowns than an all IA guild.

Inputs

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• The total points a guild member can earn is based on their age. The rough breakdown is that GE Level 1 accounts for 6%, GE Level 2 accounts for 13%, GE Level 3 accounts for 28%, and GE Level 4 accounts for 53% of a guild member’s total possible points.
• The required expedition points per GE Meter Level, the crowns per GE Meter Level, and the age breakdown of the guild was tracked over the course of multiple weeks. See the Excel file at the end of this post for the collected data.
• The baseline guild expedition values for 64 encounters are from an ongoing tracking sheet and documented values from FoE Advanced: Guild Expedition Fighting Analysis.

METHODOLOGY

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Over the course of a few weeks, the required expedition points for various GE Meter Levels, the crowns per GE Meter Level, and the number of players per age in the guild participating in GE were recorded.

EP per ge meter level

1. These values were entered into Excel and the ratio between the points required for GE Meter Level 1 and the various GE Meter Level datapoints were determined. The lowest value of these ratios was used for each GE Meter Level.
2. These ratios were then input into an Excel graph and a best fit line was plotted using a polynomial formula. The degree of the polynomial formula was increased until the R² value was sufficiently close to 1.0.
3. The polynomial formula was then used to calculate the expedition points required for each GE Meter Level, and the error ratio was determined for those levels that had been recorded.
4. If the expedition points required for the first GE Meter Level had not successfully been recorded, the value was calculated using the required expedition points for subsequent GE Meter Levels and the ratio calculated by the best-fit line formula.
5. Using the guild age breakdown, and approximate baseline total possible points per player age, the total possible points the guild could earn was calculated for each week. These values are then compared against the cumulative point totals for each GE Meter Level. The cumulative values were then used determine the ratio of the guild’s total possible points at each GE Meter Level.

Crowns Per GE METER LEVEL

1. The total number of crowns the guild could earn if they completed 25 GE Meter Levels was calculated by multiplying the crowns per GE Meter Level by 25. This step was taken as I suspected there was some rounding happening in the reported values.
2. The use of matrix equations are used to calculate the solutions to the equation |A| * |X| = |B|, where |A| is a 10×10 matrix containing the number of players per age for 10 selected weeks, |B| is a 1×10 matrix containing the cumulative number of crowns the guild could earn each week if 25 GE Meter Levels were completed, and |X| is the 1×10 matrix containing the Crowns per each player per age.
3. The inverse matrix |A^-1| was calculated using the MINVERSE Excel function.
4. The solution matrix |X| was calculated by |A^-1| x |B| using the MMULT Excel function.
5. The values reported in |X| were then divided by 25 to return the crowns per GE Meter Level per player per age.
6. A final check was conducted using the values determined in step 5 to recalculated the crowns per GE Meter Level and compared against the recorded values.

RESULTS

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EP PER GE METER LEVEL

• The highest GE Meter Level recorded was Level 22 during the week of 7/9/2019.
• The best-fit line used was a 6^th order polynomial with the following (super gross) equation:

y = 0.0000001131x⁶ – 0.0000088446x⁵ + 0.0001699651x⁴ – 0.0008507945x³ + 0.0217166013x² + 0.1516555588x + 0.8279751096

• Using the above formula, the worst error exists for GE Meter Level 2, which is off by -0.10%. However, all other calculated values are between -0.03% and 0.05% of the recorded values. The largest actual EP error was -29 EP for GE Meter Level 2 for the weeks of 9/17/2019 and 9/24/2019.
• The ratios between cumulative expedition points based per GE Meter Level and the total maximum possible expedition points for the guild are remarkably stable. This indicates a high degree of accuracy in the results of this analysis.

For a detailed breakdown of all calculations and recorded numbers, see the tables below, and the Excel file at the end of this post.

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CROWNS PER GE METER LEVEL

• A total of 22 weeks worth of data were recorded for this analysis.
• Using the results of the solved matrix equations as described in the methodology, and re-calculating the crowns per GE Meter Level results in remarkably accurate results. At the worst, the calculated values are off by 1 crown per GE Meter Level compared to the recorded values, and only for 3 of the 22 weeks.
• At this time, no conclusive pattern can be discerned for how the amount of crowns per age increases.

For a detailed breakdown of all calculations and recorded numbers, see the tables below, and the Excel file at the end of this post.

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File Attachment

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