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  1. 1. Introduction Armored Warfare (AW) is an online video game that includes loot box mechanics. Such mechanics function through virtual in-game items under various titles (ie. Loot Crates, Supply Crates) that can be redeemed for randomized selections of other virtual in-game items. The purpose of this study is to determine all the possible rewards and their probabilities of appearing in Platinum Supply Crates. Platinum Supply Crates are desirable due to their overall abundance in availability through completing special operations in Extreme and Hero modes, daily login rewards, weekly contract mission completions and daily battalion contract mission completions. Platinum Supply Crates also offer high value rewards that may be of greater interest to players compared to Gold and Silver Supply Crates, hence this particular study will focus on Platinum Supply Crates only. Figure 1.1: in-game illustration of a Platinum Supply Crate. 2. Method Our experimenters explore the possible rewards and their probabilities of appearing on the AW Public Test Server (PTS) client via the MY.GAMES GameCenter software. The PTS client version as of the time of testing is 0.33.7235. The decision to perform observations on the PTS client and not on the production client is to ensure ease of repeatability for this study. Even though Platinum Supply Crates are abundant in availability, each individual Supply Crate is consumed permanently upon revealing their contents via opening. It is therefore desirable to not consume the stockpile of Platinum Supply Crates of our experimenters, as the time required to build up a significant quantity of Platinum Supply Crates will likely impede future efforts to replicate the study. The contents of each Platinum Supply Crate are examined and recorded in manual tallies by opening each Platinum Supply Crate and redeeming their contents. The method of tallying is at the discretion of each experimenter. Reward drops are tallied separately in order to determine the range of all the possible rewards from Platinum Supply Crates. In the event of receiving Insignia items from Platinum Supply Crates, each set of 10 Insignias are tallied as one item. Insignias are always received in two discrete sets of 10 Insignias, therefore the tallies consider the event of receiving both sets of Insignias as one item. Figure 2.1: in-game illustrations of different Insignia variants. Similar reward drops are grouped into categories to further examine whether the variance in drop probabilities are indicative of unequal weighing. Chi-squared tests are performed in each category to determine the significance in drop probability variances. 3. Results 3.1 Datasets We examine a total of 842 Platinum Supply Crates collected and distributed among two experimenters. The Supply Crates are split into samples of 565 and 279 respectively and first analyzed separately, then aggregated together to determine any anomalies in the variances of their produced contents. 3.2 Results The sample size of opening 565 Platinum Supply Crate and redeeming their contents produced the following tallies: Items Quantity Reputation (50,000) 62 Credits (10,000,000) 27 Premium Time (30 days) 3 Premium Time (7 days) 7 Diamond XP Boost 49 Diamond Intel Boost 41 Diamond Reputation Boost 58 Platinum Commander Insignia 50 Platinum Crew Insignia 73 Platinum Credit Insignia 53 Platinum Reputation Insignia 48 Platinum XP Insignia 66 Gold (13) 31 Gold (17) 24 Gold (19) 28 Gold (23) 27 Gold (29) 16 Gold (37) 17 Gold (53) 8 Gold (73) 4 Gold (113) 2 Premium Vehicle (assorted, 1 day rental) 16 Total possible item categories: 22 Total quantity of item drop events: 565 Figure 3.2.1: table of tallies of Platinum Supply Crate contents with a sample size of n=565. The sample size of opening 279 Platinum Supply Crate and redeeming their contents produced the following tallies: Items Quantity Reputation (50,000) 28 Credits (10,000,000) 8 Premium Time (30 days) 1 Premium Time (7 days) 3 Diamond XP Boost 30 Diamond Intel Boost 19 Diamond Reputation Boost 24 Platinum Commander Insignia 33 Platinum Crew Insignia 28 Platinum Credit Insignia 31 Platinum Reputation Insignia 24 Platinum XP Insignia 30 Gold (13) 16 Gold (17) 12 Gold (19) 11 Gold (23) 13 Gold (29) 10 Gold (37) 1 Gold (53) 7 Gold (73) 1 Gold (113) 1 Premium Vehicle (assorted, 1 day rental) 11 Total possible item categories: 22 Total quantity of item drop events: 279 Figure 3.2.2: table of tallies of Platinum Supply Crate contents with a sample size of n=279. 4. Analysis 4.1 Proportions of Item Drops from Platinum Supply Crates In order to better illustrate the theoretical probabilities of the item drops from Platinum Supply Crates, the proportions of item drops are derived based on the tallies from each of the two datasets. The proportions are recorded as follows: Figure 4.1.1: proportions of item drops with a sample size of n=565. Figure 4.1.2: proportions of item drops with a sample size of n=279. 4.2 Chi-Squared Tests for Categories of Items Several different categories of items can be observed from the item drops of Platinum Supply Crates: rental vehicles, various quantities of Gold, Premium Time tokens, Boosts, Insignias, Credits, and Reputation. Given the similar drop rates between different Boosts and Insignias, the significances of the variances are examined using chi-squared tests. The results are as follows: Figure 4.2.1: chi-squared tests for the dataset of n=565 on the variances of Boost and Insignia drop rates. Figure 4.2.2: chi-squared tests for the dataset of n=279 on the variances of Boost and Insignia drop rates. The variances in drop rates for Boosts and Insignias in the two datasets are determined to be not statistically significant, and that the theoretical drop rates for different Boosts and Insignias should be considered to be equal in each of their categories. 4.3 Analysis of Aggregated Data Given the contextual relatedness of the two datasets, we totaled the tallies from each of the datasets in order to project results from a theoretically larger sample size. The total tallies and derived proportions of item drops are as follows: Items Quantity Reputation (50,000) 90 Credits (10,000,000) 35 Premium Time (30 days) 4 Premium Time (7 days) 10 Diamond XP Boost 79 Diamond Intel Boost 84 Diamond Reputation Boost 82 Platinum Commander Insignia 83 Platinum Crew Insignia 101 Platinum Credit Insignia 84 Platinum Reputation Insignia 91 Platinum XP Insignia 97 Gold (13) 47 Gold (17) 36 Gold (19) 39 Gold (23) 40 Gold (29) 26 Gold (37) 18 Gold (53) 15 Gold (73) 5 Gold (113) 3 Premium Vehicle (assorted, 1 day rental) 27 Total possible item categories: 22 Total quantity of item drop events: 844 Figure 4.3.1: table of tallies of Platinum Supply Crate contents with an aggregated sample size of n=844. Figure 4.3.2: proportions of item drops with an aggregated sample size of n=844. Chi-squared tests are also performed on the variances of different Boosts and Insignias for the aggregated data. The variances in each of the two item categories are found to be not statistically significant. Figure 4.3.3: chi-squared tests for the aggregated dataset of n=844 on the variances of Boost and Insignia drop rates. 4.4 Observations on Quantities of Gold Throughout the tally, it is observed that Gold item drops from Platinum Supply Crates contain fixed quantities of Gold. The probabilities of receiving each discrete quantity of Gold appear to be inversely proportional to the quantities. The only observed quantities of Gold obtained throughout the study are as follows: 13, 17, 19, 23, 29, 37, 53, 73, and 113. It is also observed that the available quantities of Gold are all prime numbers, although it is unknown if this has any practical significance. 5. Discussion To our knowledge, this study is the first of its type to examine the probability of item drops from one specific source based on the loot box mechanics in Armored Warfare. Given the abundance of loot boxes in the game it would be very beneficial to players to determine the number and probabilities of item drops from any loot boxes they may come across, particularly if such loot boxes are obtained through transactions involving real currency. Although this is not the focus of our study, value on loot boxes may be derived based on the possible item drops and their probabilities. Platinum Supply Crates in particular appear to most commonly reward Insignias, Boosts and various small quantities of Gold, therefore the value of Platinum Supply Crates may depend primarily on the value of items within these three categories. Some of these items may have fixed monetary values such as Gold which can be purchased with real currency, or Insignias which can be purchased in-game with Gold. The perceived value of the items however may vary from player to player, as it may sometimes be undesirable to further obtain items of which the player already possess in abundance. Given that the perceived values of the items are highly subjective, we have elected to not provide further comments or advice here regarding the worth of Platinum Supply Crates. The results and statistical analyses of this study is only directly applicable to Platinum Supply Crates until new information becomes available, any current extrapolation to other loot boxes may not be accurate. Nevertheless, we hope this study will encourage future similar studies to examine other loot boxes in Armored Warfare, as well as official disclosure on the item drops and probabilities of the loot boxes. Further discussions are encouraged and will be hosted on the ArmoredLabs forum and Discord servers. The forum and Discord server can be accessed with the following links: https://armoredlabs.net/ https://discord.gg/scTRpBb 6. Acknowledgements We would like to thank the ArmoredLabs community for their continuing support and contributions during this study. We express special gratitude to danlambo and Qbicle for their provided data, and dark_demigod for his data analysis. This is study is motivated purely out of casual interest and hobby. We apologize for any silliness and unprofessionalism that may have entailed, as well as any chaos that might ensue.
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