I like getting E at level one because few champions will let you farm with your Q, and your E allows you to harass from long range. One time, the enemy had a duo mid against me as Ryze (they had an argument). I dealt heavy damage by poking them with E as it bounced back and forth between them and minions 

pls update

"Sherif's embrace"...I love you Jacky.

Who wouldn't want a hug from Sheriff Caitlyn?

I dont understand... Why build a manamune on ryze? He is AP.. And it's for AD's like Jayce, KhaZix... And Frozen Heart... Why not build a Rabadons deathcap or DFG? 

It's for the toggle on what it turns into.

I citate: Muramana  UNIQUE Toggle: Single target spells and attacks (on hit) consume 3%  of current Mana to deal bonus magic damage equal to twice the amount of Mana consumed. Thats why Muramana deals way more dmg late, a deathcap or a DFG would be useless.

Technically speaking, Ryze is a mana-mage rather than pure AP as well; he doesn't gain nearly as much from the AP as he does from maximum mana.
Since he's going to want a Tear in either case - +1000 mana is big on him - but he makes less use out of the AP gained from items like Archangel's Staff/Seraph's Embrace, there's little reason not to just focus on the mana component and pick up other useful stats along the way.

Muramana toggle works on attacks and spells alike, so that's a pretty big damage boost. Frozen Heart provides an aura, CDR, and lets him actually tank quite a bit. RoA is there not for the AP, but the mana and health. With a finished build, he's doing just as much damage as a proper AP, but he's also packing all this armor and CDR and health and a bit of AD too.

With a brief look into the math of it all... Overload has a 0.4 AP ratio plus an additional 6.5% of his maximum mana.
Seraph's Embrace, no other items, no masteries, no runes: Overload deals a total of 356.48 damage (160 base, 50.88 from AP, 145.6 from maximum mana). If his mana is completely full, he can gain a 598-point shield every 120 seconds from the Seraph's Embrace active (less if his mana isn't full).
Muramana, no other items, no masteries, no runes: Overload deals a total of 440.0 damage (160 base, 0 from AP, 145.6 from maximum mana, 134.4 bonus from Muramana toggle). 305.6 of this magic damage, the other 134.4 is physical, so he's actually doing hybrid damage now. His autoattacks are additionally dealing 303.6 damage (169 AD, 134.4 from Muramana toggle).
Despite having 0 AP, Muramana is dealing considerably more damage overall. Essentially, the only reason you'd want the Seraph's Embrace is for the shield; it also does 50 more damage compared to the Muramana with the toggle turned off, but there's little reason to get into a fight without the toggle turned on.

And just because we can...
Frozen Heart, no other items, no masteries, no runes: Overload deals a total of 266.6 damage (160 base, 0 from AP, 106.6 from maximum mana).
Rabadon's Deathcap, no other items, no masteries, no runes: Overload deals a total of 303 damage (160 base, 62.4 from AP, 80.6 from maximum mana).
But! Frozen Heart is 300g cheaper, provides an additional 95 armor, 400 mana, 20% CDR, and reduces the attack speed of nearby enemies by 20%. So in this instance, Frozen Heart is actually on-par or better than a Deathcap! And with masteries added into the mix, you can get your max 40% CDR with nothing more than the Frozen Heart (20% from FH, 10% from Overload's passive, and 4%+6% from masteries).

Another pro on building mana instead of AP: Veigar can't deal high damage with his ultimate

Quote from thechosenone124 »

Another pro on building mana instead of AP: Veigar can't deal high damage with his ultimate

Yeah, Veigar isn't a terribly common pick lately, but Ryze is by far one of the best AP counters to him. In a Veigar matchup, it's very important not to build Archangel's Staff against him, or you're just throwing your advantage away! (you still probably want RoA and/or Void Staff, but you can even replace those and still do well as Ryze.)

Im dazzled by the fact that noone mentions boots of fuhrer.

I think item build is a mess. I would rather have a core build and a list of situational items that includes when and why you should build them. For me it would look something like this:

Core: Tear of the Godess > Catalyst > Sorcerer Shoes > Rod of Ages > Muramana

Situational:

1. Banhee's Veil, get it mostly for it's passive shield. Works great against team with strong CC engages such as Malphite, Amumu and Blitzcrank. If enemy is mainly dealing physical damage it might be wiser to get Zhonya's Hourglass.

2. Frozen Heart, great combination of stats for Ryze. This item is always viable but works best against a physical oriented team that relies on attack speed.

3. Will of the Ancients, works great when fights tends to drag out and the spellvamp from your ultimate is not enough. Remember this item will set your damage back, sometimes it's enough to build Hextech Revolver early and continue with other items. Needless to say, Will of the Ancients works best if your team benefits from the aura it provides.

4. Void Staff; should be bought when you notice priority targets are stacking up magic resist. Don't get it only for tanks, Ryze can naturally deal with divers and your team together can deal enough damage to them without your penetration.

I like the build you have, but in place of Frozen Heart, try Iceborn Gauntlet. I realize you aren't spamming auto attacks after each spell, but it really gives him a LOT more unexpected burst, plus a VERY nice slow on your opponent. 

what about a banshee vile for some mr instead of roa if u struggling in lane?

Does muramana add another 6% of your mana ratio to your Q and W? Because the toggle grants you this: 

Single target spells and attacks (on hit) consume 3% of current Mana to deal bonus magic damage equal to twice the amount of Mana consumed.

So the singletarget spells (q,w) deals another magic dmg equals to 2*3%of your mana. Your mana ratio on your Q is 6,5% and on your W is 4,5%. With muramana its 12,5% and 10,5%. This actually doubles your damage if you forget about base dmg of spells.

Does it really work like this?