Stats

Armor, magic resist, mana and attack speed are the same at every star level.

Annie

1 star: Passive: Heal ? Health when damaging a Burning enemy. Active: On first cast, hop on Tibbers, gaining ? max Health and Stunning enemies within 2 hexes for 1.5 seconds. Deal 150 magic damage, Burn, and Wound enemies within 2 hexes for 5 seconds. Burn: Deal 1% of the target's max Health as true damage every second Wound: Reduce healing received by 33%
2 star: Passive: Heal ? Health when damaging a Burning enemy. Active: On first cast, hop on Tibbers, gaining ? max Health and Stunning enemies within 2 hexes for 1.5 seconds. Deal 225 magic damage, Burn, and Wound enemies within 2 hexes for 5 seconds. Burn: Deal 1% of the target's max Health as true damage every second Wound: Reduce healing received by 33%
3 star: Passive: Heal ? Health when damaging a Burning enemy. Active: On first cast, hop on Tibbers, gaining ? max Health and Stunning enemies within 2 hexes for 1.5 seconds. Deal 2000 magic damage, Burn, and Wound enemies within 2 hexes for 5 seconds. Burn: Deal 1% of the target's max Health as true damage every second Wound: Reduce healing received by 33%

3 patches changed Annie, read out of Riot’s game files.