User:AureusAve/Reward Tables

Overview
This article presents an analysis of the Warframe reward tables released by Digital Extremes (the developer of Warframe). The aim of the article is to inform readers using this data about the reward tables in Warframe and statistical tools to assist Tenno to form effective strategies to gather items. The data is derived from the values presented in the reward tables webpage, which is referenced in this post in the Developer's Workshop section of forums.warframe.com. Tables are provided, displaying the probabilities of receiving rewards and estimates of the average rates rewards will be selected, based on the released reward tables, for use as tools for the reader to estimate the effort required to gather items.

Article Status
This section provides information on the status of the article.
 * Data Collected - specifies the date and time the source reward tables were read from.
 * Article Generated - specifies the date and time this article was generated.
 * The data this article currently displays has been randomly generated to provide an example for review before generation of articles using the released reward tables.
 * The article author wishes to review feedback from the community before further development.

What is a Reward Table?
A reward table is a list of rewards and a measure of the probability of each reward being selected from the list. A reward is selected from a reward table upon certain conditions being met. In Warframe, many game objects have one or more reward tables, such as missions and enemies, and conditions that cause selection of a reward from a reward table include completion of mission objectives and defeating of enemies. Reward tables are sometimes refered to as "drop tables" and rewards from reward tables are sometimes referred to as "drops". However, since not all cases where these tables are used result in an enemy literally "dropping" a reward, the term "reward table" is used in this article. Reward tables are assumed to have an implicit "no reward" entry, even though it may not be listed. For example, many enemies have a reward table that rewards a mod with a probability of 3%, and no other entry; these tables have an implicit "no reward" selected with a probability of 97% (100%-3%).

When are Rewards Selected?
While this article will not provide an exhaustive list of all the ways Tenno receive rewards in Warframe, enough information will be provided to make use of the tables in the article. The conditions upon which rewards will be selected from reward tables are sorted into two categories:
 * Defeating enemies.
 * Completing mission objectives.

Defeating Enemies
Most enemies have a reward table and when an enemy is defeated on a mission, a reward is selected from their reward table. For these enemies, the more of them defeated, the higher probability of Tenno receiving rewards from their reward table.

Completing Mission Objectives
The number of reward tables a mission has and when rewards are selected from them depends on the mission type. Rewards are selected either after completing a round of the mission, or after reaching the extraction point of the mission. Tenno only receive rewards upon successful completion of the mission. The following sections describe when rewards are selected from their mission types.

Arena, Assassination, Capture, Exterminate, Mobile Defense, and Rescue
Missions with a type listed in this section's title select one reward from their reward table when the Tenno squad reaches the extraction point.

Defection, Defense, Excavation, Interception, and Survival
Missions with a type listed in this section's title are known as Endless-Type Missions; these missions go through a sequence of rounds of increasing difficulty, until the Tenno squad reaches the extraction point. The squad must at minimum complete the first round before they can extract from the mission. These missions have three reward tables (A, B, and C) and a reward is selected every time the Tenno squad completes a round of the mission. The reward tables are selected from in the sequence AABC for the first four rounds and repeat after the fourth round. What constitutes a round of the mission depends on the specific type and is summarized in the following table:

Rescue
Rescue-type mission rewards are explained in more detail [warframe.wikia.com/wiki/Rescue#Rewards here]. The selections from reward tables A, B, and C correspond to the points gained in the referenced article, (A,B,C)=(1,2,3). Rescue-type missions that lack a reward table A do not give any awards for simply rescuing the hostage. In order to get a reward from table C, the Tenno squad must rescue the hostage, without triggering the execution sequence, and kill all the wardens.

Spy
Spy-type missions select a reward from their reward tables (A, B, and C) every time an objective is succussfully hacked. Table A is selected from on the first successful hack of the mission, table B on the second successful hack, and table C on the third successful hack. All three terminals must be successfully hacked in the mission in order to get a reward from table C. The Tenno squad must successfully extract to receive their rewards.

Reading This Section
This section is divided into sections by mission type, the set of missions in that type, and the reward tables (rotations) in the missions. Each mission section contains two tables for each reward table:
 * Probability
 * Average Selections

Probability Tables
These tables list the probability that is selected from the reward table, followed by the estimated number of times rewards must be selected from the reward table to have a 50%, 90%, and 99% chance of the reward being selected at least once. The columns are as follows: Consider the following table as an example: The probability Item02 is selected from the reward is 0.15. After selecting a reward 5 times from the table, the probability of having selected Item02 at least once is 0.5. After selecting a reward 15 times from the table, the probability of having selected Item02 at least once is 0.9. After selecting a reward 29 times from the table, the probability of having selected Item02 at least once is 0.99. As the example illustrates, while the more times rewards are selected from a table and are not a particular reward in the set of possible rewards, the greater the probability the next selection from the table will be that reward. No finite number of selections has a 100% chance of selecting a particular reward. It can be estimated what percentage of the population of Tenno that have received a reward from a reward table and not received a specific item in the table as a reward. If a Tenno has received rewards from the example reward table 29 times but have not received Item02, the Tenno is in a group composed of approximately 1% (100%-99%) of the population of Tenno that have received rewards from this table.
 * reward - a description of the reward.
 * probability - a ratio, rounded to 4 decimals, expressing the expected proportion of times the reward is selected compared to the number of times the reward table is selected from; thus, a value of 0.7501 indicates a 75.01% chance of the reward being selected.
 * 0.5 - the estimated number of times the reward table must be selected from to have a 50% chance of the reward being select at least once.
 * 0.9 - the estimated number of times the reward table must be selected from to have a 90% chance of the reward being select at least once.
 * 0.99 - the estimated number of times the reward table must be selected from to have a 99% chance of the reward being select at least once.

Average Selections Tables
These tables display the average number of times a reward has been selected. The column values are rounded to 4 decimal places and are listed as follows:
 * reward - a description of the reward.
 * avg - the average number of times the reward has been select at this round.
 * avg/round - the average number of times reward has been selected at this round per number of rounds.

For missions with multiple rounds, avg is the sum of the average number of selections of the reward at this round and previous rounds, and the avg/round is avg divided by the number of rounds. Average selections per round provides a metric to evaluate the number of reward selections versus efforts invested to receive the reward. This value can be compared between Average Selections tables of the same mission, as well as Average Selection tables of different missions, even those that differ by type. Tenno should take into account the relative effort required for them, and their squad-mates, to complete a round of a mission when using this data. Consider the following table:

The above table represents a relatively complex example of reward distribution. This table displays the average number of times each reward listed has been selected after round 3 of the Mission Y (Interception) mission is completed. The avg entry for each reward listed is the sum of the average number of times the reward is selected from each of the 3 mission rounds. Since this table is for an Interception mission we know that it has three reward tables, A, B, and C, and since this table is for Round 3 of the mission we know that at Round 3 a reward was selected from reward table B, and that a reward was selected from table A, twice, for each Round 1 and Round 2; thus, any of the rewards listed could have come from table A or table B or both. The entry for Item01 indicates Item01 has an avg of 0.1875 meaning that after the completion of the third round of this mission the reward will have been selected an average of 0.1875 times. The entry for Item01 has a avg/round of 0.0625 (01875 / 3 rounds) meaning that the average number of times this reward is selected per round at Round 3 is 0.0625 times. Assuming that it takes a Tenno or squad the same time and effort to complete one round of any mission, the avg/round for Item01 can be compared to the avg/round for the Item01 entry on any other Average Selections table to determine which would yield more selections of the reward for the time and effort invested. For new Tenno, this may not be a fitting comparison since the difficult in completing Round 1 of a mission may be far less than completing Round 3 of the same or another mission, but as Tenno acquire more Equipment, Modules, and increase their ranks the difficult between rounds of missions will become less significant. For Tenno that find a particular type of mission more difficult or time-consuming, the avg/round can be adjusted by a factor based on how much more effective the Tenno is at completing one type of mission over another. For instance, if the Tenno takes 2 times as long to complete Interception mission rounds, compared to Exterminate missions, then the avg/round for Interception mission rounds when compared to Exterminate missions should be divided by 2 since one round of Interception takes the same time(effort) as 2 rounds of Exterminate. For Rescue and Spy mission, the efficiency can be greatly improved if a Squad of three or more Tenno coordinate to achieve the three objects in parallel, effectively completing three rounds in the timespan of one. Tenno considering the tables for these types of missions should consider what strategy their squad is using when comparing them.