And realistically, some real non-cheating players will by chance just have similar statistics to bots, especially since the bots will start doing their best to mimic real players.
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.
Also also reminds me of the "you can't respond in less than 100ms, and if start the sprint faster than that after the starting pistol then you're disqualified"-type stuff they have in the Olympics – some people can consistently respond faster and there's a bunch of false positives. Not great.
Because if you force all the cheaters to hide well enough to look like "normal" players, no one will know, and the game feel will not be negatively impacted. Outside of the tippy top of competition where money becomes involved, it's kind of irrelevant if the game is technically fair, as long as it feels fair to everyone.
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.
Didn't Magnus Carlsen say he only needs a single move from a chess computer in the right moment to be virtually guaranteed win
That's because he's an elite chess player. Him cheating once per game could make the difference between being number 1 or number 10 but either way he's up there.
But for you or me, cheating once per game wouldn't make a difference. We'd still be ranked as nobody plebs. To get ranked high enough for people to know our names we would have to cheat dozens of times a game, and experienced players would easily peg us as cheaters.
Try cheating on chess.com, if you cheat enough to make a meaningful difference their servers will automatically nail you with statistics.