PSA: AP Ratios for all champs in the game with an AP ratio except Azir.

Hope this helps anyone who wants to pick an AP champ to try out. Taken from http://www.gamefaqs.com/boards/954437-league-of-legends/69134114

Most interesting is the 5 second burst information, confirming that Cassiopeia, Karthus and Fiddle are the AP carries, while Kog and Zyra are actually very good mids, and why Brand/Vel'Koz always seem to have a good lategame despite "low" AP scaling:

1-10.

Cassiopeia: 2720 base + 7.15 AP scaling. Fiddlesticks: 2960. 5.85 AP scaling. Heimer (RW): 1969 base. 6.33 AP scaling. Karthus: 2300 + 4.6 AP scaling. Zyra: 2440 base. 4.25 AP scaling. (Assumed 2 frenzied plants.) Kog'Maw: 2340 base. 2.7 AP scaling. Add an additional potential 40% of their HP from AA's. Rumble: 2107 base. 3.7 AP scaling. (Danger Zone numbers included.) Brand: 1818 base + approx 12% max HP, with 3.45 AP scaling on a single target. Vel'Koz: 2495 base with passive. 2.95 AP scaling. Fizz: 1815 base. 20% missing HP. 4.1 AP scaling.

11-20.

Syndra: 2014 base. 3.19 AP scaling. Viktor: 1575 base + 4.03 AP scaling. Jax: 1694 base. 3.2 AP scaling. Morgana: 1550 base. 3.95 AP scaling. Kennen: 1530 base. 3.85 AP scaling. Swain: 1416 base. 4.08 AP scaling. Xerath: 1610 base. 3.4 AP scaling LeBlanc. 1435 base. 3.7 AP scaling. (RQ/E.) Poppy: 2080 base. 1.96 AP scaling. Katarina: 1325. 3.75 AP scaling.

21-30.

Nunu: 1400 base. 3.5 AP scaling. Corki: 1652. 2.25 AP scaling. Lux: 1760 base. 2.05 AP scaling. Malzahar: 1170 base. 2.9 AP scaling + 60% max HP. Cho'Gath: 1470 base 3.3 AP scaling. Anivia: 1450 base. 3.25 AP scaling. Nautilus. 1370 base. 3.45 AP scaling. Orianna: 1310 base. 3.4 scaling. Lissandra: 1260 base. 3.2 AP scaling. All of it's AoE. Ahri: 1314 base. 2.978 AP scaling.

31-40.

Mordekaiser: 1060 + 34% max HP. 2.46 AP scaling. Veigar: 1080 base. 2.8 AP scaling. + 80% of the target's AP to this damage. (With Q stacks Veig can move higher.) Diana: 1100 base. 3.3 AP scaling. Kassadin: 980 base. 3.5 AP scaling. 5% max mana scaling. Tristana: 1020 base. 3.3 AP scaling. Ezreal: 1290 base. 2.85 AP scaling. Varus: 942 base + 25% max HP. 2.25 AP scaling. ZAC: 1270 base. 2.2 AP scaling. Add 16% of their max HP + 2% 100 AP per W. Maokai: 1430 base. 2.7 AP scaling. Karma: 1305 base + 2.7 AP.

41-50.

Vlad: 1675 base. 1.96 AP scaling. 16% bonus HP. Annie: 1045 base. 3.15 AP scaling. Akail: 1140 base. 2.7 AP scaling Sejuani: 1130 base + 12% max HP. 2.6 AP ratio. 10% bonus HP scaling. Rammus: 1275 base. 2.5 AP scaling. Ziggs: 1265 base. 2.55 AP scaling. (Assumed they only walked over 1 mine.) Gragas: 1180 base, 2.5 AP scaling. Skarner: 1039 base damage. 2.5 AP scaling. Blitzcrank: 1100 base. 2.2 AP scaling. Nami: 1130 base. 2.1 AP scaling. Leona: 1368 base. 1.9 AP scaling. (Assumed 4 procs of Sunlight.)

51-60.

Volibear: 1383 base. 1.8 AP scaling. Galio: 1156 base. 1.94 AP scaling. Amumu: 924 base + 13.5% of the enemy's max HP. 2.0 AP scaling. Evelynn: 590 base. 25% current HP. 2.35 AP scaling. Elise: 675 base + approx 16% enemy max HP. 1.6 AP scaling. Kayle: 560 + 2.6 AP scaling. Singed: 610 base damage. 2.25 AP scaling. Thresh: 975 base. 1.9 AP scaling. (Thresh can move higher due to his souls giving him additional AP.) Malphite: 890 base. 1.8 AP scaling. Lulu: 980 base. 1.5 AP scaling.

61-68.

Alistar: 707 base. 2 AP scaling. Sona: 984 base damage. 1.4 AP scaling. Zilean: 640 base. 1.8 AP scaling. Sion: 600 base damage. 1.8 AP scaling. Soraka: 560 base damage. 1.2 AP scaling. +5% mana scaling. Twisted Fate: 535 base. 1.65 AP scaling. Janna: 545 base. 1.15 AP scaling. Shen: 410 base damage. 1.1 AP scaling.