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):
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):
Negotiation EP vs. Negotiation Rounds 
Negotiation EP vs. Goods 
Negotiation EP vs. Fighting EP
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