> Also many players don't need to cheat all the time; just in that critical moment when it really matters. Didn't Magnus Carlsen say he only needs a single move from a chess computer in the right moment to be virtually guaranteed win? Something like that probably applies to a many people and fields. This is even harder to detect with just statistics.

The difference is that IRL chess and a typical FPS game have very different availability of datasets. IRL chess has both fewer moves per game, and fewer games played in short succession than typical FPS games. Also, with FPS games there is a single metric to evaluate -- the shot landed or missed -- compared with chess where moves are ranked on a scale.

So I'd argue that it would be much easier to do a statistical model to predict a cheating aimbot than it would a cheating IRL chess player. I don't believe Magnus's proposition holds for prolific online chess players when they do dozens or more blitz/bullet games in a single day.