How Drop Rates Work (Simplified) and the Factor of Luck Elixirs

[Physiologic]

How Drop Rates Work (Simplified) and the Factor of Luck Elixirs
by Physiologic

Check out my other Pocket Legends guides:
Post-Global Cooldown (GCD) Video Runs at Balefort Sewers
In-Depth Guide to Farming Balefort Sewers
Comprehensive Archer Skills and Equipment Guide
Complete Lv 55 Archer Gear List
Pocket Legends Enemy, Boss, and NPC Compendium
How to Craft Lv 55 Gear
How to calculate your attributes using STR, DEX, and INT
Ring List
Guide to Advanced Mechanics in PL: DPS, Crits, etc.
Void Set versus Sentinel equips: An Unbiased Analysis
In-Depth Guide to Farming Alien Oasis 3: Victory Lap

Check out my other Star Legends guides:
Star Legends General Attributes (STR, DEX, INT) Guide
Prefix/Suffix Compendium for Weapons and Armors
Lv 20-21 Operative Weapons and Equips

I. Drop Rates

First off, drop rates are completely random. No amount of animal sacrifice or any other bizarre ritual, legal or not, will help you get a better drop rate. This is evidenced by Asommers (main developer/admin) himself:

The fairest solution is the one we have, drops are random.

-ALS

That being said, drop rates are also completely independent. If a drop rate of a pink item is 1%, then everyone has a 1% independent chance of getting that pink item - nothing player A will do will cause player B to have a higher or lower drop rate.

Drop rates are also governed by the type of items and the campaigns themselves. For example, pinks in the campaign Skeller Krunch will drop at a much higher rate than pinks in the campaign Balefort Sewers, so pinks in Balefort Sewers will generally be more expensive due to their rarity (and obviously also because they are considered end-game gear, for now).

The only factor that will alter your drop rate is the use of Luck Elixirs or the Big Luck hat (limited event only - it is no longer obtainable). Depending on the type of elixir you purchase you will have a 25 or 35% chance to re-roll. Through a series of testing conducted by other forumers, the Big Luck hat will increase your chance to re-roll at about 15%. The mechanics of Luck Elixirs will be discussed in the next section.

Definition of re-roll: When the game system decides to "roll again," or gives a second opportunity for you to loot an item.

To summarize:
1. Drop rates are RANDOM.
2. Drop rates are independent.
3. Drop rates differ from campaign to campaign, and from item to item (not all pinks have the same drop rate).
4. Luck Elixirs or the Big Luck hat are the only things in Pocket Legends that can currently increase your drop rate to some degree, through a chance to re-roll an item.

II. The Factor of Luck Elixirs

Your drop rate can be raised either by Luck Elixirs or by the Big Luck hat, which is no longer obtainable. Luck Elixirs were at one point purchasable by themselves at a 25% chance to re-roll and a 35% chance to re-roll, but those elixirs are no longer sold by themselves but rather through the "mixture elixirs."

35% Chance to Re-roll
Wicked Dumpster Punch - 3x combo elixir, has 35% chance to re-roll elixir, 20 Platinum, 30 minute duration
Crazy Dumpster Punch - 2x combo elixir, has 35% chance to re-roll elixir, 8 Platinum, 30 minute duration

25% Chance to Re-roll
Trash Can Punch - 1.5x combo elixir, has 25% chance to re-roll elixir, 7000 gold, 5 minute duration
Hardcore Trash Can Punch - 2x combo elixir, has 25% chance to re-roll elixir, 3 Platinum, 5 minute duration
Insane Trash Can Punch - 3x combo elixir, has 25% chance to re-roll elixir, 5 Platinum, 5 minute duration

15% Chance to Re-roll
Big Luck hat (vanity) - approximately 15% chance to re-roll elixir effect when equipped

I don't know if drop rates stack, i.e. Big Luck + 35% Elixir = 50% chance to re-roll, but I doubt they do, unless someone can prove otherwise.

Luck Elixirs are a bit tricky to figure out. Obviously, a luck elixir will have a % chance to activate every time the game registers that you got a drop. There are two distinct check systems that work. Here is the first check system:

Game registers a drop from an enemy.
Scenario 1: Luck Elixir fails to activate. You simply receive the drop noted in the chatbox, and nothing more.
Scenario 2: Luck Elixir activates. You get "Feeling lucky..." in the chatbox and the game will roll another drop, hidden from view.

From Scenario 2 the game goes on a second check system. It will compare your first drop to your second (re-rolled) drop.

Scenario 2a: The game compares your first drop to the second drop. If the first drop is better than the second drop (for example, your first drop is orange and your second drop is white), then you will simply receive the first drop. The second drop is discarded and you won't know what it was.
Scenario 2b: The game compares your first drop to the second drop. If the first drop is worse than the second drop (for example, your first drop is white and your second drop is orange), then you will get the message "You ARE lucky! Rerolled for better loot!" and you will receive the second drop. The first drop is completely discarded and you won't know what it was.
Scenario 2c: The game compares your first drop to the second drop. If the first drop is equal to the second drop (for example, an orange drop compared to an orange drop), then you will get either/or drops (the game will either say nothing or it will say "You ARE lucky! Rerolled for better loot!"

Note: Scenario 2c is still not definitive, but I've personally seen instances in Balefort Sewers in which an orange drop was considered to be a "You ARE lucky! Rerolled for better loot!" drop, even though an orange drop is the lowest drop you can get at that campaign.

III. How Luck Elixirs Affect Pink Drops

Now that we got the basics down, time for some math. We will find out how effective Luck Elixirs are at increasing your chances of getting a pink drop.

Example 1:
Let's assume a pink drop at Balefort Sewers drops at 1% (or 1/100). This is not absolutely true, as the drop rates of any item is only known by the devs, but we will use 1% as an example. You happen to use a Trash Can Punch which gives you a 25% (or 1/4) chance to re-roll for loot for 5 minutes.

(1/1)(1/100) = Your first initial drop rate, 1/1 being your drop rate when you kill a boss - always 100%.
(1/4)(1/100)(99/100) = Your second drop rate, 1/4 being your chance to re-roll using the Trash Can Punch. The 99/100 is necessary for when you happen to roll a pink and re-roll a pink.
(1/1)(1/100) + (1/4)(1/100)(99/100) = 0.012475

Your chance of getting a pink drop at Balefort Sewers, if pinks drop at a 1% rate and using a 25% Luck Elixir, will be increased from 1% to 1.2475%.

Example 2:
Let's assume that a pink drop is slightly better at Balefort Sewers - this time at 5% (or 5/100 = 1/20). We will use a Dumpster Punch which will give us a 35% (or 35/100 = 7/20) chance to re-roll.

(1/1)(1/20)
(7/20)(1/20)(19/20) = Again, the 19/20 is needed when you roll a pink and re-roll a pink.
(1/1)(1/20) + (7/20)(1/20)(19/20) = 0.66625

Your chance of getting a pink drop at Balefort Sewers, if pinks drop at a 5% rate and using a 35% Luck Elixir, will be increased from 5% to 6.6625%.

As you can see there is very minimal effect in using anything to improve your luck at drops. In general though, the higher the inherent drop rate for a given item, the larger the effect of the Luck Elixir used. But once again we will never know the drop rate of any item since that's ultimately the devs biggest secrets...

Feel free to add insights or questions you may have, or anything that needs to be clarified.