I don't quite know what froggen does (other than Warmog's), but I'm finding that this lane build is pretty strong, if not ridiculous. Like anything, it is not infallible, and it has its weaknesses. But for the sake of arguments and non-GD-like troll behavior, I decided to post here and ask for thoughts and opinions on this strategy.
-- Vs. AP champion.
-- Laning phase to early-mid game.
-- You can usually rush Chalice on your first back by level 6, if your last-hitting isn't bad. If their jungler ganks early, you might be forced back earlier, but just play it out as best as you can.
-- In comparison, Catalyst comes later, unless you get a kill. It costs 1325 gold. In comparison, Chalice + Doran costs 890 + 475 = 1365. Catalyst does give you more general survivability with its HP and HP5 bonus on leveling, but Chalice + Doran gives you an acceptable substitute on survivability versus magic damage, and has superior mana regen for the long-run.
-- Chalice + 2x Doran lets you farm lane indefinitely with level 1 R. I've done the math. If you get blue buff, feel free to farm your jungle and their jungle too (though the latter presents some complications).
-- Farm. Lots and lots of farm. Anivia can pump out rather nasty amounts of damage if played right.
-- Anivia's Glacial Storm is one of the fastest farming skills in the game. Its drawback is that it is a mana black hole. But if you can abuse it endlessly (as this build lets you do), the usual result is that the minions get pushed into the enemy turret, dealing damage (it builds up over time), and causing the enemy champion to compete with the turret for minion kills. The net result is that you outpace your opponent's farming, and you become a force to be reckoned with mid-late game.
-- Since you're pushing the minion waves to mid's turret constantly, they're forced to make hard decisions. Either gank lanes and lose mid, or waste mana defending mid and be unable to gank.
Points of attack:
-- A wild jungler appears! Wild jungler ganks Anivia! Yes, the potential wild card, where pushing a lane constantly is much more likely to summon it. Nothing that map awareness and warding can't solve. Since you're going to be making a gross amount of money, assuming you didn't die twice, you can afford to support yourself with wards. If you can only ward one side, I would prefer bottom side, since Wraiths are popular, and it synergizes with bottom lane's warding. Unless they're wall hopping junglers like Fizz.
---- If the jungler gets Oracle's, well, that sucks. Player smarter I guess. Gank the jungler with your jungler?
-- This build delays building mana. You may find yourself unable to spam skills at the speed that you want if you're trying to kill someone or someone needs help, or if an extended fight happens. Ouch.
-- This build was not made for dueling necessarily. Anivia isn't known for a good early game anyways. However, she is good at farming at a relatively safe distance, and most of her skills can be used for escaping. So if you're going to duel someone, do it at your own risk.
-- You lose a significant advantage if your opponent is able to farm minion waves comparably fast as you can, and can do it for a long time.