Ability Hitbox Glitch

So whenever I play someone who has skillshots, my abilities go DIRECTLY through people and don't hit. When I check the replay my abilities are off by a mile. I play at 24ms of ping. Is this my side or the enemies? I can't deal with this... It happens almost every game. How do I hit spells when the enemy has 200-500 ms of ping? That isn't even remotely fair.