I was just sitting around. I was thinking about league of legends and decided to calculate the damage output of AP casters. I decided to set the duration to 16 seconds. The calculations are the optimal damage for most champions. However, it is up to a point somewhat realistic.

The champions I calculated are Annie, Anivia, Akali, Cassiopeia, Fiddlestick, Kassadin, Karthus, Ryze, and Veigar.

For most pure AP, I set their AP to 500. I feel this is usually the realistic AP you get in the game very late game unless you get mejai's or other atypical items that super boost only AP and not care about defense or money at all.

For Akali, I set AP = 300 and AD = 200.

For Veigar, I set AP = 700 because you can farm that way.

For Kassadin, I set AP = 300. This is because, for the kind of calculation I made, you need to buid Kassadin tanky.

For Ryze, I set AP = 220 (RoA, Staff), Mana = 3.8k.

The damage calculations assume just one enemy. This might not seem fair for AOE's. However, I assumed most AOE's do damage for the whole duration of the spell, so it shouldn't be really unfair.

Calculations are shown as:
Spell base damage added
Spell AP ratios added
Others(MANA damage or Attack Damage ratio added, etc)
Total Combined Damage.

So in 16 seconds,
4Q 2W 1R. (Bear keeps attacking a champion for 16 seconds and also do the damage for staying near the champion).

980+560+450+1300+560=3850
2.8+1.5+.7+3.2=8.2
4100+3850=7950

2Q 2E Constant R.
Q always double proc.

720+700+2560=3980
2+2+4=8
7980

So for Akali and Veigar, I should've put the lichbane damage in. But I didn't... But then, for Akali, I assumed akali to do E for each cool down, so yeah. I also assumed Akali to hit the target after a Q every time.

1200+650+750=2600
3.2+1.5+1.5=6.2
3 ad
1860(300AP)+600(200AD)+2600=5060

Part of the reason I did these calculations.
Assumed 32 E. 5 Q 1 R Constant W.
Somewhat unfair because of the casting time, inability to press E that fast with arthritus, etc. But then it is also assuming no CD reduction, so it should be fine.

1175+975+6400+450=9000
4.5+2.25+17.6+.6=24.95
12475+9000 = 31475

Assumed all aoe damage done. Constant drain. But only one E, although the cd is about 10 sec. Instead, the E bouces 5 times.

1625+725+2880=5230
2.25+2.25+7.2=11.7
5850(500AP)+5230=11080

Assumed 1.5 attack per seconds, realistic when he gets hit with magic damage. Also assumed that he stays on a champion and autoattacks for 16 seconds (which is where much of the damage comes from).
2Q 2E 4R

560+560+480+4800=6400
1.4+1.4+2+2.1=6.9
2070(300AP)+6400 =8470

Last 3 seconds are spent channelling ulti. The ulti hits 5 champions.

13Q, 16 seconds of E, 1 R

3120+1760+2750 = 7630
7.8+4+3 = 14.8 AP
15030.

This one was hard to calculate. I put CDR 40% on him because you usually get that on his core build. 10% passive, 20% from frozen heart, ~10% runes and masteries. If not, you can drink an elixer.

So the sequence of skills is Q R Q W Q E Q Q Q W Q E Q Q Q W Q.
11Q, 3W, 2E
1540+ 600 + 780=2920
2.2+ 1.8 + 2.1 AP=6.1
88+15MANA =103
2920+1342+3955.2=8217.2

I originally did not put lichbane in. But I realized that is unfair.
Original Calculation.
1040+320+500= 1860
2.4+1+2=5.4
5640 (700AP)

Lichbane: can proc about 7~8 times. 5600 Damage.

Added: 11240.

1. Cassiopeia=31475
2. Karthus=15030
3. Veigar with 8 Lichbane proc = 11240
4. Fiddlestick =11080
5. Kassadin=8470
6. Ryze =8217.2
7. Anivia=7980
8. Annie=7950
9. Veigar without Lichbane=5640
10. Akali=5060

There are obvious controversies with these calculations.
1) Does not account for CC.
Hey, who gets drained by Fiddle 16 seconds? No one has silence or stun?... Yeah, but then this is just the damage a caster can do in optimum situation for 16 seconds. It should give you some basic idea of the dps-ness of each casters.

2) Does not account for death.
I feel like Cassiopeia is the most squish mage in 5vs5 because her only protection spell is her ulti and summoner's spells. So pretty often, you can't just stand still in one place and press E for over 3~4 seconds. Otherwise, you are dead. Same with Karthus. Karthus pretty much dies in most of the team fights because he has to get up close to do a lot of damage. Kassadin and Akali is assumed to stick on an enemy champion and deal constant damage, but Kassadin does not do that in real 5 vs 5, I think. So what I am saying is death will prevent the mages from doing the stationary damage dealing. If not, why not make Ryze with 4 Staff, 1 RoA, 1 Rabandon?

3) Assumes nearly perfect skill shots.
Anivia always double proc Q, Veigar hits 8 Lichbane proc (I don't really play Veigar, but 5 at most seems more reasonable), Akali hits an autoattack after Q every time, etc. So these skill shot champions' damages are overestimated compared to less skill shot champions.

Other Minor controversies.
1. Skills with durations hit for 16 seconds: These skills are usually AOE in this list, and I am assuming only 1 target gets hit by these AOE's, so it does not seem skewed too much
2. Some damages like autoattacks are omitted. Akali autoattack after Q, Veigar autoattacks are ignored. These account for about 800 damage, I think.
3. Magic resist and reductions are not accounted for. Pretty much assumed magic damage is true damage. But as a comparison method, since most of the damages done by these champions are magic damages, it should be reasonable. If you want, you can just multiply these numbers by .5~.6 (assuming you have 55% MP and the 36 or so MP and the enemy has one 100~130 MR). It does not account for damage amplification by Karthus wall or Fiddlestick passives. But then Fiddle is already overestimated because of the constant drain and Karthus is a little overestimated too (Q hits everytime?) and wall reduction lasts only 5 seconds.

Usefulness of these calculations.

1) Neutral Monster Objectives.
Who lacks CC and is stationary? Dragon! Baron, too, up to a point (he has some CC). These are very important. I think about 20~30% of Karthus' usefulness comes from how fast he can kill these monsters. Same with Cassiopeia, although somehow I have not heard people mention that on her very much.

2) Dominion!!
A lot of the situations I mentioned that seems impossible actually do happen in dominion because there are so many 1 vs 1's and 2vs2's with nearly full builds. For example, Kassadin can actually stick to an enemy and autohit him to death in 1 vs 1 (done something like that before). Cassiopeia can also do those crazy damages without worrying about death when there are not many enemies. I once had about 2 bars of health or less left, but killed full health enemy champions(not sure if it was 1 or 2) with R Q W EEEEEQEEE (or something like that in button mashing). These things are all viable scenarios for small squirmishes. Not as likely in 5vs5 because of reduced CC's and reduced damages.

I just did this because I got bored. But then, it seems like an useful data. I guess if someone calculates burst damage data (as in how much a caster can do in one combo or 2~3 seconds of spells), and think about the difficulties of the skills, CC effectiveness, or survivability, etc, it can be good information on understanding each caster champion.

AP Shaco has a 90 second cool down ulti that is possibly the biggest burst damage, but requires high skill. You put 9 Jack in the Boxes (with 40% CDR) on somewhere you predict the enemy will walk near in 90 seconds. The 5 seconds burst damage is super high, but then the skill-demand is also super high (so you can think of it as 90 second channeling burst magic that can be stopped if someone with oracle/red ward knows what you are doing.) Anyway, the calculation for 16 seconds is

7032.825+7644.375(500AP)+400+1000+600+500=17177.2

17177.2

This is from the 5 second 9 box damage plus 2E plus 1 R explosion. The attack speed of the boxes were incorporated in the calculation.

I don't think I ever managed this ultimate skill (I play Shaco very rarely). But I have seen people do 5~6 boxes pretty often.

I have thought of Heimerdinger as a fine caster with two Ashe's bodyguarding him. If the enemy do not kill you, but chase you around in circles near the two turrets, then you get this damage.

2480+1140(4hits)+600=4220
8+2.2+1.2=11.4

9920(500AP)

W is used twice and hits 4 times in this calculation.