Regardless of the items on PBE, because we don't know actual stats until the patch is out, AP's are not really fine on Dominion.

Ahri, Akali, Anivia, Annie, Elise, Fiddlesticks, Gragas, Heimerdinger, Karma, Karthus, Kennen, Leblanc, Lux, AP Malzahar, Morgana, Orianna, Rumble, Soraka, Syndra, Twisted Fate, Veigar, Viktor, Vladimir, Xerath, and Zigg's all need help and have seen very little, if any, tourney play. (elise is new so you can keep her out)

The most common AP's in tourneys are Brand, Cass(bot only), Diana(bot only), Eve(ZaberZ only), Fizz, Kassadin, Kat, Mordekaiser(bot only), Ryze, Swain, Zilean(Pooterss/MMKH), Zyra.

AP's need a little help, not to mention itemization is fairly stale currently.

Edit: Updated the list. Removing "tanks" such as Cho, Galio, and Sej for the first list and Amumu, Leona, Lulu, Malphite, Maokai for the second. As you can see, this tips the scales further into list 1's favor. I would like to also point out that several of the viable champs are only viable Bot(Cass, Diana, and Morde[I actually question Morde's viability now with the DFG nerf])

Gragas hasn't been played bot in ages, regardless if you "meant to play him" or not. Ahri hasn't seen play in months because of the repeated nerfs to her due to her dominance in SR. Feedski has yet to play Leblanc in a tourney and MMKH hasn't touched her in months either, opting for Blitz, Singed, or Talon.

First of all, why is Sejuani in your list of APs?
Also, Cho, Galio, and Sej are all more "tank" than they are "AP mage", so I'm not sure you should be lumping them in that list.

We meant to run Gragas bot a few weeks ago, but I didn't own him then, so we had to use something else.
Konf used Ahri a few months ago back when we still didn't have that many things to deal with Jjajas Udyr and Elalyas Yorick bot, and I'm pretty sure shes still a decent mage top too.

We've actually *banned* Rumble against Zakkers and Lerch, because they actually know how to play him properly.

I'm pretty sure LeBlanc has seen tourney play by Feedski and MMKH at some point.

The point I'm making is that I think more APs are competitively viable than you give them credit for, and even if its still a rather small pool, you have to remember that tourney play is a tad less open-ended than normal solo q play in terms of champion viability.
Even in the S2 World Championships, most teams would pick and ban the same 15-20 champions over and over.

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As to your other question about what APs can buy and what ADs can buy, I'm only going to bring up offensive items, because everyone gets FH.
*Actually, I see APs get a greater variety of defensive items than ADs, because it's been awhile since I've seen an AD get thornmail, but a few of my APs get it as their core armor item.

AP: sweeper, rylais, void staff, deathcap (it sees use on a few champs like Annie and AP burst assassins in general), abyssal, hourglass (a niche item, but sees occasional play, and most Zyras I see get it), RoA, Lichbane (Fizz/Diana/Elise) guise, superchalice, nashors (Teemo/Kayle/Diana) and occasionally WoTA (sustainers like Swain/Nunu)

That's 12 items.

AD: Triforce, IE, PD, Maw, Atmas, Ex Calling, Sanguine, LW, Brut/Youmus, Frozen Mallet, and Manamune (Blitz/Malz)

That's 11 items.

Now, I might have missed some things, but I think I covered all the items that would be considered "viable" on mages and ADs in Dom, and although some of them are a tad niche, they're still perfectly fine on the champs who can use them.

Don't give me that "stale itemization" stuff, cause I ain't buyin it.

Wow, you are just determined to make Amumu god of Dominion, aren't you?

We are, that is why AP need better items so AD do not outclass them. The "Viable" pool in Dominion is less than half the size of the viable pool in other modes, and it is AD dominant. At the moment an AP's endgame scaling comes from Thornmail, without one they can't compete unless they don't get hit at all which is an extremely unlikely situation.

Let me explain my intentions a bit here.

The AP item changes are set to do a few things.
1. Inch the general Dominion populace towards better purchasing habits.
2. Act as a transition to Season 3.
3. Test the waters for how imbalanced AP really has to be to see broader viability.

I'm not too worried about its impacts on Dominion competitive right now, because there's such a huge disconnect between what's popular in competitive and what's considered overpowered for the remaining 99% of the community. Now, is it possible that these items make the existing competitive AP much stronger? Sure--that's a given. But competitive should adjust fairly quickly, and in general, if these strong APs have been good enough to be ban/pick worthy already, they'll continue to be ban/pick worthy. That's sort of the worst-case scenario for competitive, which really isn't all that grim to me. What could also happen is that these changes push a few more champs into viability, and that's what's more important. The gap between viable AP champs and nonviable AP champs is pretty big right now, and it speaks a ton about the health of APs when you can potentially ban out most of them and leave mostly conditionals and unviables left. It's reminiscent of when there weren't many support champs, and you could ban out most of them in SR and pick the one you really want for yourself--granted, this wasn't a good strategy on SR, but Dominion's picks are slightly more compartmentalized and power-centric than SR's.

tl;dr
Consider this a test. Wait until S3 hits to form finalized opinions. Have fun with imba items until then!

My body is ready for Blackfire Torch Amumu. All hail your new tank caster assassin god :P

Nome, I asked before, but will ask again. How do BFT charges gonna work?

Let's say I have a 4 second DoT, I hit you, I expend 3 charges and you have 3 on you. A second passes, you have 2 charges, my DoT ticks once more, you're back at 3 charges.
Have I expended 4 charges (3+1), or 6 (3*2)?

Furthermore, Nome, could you please unpack #1?
"1. Inch the general Dominion populace towards better purchasing habits."
What exactly do you mean by that? More penetration, CDR, mid-game items?

I think one of the things that limits viability of casters on TT is the lack of blue buff. Not so much the mana aspect, as Chalice can pretty much fix most of that, but the insane cooldown reduction it gives. There simply aren't enough items that give cooldown reduction in addition to other stats. Take Brand for example, without getting 30%-40% CDR he is going to combo once and then be useless for a whole fight. It works in SR because there is more poking gameplay since a mistake means 5 enemies can pounce on you -- there is much less of a threat of being instant gibbed on TT because only 3 people are hitting you instead of 5. Without the ability to constantly use spells and maintain a strong presence casters will most likely never be viable choices.

Solution? If you want to work on the itemization paths then there needs to be some heavy cooldown caster items (both with mana and without mana). The new items that help casters stay on par damage wise like Blackfire Torch is a great start, but what good is BFT when you have 10+ second long cooldowns that limit your ability to use your skills?

The new Ichor helps majorly with that too.

Also, we're on the Dominion part of the divide, Stexe
Also, the BFT on the PBE right now has CDR.

Yes I want a 20% CDR item for casters (morello's evil tome do not counter, it sucks)