There was lot of question about anivia – why she isn’t tier 2 or 1, why annie is better etc. so I did some math – I calculated annie and anivia burst at lvl 6, 11 and 18, with and without ap. I also calculated how much damage you can deal in 10 seconds
Anivia
Q-flash frost
Damage: 60 / 90 / 120 / 150 / 180 +0.5 ap. You can double hit someone with it.
Cooldown: 13 / 12 / 11 / 10 / 9
E-frost bite
Damage: 55 / 85 / 115 / 145 / 175 +0.5 ap. Damage doubled when target is chilled
Cooldown: 5
R- glacial storm
Damage 80 / 120 / 160 +0.25 ap per second, channeled (but you can move / use skills when channeling)
Cooldown: 10
Annie
Q-disintegrate
Damage: 90 / 130 / 170 / 215 / 260 +0.6 ap
Cooldown: 4
E-incinerate
Damage: 85 / 145 / 205 / 165 / 325 +0.6 ap
Cooldown: 8
R-summon: tibbers
Damage: 200 / 325 / 450 + 0.7 ap + aoe dmg (idk how much, I think its like sunfire cape – 40 dmg) + 80 / 105 / 130 tibbers attack damage
Cooldown: 120

Annie has much higher damage from skills, but lower ap ratios than anivia. Also Cooldown on tibbers is high, but it’s almost always ready in team fight.

CARE! LOT OF NUMBERS HERE!

Burst damage:
Lvl6 0 ap:
Anivia – Q-1, E-3, R-1
60+60+115+115+160 (ulti, 2 seconds channel)= 510 damage
Annie – Q-1 W-3 R-1
90+205+200+80(tibbers aoe 2 seconds)+80(tibbers 1 attack)=655
At low level annie deals 145 more damage than anivia
Lvl 11, 100 ap:
Anivia: Q-4 E-5 R-1*
150+50+150+50+175+50+175+50+80+50=810+250=1060
Annie: Q-3 W-5 R-2
170+60+325+60+325+70+80+105=1005+190+1195
Still annie does more damage than anivia – 135 more
Lvl 11, 200 ap:
Anivia: 810+500=1310
Annie: 1005+380=1385
Still Annie does a bit more damage- just 75 more
Lvl 18 – 400 ap
Anivia: 180+200+180+200+175+200+175+200+320+200=1030+1000= 2030
Annie: 260+140+325+240+150+280+80+130=1245+760=2005
With 400 ap at level 18 anivia does a bit more damage – 25 more dmg
Lvl 18 – 600 ap
Anivia: 1030+1500=2530
1245+1140=2385
With 600 ap anivia does more damage-but this amount doesn’t matter-just 145
So overall annie has better burst than anivia – a bit more damage, and her combo is easier to make. However, anivia can do full combo every 10 seconds – annie every 120 seconds.

Damage done in 10 seconds ( same skill levels as above):
Lvl6, 0 ap:
Anivia ( 1 Q, 2 E, 10 seconds R): 60+60+115+115+115+115+800=1380
Annie (3Q, 2E, 1 R, 6 tibbers attacks, 10 seconds tibbers aoe): 90+90+90+205+205+200+400+480=1760
Annie does 380 more damage than anivia
Lvl 11, 0 ap:
Anivia: (2Q, 2E, 10 sec. R)=150+150+150+150+175+175+175+175+800=2300
Annie (3Q, 2E, 1 R, 6 tibbers attacks, 10 seconds tibbers aoe): 170+170+170+325+325+325+400+630=2515
Annie does 215 more damage than anivia
Lvl 11, 100 ap:
Anivia: 2300+650=2950
Annie: 2515+370=2885
With just 100 anivia does more damage – but it’s just 65
Lvl 11, 200 ap:
Anivia: 2300+1100=3400
Annie: 2515+740=3255
With 200 ap anivia does more dmg than annie – 145 more
lvl 18, 400 ap:
Anivia: 3220+2600=5820
Annie: 3980+1480=5460
Anivia does 360 more damage
Lvl 18, 600 ap:
Anivia: 3220+3900=7120
Annie: 3980+2220=6200
Anivia does 980 more damage with 600 ap.

*I usually put only one level in glacial storm – higher levels add just more damage, and cost more mana – it’s used mainly for slow, and combo with frost bite


So annie has higher burst – her damage comes from skills, not from ap (she isn't that item dependent like anivia) – anivia damage comes mainly from ap. It’s much harder to make full combo with anivia – but her skills has low Cooldown, so if you miss with one or two flash frost’s doesn’t hurt – missing with tibbers – hurts (but it’s not easy to miss with tibbers ;p).
Anivia has more utility - you can save allies or block enemies with crystalize, slow them with glacial storm or flash frost, and you can always save your stun for interrupting dangerous skills – death lotus, heart seeker strike, crow storm, absolute zero, etc. You can do same thing with annie – but waiting with tibbers for kat shunpo>death lotus combo can cost you team fight. And let me quote someone:

Quote:

Originally Posted by Volpes I've said it before and I'll say it again--Annie is a one-trick pony with Tibbers stun, but it's a **** good trick.