Originally Posted by Eledhan
Although your math is correct (DPS calculations), I feel your assumptions are flawed...
I am by no means supporting AP over AD (or any build over another), I'm just pointing out that it's not nearly as easy a decision as you let on. There are more things than damage to consider between the two builds (such as the ability to obtain massive ARM, MR, and HP with AP builds compared to AD builds), and the damage component is only one part of that.
I would contest that her entire kit is designed to get her safely into melee range and keep her there. Her E gets you right into melee range. Her Q resets her autoattack and stuns the target for 1.25 seconds. This means you can E, autoattack, reset autoattack with Q for more damage plus stun, and still have time for another attack. Combined with Phage, this locks down one person indefinitely. W keeps you alive and continues to stack the Sunlight passive without the need for fancy target switching which is at best unfocused and at worst unreliable. Instead of needing 3.5 seconds to match the AP *including* the ult, you have now done three autoattacks in the span of 2.5 seconds, a total of 3.0 ratio. In 0.5 seconds, you will have matched the single target AP Burst and can still be doing damage until your abilities are off cooldown. Overall, once the abilities are off cooldown 9.4 seconds later, you have dealt somewhere between two and three times the damage of the original AP Burst build and will continue to do so the longer the teamfight lasts.
Concerning the multi-target AP Burst, if we assume that you don't manage to kill someone in your initial burst, we must then examine what happens afterwards. First, a question: if you are a one-trick pony, as AP Burst is, what point is there to target you after you have used your abilities? By building AP Burst and successfully landing your abilities, you immediately fail your job as a tank, as you now draw no threat.
But let's say that they do consider you a threat. When your abilities come off cooldown, will you will do another 5.1 of AP ratio? No. Because your ultimate is down, you will only deal 2.7 AP ratio worth of damage in your next burst. So over the course of two sets of cooldowns, let's say 9.4 seconds, you will actually deal 7.8 AP ratio worth of damage, assuming you hit three targets again (despite how unlikely that probably is). Adjusted by price, an autoattack at 1.0 AS would need 14.43 seconds to deal the same amount of damage as the AP Burst.
So we can safely say that at 14.43 seconds into a teamfight, AD damage matches AP damage, not including the Q reset autoattack trick. If we continue the trend, we see that AP falls off quite quickly while AD rises consistently. If you plan for teamfights to last less than 14.43 seconds, AP Burst seems superior. If you plan for teamfights to last longer than 14.43 seconds, AD is the superior choice. Since I am uncertain how long a teamfight will last or whether or not I can hit three people at once but am sure that I will always be in melee because of my E, Q, and Phage, I prefer AD.
We have yet to consider another aspect of AD, however: utility. Unlike AP, AD can be used more efficiently for all of the following tasks: farming, taking down towers and inhibitors, jungling/dragon/baron. This alone is a very strong case for AD builds: being able to help your team with tasks other than teamfighting means your character is not completely useless in other parts of the game.