It's time to review and change how champions are officially classified (Assassin, Mage, etc).
Xerath being classified as an assassin, I assume simply because his ultimate can snipe people is just absurd. He is one of the mageiest mages in the game. By that I mean he's meant to do huge AoE damage at long range. He doesn't jump in and burst single target damage or anything like that.
Ahri is more of a slippery mage than an assassin. Her kit isn't instant or all that bursty and she relies on her utility and mobility more than damage.
Jax is just a massive, massive failure when built like an assassin. He's THE biggest hybrid of LoL, scaling almost equally well with AD, AP, MR, and AR. He has awful AD ratios so it's not like you can just jump on someone and explode them like you would assume an assassin can. Jax should be either fighter/tank due to his AA based nature and his defensive ultimate, or just Fighter. Assassin should not appear anywhere in his classification.
There are quite a few weird errors that should be addressed. It might even help players get a better sense of how to play certain champions, or find champions more like their playstyle. I remember seeing far too many Jax's that built Hydra, Ghostblade, Black Cleaver, probably because they just assumed Jax was the same as Zed or Riven. Adding a specialist class also wouldn't hurt. I think it would be a better way to describe the harder to classify champions such as Galio, Ahri, Heimerdinger, etc.
being secondary mage, because he can build AP quite effectively.