How to check if someone is cheating/hacking?

Without a video of their gameplay, it's hard to really say if they're cheating or not. Maybe they did improve to the point they can beat out other players, maybe they are cheating. I can't really give criteria either, because it'll always fall back to, "Maybe they aren't cheating, and if they aren't, you just booted someone out for no reason." 

Was this like a very gradual improvement, like you played with them a month ago and they were terrible, and now they're really super good at the game? Or was this a sudden change, like a week ago they were garbage, and now they're making diamond plays?