Counter Strike is a pretty good example that the statistical analysis alone doesn't work at all...at least not now. Valve has been collecting data since at least 2017 for their VAC Live system and it still doesn't work well enough to prevent or decrease the amount of cheating. The model only gives a cooldown of 20 hours if it flags your gameplay as irregular, and that cooldown resets over time.

It usually takes months, if not years for cheaters to get banned, but it takes a couple of dollars for a cheater to get a new account and start cheating again. Every time Valve fine tunes their models, they end up accidentally banning more innocent players in the process, so nobody has trust in that system anyways. There's too many datapoints to handle in competitive games, and there is no way to set a threshold that doesn't end up hurting innocent people in the process.