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Besides that, statistics is an unbeatable tool against cheaters.
Only if you want to cap the skill limit. Otherwise you would typically have a hand full of players that are genuinely just good or rather far outside the normal skill range. I guess with a lot of data collection one might be able to determine if there was some kind of natual progress or sudden skill jumps, but all in all it could weed out legitimate players.
You can detect the hit ratio for shooters and win rates for games with matchmaking, those are really good indicators for cheating.
Agreed. For detecting cheaters, statistics work like a Dream