Stat

Luck

At 10, the game describes Luck as: “You have 10% more chance of finding items or consumables when you kill enemies. Also increases the rarity of items in the shop and level upgrades.” 10 items give it, 7 take it away, 2 weapons scale with it and level-ups offer it at 4 tiers (Brotato 1.1.15.4).

What the game says at each value

1
You have 1% more chance of finding items or consumables when you kill enemies. Also increases the rarity of items in the shop and level upgrades.
5
You have 5% more chance of finding items or consumables when you kill enemies. Also increases the rarity of items in the shop and level upgrades.
10
You have 10% more chance of finding items or consumables when you kill enemies. Also increases the rarity of items in the shop and level upgrades.
20
You have 20% more chance of finding items or consumables when you kill enemies. Also increases the rarity of items in the shop and level upgrades.
50
You have 50% more chance of finding items or consumables when you kill enemies. Also increases the rarity of items in the shop and level upgrades.
100
You have 100% more chance of finding items or consumables when you kill enemies. Also increases the rarity of items in the shop and level upgrades.
-5
You have 5% less chance of finding items or consumables when you kill enemies. Also reduces the rarity of items in the shop and level upgrades.

Formula

Luck multiplies the wave part of the shop's tier chances (×(1 + Luck ÷ 100), divided instead when negative) and the chance of enemies dropping consumables and crates. The shop odds calculator shows any wave and Luck.

Source

Ported from the game's scripts (run_data.gd, item_service.gd, utils.gd, weapon_service.gd, player.gd); the texts above are its own descriptions.