Ryze's in a spot where you have to nerf him to the ground so he isn't overwhelming or buff him to compensate his strength into weakness. As we've seen, it doesn't work. Ryze needs a extremely bad early and a hard counter to lose his lane and the progress he has made. If nothing else, he's a manaless, powerbursting, CCing and unkillable mage tank who profits too much from a source that is mostly given due to tank items - Mana.
However, I'm not talking about taking off Mana as Ryze's resource. The following things are my thoughts how Ryze could be improved. Even though it might sound strong what I suggest, keep in mind that to follow up his kit tweakments, he should also receive several changes as - ability cooldown in early, mid or late increased - mana & ap.ratio decreased.
Passive, Q, W, and E stay as it is.
R: Upon activation, Ryze's abilities can connect from one enemy unit to another, provided that the second target is within 350 range of the primary target. This means that once Ryze activates any of his basic abilities, the ability will bounce on the next target, and the next target, and so on - it depends on how many enemy units and if enemy units are staying close together.
Imagine following situation: Ryze activates his Ultimate - teamfight starts - enemy team is grouping up - Ryze casts W to bind a target, that bind goes to nearby enemy targets too. Ryze uses his Q, that Q goes from the primary target to other targets nearby. E will bounce more frequently.
Right now Ryze uses his Ultimate only to create a huge damage spike for his engage. The aspect of his AoE is a secondary aspect that is no strategy to be used, but more or less a bonus to the damage bonus. With my suggestion, Ryze becomes passively (when the fear of his Ultimate popping up) and actively a kind of Champion that forces the enemy team to stay away from each other, as Ryze is able to bind multiple targets and use his strong abilities on many.
In my opinion, Ryze should be a fighter/mage best used in group fights. Right now, he's a tanky and bulky hulk who rapes in 1v1 because he's tanky enough for teamfights, and provides damage like a 5 man team against one. My suggestion is that his kit should be tweaked to appeal more in teamfights than in solo fightings, so that the player has to choose: To buy items to be able to sustain and deal proper damage in teamfights - or to buy items to be able to deal outrageous damage in single fights.