Drops are a mechanic, added in the 3DS v1.3.10 and Mobile v1.6.4 updates, for repeated stages, giving players chances to collect rewards from replaying a stage on which they already caught the target Pokémon.
Repeated Special Stages usually provide Drops, and repeated Main Stages provide Drops, but only start appearing in Blau Salon (Stages 401+), and they only drop Skill Boosters. For Special Stages, the stages only provide drops if stated so in the event description (usually repeated events will offer drops, first-time events won't). The stages will not provide drops if the player has not yet caught the Pokémon.
Once the requirements stated above are met, the game will offer chances to drop the rewards (for example, Coins, Skill Boosters, etc, stated in the event description). Each attempt will give three chances for drops, each one having an independent drop and an independent probability. These chances happen by crossing the 25%, 50%, and 75% HP thresholds. Additionally, they are assigned randomly each attempt, which means the chances can happen in different orders across attempts. A sound will play for each item drop as it happen, and gift box icons will appear above the target Pokémon name (a small gift box for common items and a large gift box for rare items). The drops are rewarded after the end of the stage, but only if the player cleared it. In the case of Skill Boosters, they are used immediately, while other items are added to the player's inventory.
|Drop 1||Skill Booster S||100%|
|Drop 2||Skill Booster S||50%|
|Drop 3||Skill Booster M||25%|
The player starts an attempt on this stage. Drop 1 is assigned to 50% threshold, Drop 2 is assigned to 25% threshold, Drop 3 is assigned to 75% threshold. When the player crosses the 75% threshold, they will trigger a 25% chance for a Skill Booster M to drop. When the player crosses the 50% threshold, they will trigger a 100% chance for a Skill Booster S to drop. When the player crosses the 25% threshold, they will trigger a 50% chance for a Skill Booster S to drop.
As a side note, the way to calculate the probability of no item drops for a stage attempt, multiply all three (100%-chance). For example, Kyogre's drops were all Skill Booster, with chances of 25%, 3.125%, and 1.56%. The probability of no skill boosters on an attempt is (75% * 96.875% * 98.44%) ≈ 71.5%. The probability of no drops from the Eevee stage example above is 0% because Drop 1 has a 100% chance to drop.