Enemy team comp in that game was pretty terrible. Both stuns on that team were hard to use. If you jump in after vagir his only chance is to run away and put up his stun thing behind him. No one else can save him.
Against a team with an easier to use/lower cool down form of CC Jax would have been toast.
Also, you should never go 1v1 with Ryze, it is just bad. In general running in as a melee character against someone with a stun will result in dealth. A 2 second stun is 2 seconds without life steal + 2 seconds of damage from them.
The trick with characters like Jax or Shaco has always been to know your targets and go for them. You have to wait until Ryze blows his rune prision or Annie blows her stun. Same is true of Fiddle. It is incredibly important to let your tanks or soaks put the enemies into cool down mode and on the flip side it is important to save your get out of jail free card, like blind, on hiemer or Teemo.
I have been kind of considering making a new account and running around with Shaco again or something. I don't think level 1-15 people are prepared for the things you can do.
If you don't get rod of ages in the first 15 minutes, you start really limiting how much value you can get out of it as therod has less time to build up.