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There are many different items that can be collected throughout the course of a normal Prodigy Journey, such as Wands and Staffs, Miscellaneous Items, Buddies, Outfits, Hats, Boots, Key Items and Coins.

Rarity

All items except Buddies, Coins and Key Items have a rarity on them which affects it's drop rate in battle. Not all items are droppable.

They have their own rarity name with their own colour ranging from least to greatest;

Name Rarity% (Classified via Items.DROP_RATE_BY_RARITY) Array
Common
1% 0
Uncommon
0.75% 1
Rare
0.50% 2
Epic
0.25% 3
Legendary
0.10% 4

As well as their own drop rate for their specific item-type;

Name Rarity% (Classified via Items.DROP_RATE_BY_TYPE) Value (s)
Outfits 0.0004% 200
Wands and Staffs 0.0005% 300
Hats 0.001% 150
Boots 0.001% 50
Items 0.025% 50

Calculation of Drop Rate

Drop rate of these items use algebra where Items.DROP_RATE_BY_TYPE is the equivalent of the rarity percentage of it's item-type, and s being the equivalent to any of the values for the specific item type (ex. oufits), while Items.DROP_RATE_BY_RARITY is equivalent to any of the corresponding percentages for the rarity's name (ex. Epic).

Calculation(?):
Items.DROP_RATE_BY_TYPE * s * Items.DROP_RATE_BY_RARITY * 100

An example of calculation would be for example, calculating the drop rate of a Vitrium Hat. It is a hat, which means that it's s value would be 150. It's also a common item type, as it has an array of 0 which means it has a 1% drop rate and is the Items.DROP_RATE_BY_RARITY. Hats have a 0.001% chance drop rate which would mean that it's the Items.DROP_RATE_BY_TYPE, so the final math would be 0.001*150*1*100 which means it has a 15% chance of dropping.

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