Annie is fucking terrible, holy shit. If your opponent knows anything about the game, they shove you in and rape you so you can't roam. For being a burst mage, she is out bursted by most of the roster- and at a higher range. Her mana pool is pitifully low, meaning early trades for her put her at a massive disadvantage, so if you all in at 6, (her "spike"), you need 290 of your 500 mana. Hopefully you haven't used your W ever to push the wave before the fight, because if that's the case, you'll need 385 of your 500 mana! With your last 115 mana, you can cast one (1) Q in 4 seconds, or one (1) W in 8 seconds.
Here is your full combo at 6 with aggro annie runes and a doran's ring. I'm also including ignite, just to give annie a better chance, though TP and ghost are just as popular because her lane is so shit: AA: 44, R: 150(+29) Ignite: 170 W: 115(+32), Q: 105(+29) Electrocute: 87, Cheap Shot: 20, Tibbers 3 AA: ~165, Tibbers Burn: ~21 (these are assuming a full 1.5 seconds of tibbers sitting and attacking them) AA(2): 44
Against an Orianna, which is a popular pick right now- also at level 6 with a MR rune, post mitigation damage is ~729. She has 1100 hp assuming she also bought a doran's ring and will not use any shielding (generous for annie). This combo against a player with a brain also requires flash to pull off. So, to sum it up, using every single resource at Annie's disposal ("Burst" mage), nearly emptying her mana and putting both summs on cd 80% of the time, you get to do 2/3 of your opponent's hp. And if you get a second Q off, (literally emptying your mana pool), you can bring that total damage post mitigation up to ~835, leaving you ~300 hp short of killing your lane opponent. If you wanted to deal enough damage to kill, you would need to add 6 auto attacks somewhere along the lines (pretending the ori doesn't regen at all). Annie autos are pretty good, but too slow to deal constant damage and are easily shrugged off by a pot.