Hextech Chest Drop Rates Published

Some important things to note

Big Drops, Free Unlock: Ultimate and mythic skins drop as auto-redeeming permanents (no orange essence required to upgrade them). If you already own the skin, you'll be able to disenchant them for orange essence.

Bad Luck Protection: You can't open three chests in a row without dropping at least one skin shard. This raises the effective drop rate of skin shards to roughly 57 percent.

Beginning during patch 8.7, Masterwork Chests will be purchasable from the store for 165RP (225 RP for a chest and key), or 2250 RP for a bundle of 11 chests and keys.

Masterwork Chests are basically superior Chests that only drop Skin Shards, 525 Orange Essence, Ward Skin + 150 OE, and basic bonus drops.