FoE Advanced – Sanctuary Strategy Shop

FoE Advanced: Guild Expedition Negotiation Analysis

PURPOSE

This post summarizes the results of data tracking for the amount of Expedition Points (EP) gained through negotiating Guild Expedition (GE) encounters.

Conclusions

SUCCESSFUL NEGOTIATIONS
The amount of EP gained through successfully negotiation a GE encounter is based exclusively on the following:

The baseline fighting points for each encounter. These values are determined by the player’s age, the number of units that are defeated, and what GE segment the encounter is in. See FoE Advanced: GE Fighting Analysis for more details.
The number of negotiation offers made (note: not negotiation rounds). The EP rewarded is determined by the baseline fighting EP for the encounter times a multiplier, m. The multiplier is as follows:
- m = 100% + 1.67% x (n– 10); where n = the number of offers made

NOTE: There also appears to be a slight correction factor applied to the baseline fighting EP values of 100.021%. However, since this is such a small value, and the results without it are only off by a few EP, this correction factor can reasonably be ignored.

Example 1:
If you completed a negotiation with a perfect selection of only 5 offers (i.e. you got all 5 right in the first negotiation round) you would make:
m= 100% + 1.67% x (5-10) = 100% + 1.67% x -5 = 100% – 8.35%
m = 91.65%
Therefore you would only make approximately 92% of the EP value obtained from fighting.

Example 2:
If you completed a negotiation with 13 total offers you would make:
m= 100% + 1.67% x (13-10) = 100% + 1.67% x 3 = 100% + 5.01%
m = 105.01%
Therefore, you would make approximately 105% of the EP value obtained from fighting.

As the values for a winning a GE encounter negotiation depend on the number of offers made, there is some variability in the overall point totals possible to achieve for negotiation. However, the approximate breakdown for the Progressive Era is:

Level 1: ~6.5% of total
Level 2: ~12.5% of total
Level 3: ~28.0% of total
Level 4: ~53.0% of total

The following has been confirmed NOT to impact the number of EP earned for successful negotiations:

The total number of goods, previous or current era, spent
The total number of coins, production, or medals spent
The number of negotiation rounds it takes to succeed
The number of failed (red) negotiation offers
The number of mismatched (yellow) negotiation offers

FAILED NEGOTIATIONS
The value of the points earned for a failed negotiation is confirmed not to be scaled to the current GE segment, and appears primarily effected by the number of correct (green) offers made before the negotiation was abandoned. These point values are trivial (~50 EP for 4 correct offers in the Progressive Era), and are therefore not useful for generating a meaningful increasing in the overall score a player can make.

Methodology

The following were tested and tracked in an Excel file (attached at the end of this post):

The number of EP awarded per negotiations (successful and failed)
The number of goods/coins/production/medals required for each offer
The breakdown of correct (green), mismatched (yellow), and incorrect (red) offers made each negotiation round
The total number of negotiation rounds
The total number of goods/coins/production/medals spent per negotiation

The above data was collected by taking iOS screenshots, and then manually entering data into the Excel file.

The ratio between the recorded EP earned by negotiation and the recorded EP earned by fighting was then calculated for each encounter. To better control potential differences in these values due to rounding, separate ratios were also calculated for the smallest values that would round up to the reported values (i.e. -0.5 EP), and the largest values that would round down to the reported values (i.e. +0.4 EP).

The variability in point values were then compared to the various metrics recorded. This included the number of negotiation rounds, the number of negotiation offers, the number of incorrect (red) offers, the number of mismatched (yellow) offers, the total resources spent, and the cost of each negotiation offer.

Once the element that could be correlated with the variability could be determined, the minimum and maximum possible multipliers were calculated using the minimum and maximum ratios calculated using the various worst-case unrounded values described above. The overall minimum and maximum multipliers were then determined by the limiting case multipliers which would cover all ratios of a given type.

The multiplier was then determined experimentally by comparing the recorded negotiation EP values to the rounded values calculated by applying the multiplier to the worst-case lowest unrounded, the reported, and the worst-case highest unrounded fighting EP values . The multiplier was considered “close enough” when the values calculated through this process had at least one of the three calculated results match the recorded negotiation EP values.

Results

Once the data was compiled, it became fairly clear that the number of negotiation offers made was the principle factor accounting for the variability of the EP reward in comparison to the baseline fighting EP. The following graph demonstrates the direct correlation between the EP (as a percentage of the baseline fighting EP) and the number of negotiation offers made.

The minimum multiplier was determined to be 1.66854% per offer above or below 10, and the maximum multiplier was determined to be 1.67113%. In the process of looking at the multipliers, it was revealed that the baseline fighting EP values were between 0.01% and 0.043% higher at the for the baseline negotiation value at 10 offers. Therefore, a correction factor was applied to the baseline fighting EP values.

Ultimately, a multiplier of 1.67% and a correction factor of 100.021% were determined which resulted in every encounter having at least one correct rounded EP result per encounter, and a total of 137 out of the 234 calculated rounded results, or 59%, being correct.

Additionally, it took 733 previous era goods, 878 current era goods, 41,192 gold, 34,264 production, and 650 medals to negotiate all 64 Progressive Era encounters. These numbers are only intended to be illustrative of the scale of goods required to negotiate GE. Luck and negotiation skill will cause these numbers to vary. See the below graph for the cumulative costs vs GE encounter:

The following Excel file contains all of the analysis and plots for perusal (yellow highlighted cells are missing or uncertain data):

GE Points Tracker – Negotiate Download

The following charts visually represent some other relationships, or lack-thereof, between the EPs earned and the corresponding data (these are from the above Excel file):

FoE Advanced: Guild Expedition Meter

Purpose

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.

The GE Meter (Shown at the bottom). Showing Earned Expedition Points, Required Expedition Points, Crowns per GE Meter Level, Total Collected Crowns, and next GE Meter Level.

CONCLUSIONS

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:

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

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

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

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.
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.
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.
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.
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

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.
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.
The inverse matrix |A^-1| was calculated using the MINVERSE Excel function.
The solution matrix |X| was calculated by |A^-1| x |B| using the MMULT Excel function.
The values reported in |X| were then divided by 25 to return the crowns per GE Meter Level per player per age.
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

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.

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.

File Attachment

GE Points Breakdown Download

FoE Advanced: Rapid Goods Transfer

It is possible to rapidly transfer goods between players through the use of unfair trade pairs. An unfair trade pair is defined as two (2) separate market offers of the following format:

TRADE	YOUR OFFER	NEEDED GOOD	RESULT
1	1 x Good A	2 x Good B	-1 Good A / +2 Good B
2	1 x Good B	2 x Good A	+2 Good A / -1 Good B
TOTAL			+1 Good A / +1 Good B

In this way, each trade pair results in doubling the amount of goods offered in the “Your Offer” column. This method quickly allows goods to transfer between players, even if the player being transferred to has few goods to start with.

Example

Let’s say the player being transferred to ONLY has 5 Wine and 5 Marble.

——Trade Pair Round 1——

TRADE	YOUR OFFER	NEEDED GOOD	RESULT
1	5 x Wine	10 x Marble	-5 Wine / +10 Marble
2	5 x Marble	10 x Wine	+10 Wine / -5 Marble
TOTAL			+5 Wine / +5 Marble
FINAL AVAILABLE GOODS			10 Wine / 10 Marble

——Trade Pair Round 2——

TRADE	YOUR OFFER	NEEDED GOOD	RESULT
1	10 x Wine	20 x Marble	-10 Wine / +20 Marble
2	10 x Marble	20 x Wine	+20 Wine / -10 Marble
TOTAL			+10 Wine / +10 Marble
FINAL AVAILABLE GOODS			20 Wine / 20 Marble

——-Trade Pair Round 3——

TRADE	YOUR OFFER	NEEDED GOOD	RESULT
1	20 x Wine	40 x Marble	-20 Wine / +40 Marble
2	20 x Marble	40 x Wine	+40 Wine / -20 Marble
TOTAL			+20 Wine / +20 Marble
FINAL AVAILABLE GOODS			40 Wine / 40 Marble

As each Trade Pair Round results in doubling both goods, in three (3) rounds the player receiving goods has 8 times the number of goods they started with.