Azir's midgame sucks bc of his inability to level up w (his attack speed steroid) until lv 10-14. This renders him unable to attack fast enough. Also, he is forced to buy rylais and nashors tooth first, which gives him about 155 ap. I remember his w has a 60% ap ratio when I read a diamond guide(it doesn't show on wiki for some reason), which gives him a whopping 93 damage per hit disregarding mr added on to the damage per level as shown here. If azir is lv 10 when he gets his second item, he is dealing 93+72=165 damage per hit disregarding mr. Then, we get his lv 1 sand soldier which gives 20% attack speed with nashors which gives 50% along with his scaling. His attack speed is 1.2 approximately. This is a dps of 216 without the q. The q does 145+(0.5*155) which equals 222.5 damage. His e is only used offensively all in when he also ults. He can kill mages, but most mages can kill each other. Azir also only offers his q slow and r ult for utility, and its not safe to do azir r insec as there are ways to fail unless one is an experienced azir main that is good. With the prevalence of divers, azir falls easily due to his low base stats.
50 / 52 / 54 / 56 / 58 / 60 / 63 / 66 / 69 / 72 / 75 / 85 / 95 / 110 / 125 / 140 / 155 / 170
Cass doesn't need to build boots, allowing her to get second item faster. Also, you get roa and rylas, which grants 20 additional ap. Also, her e, available every 2 seconds, 88+(1750.1) + 130 + (0.35175)=296.75 which is a dps of 148 not including her other spells, which may be less than azir, but she gives more utility with her grounding and ult. She is also tankier with roa, and azir's soldiers are avoidable while cass has a point and click. Her poison is easy to land with grounding, so cass has reliable damage. She starts ramping up in late mid game. She also has self peel that is reliable as azir's wall could be flashed and her mobility can kite.
For ryze, he typically builds roa and then Morello, giving 200 ap. We won't count the bonus mana that the q scaling has bc it depends on how much the ryze spammed. 160+ (0.45200) is 250 damage from unboosted q while boosted q is (2501.55 (bc of flux's rank) which equals 387.5 damage. If a full combo is done, which can occur in a few seconds, that's 160+387.5 3+2(75+(0.3200))+160+(0.2*200) which equals 1792.5 damage. If the combo isn't done, he can recharge skills quickly enough to do more damage. Mind the fact that q and 3 recharges quickly, which allows ryze to do qeq combo soon afterwards. Ryze also gets a bit durable due to the items he build, allowing him to do devastating damage throughout a fight in the frontline. His w also allows his team to secure kills. Divers can't kill him easily as he would kill them.
(These champions were calculated at lv 10 with 2 core items)
Azir has a decent dps, but soldiers can be walked out of easily due to their nerfed ranges. Azir is also nothing without his insecs as his numbers aren't enough. Cass has a bit lower, but she has reliable damage that can be used. Cass needs to actually hit qs to be good and use ult properly. Ryze has a lot of damage in his kit, but misproper usage of ults could cause his lower winrate as well has improper combos. All three of these champs are incredibly high skill cap champs that are better in diamond+. Plat allegedly is apparently still learning the basics of the game, so I decided not to follow their winrates. Azir had a winrate of about 45%, around where ryze and Cassiopeia stands right now, and was considered rlly good. However, his nerfs put him in the garbage can. It is still possible to do well on azir, as shown on the dedicated high elo azir mains, but Cassiopeia and Ryze are better picks. Ryze is considered strong in high elo due to his potential. Cass is ok, but she is better than azir. I don't agree that cass and ryze are go to picks, but I consider both of these champs much better than azir.