MartinCarpenter wrote:
There's probably a very different standard of proof used by LiChess/chess.com etc vs what you'd really want to accuse someone in person.
Note also that if a player is banned from some site, this doesn't
necessarily tell you much about the probability of them having cheated.
Suppose 1,000 players join a site and over the time that they have an active account, 5% of the players cheat. Also assume a 1% false positive rate by the anti-cheat algorithm over the entire lifetime of an account. Note that if an honest player maintains an account for 5 years, this false positive rate is equivalent to a monthly false positive rate of about 1 in 5,970.
Therefore, if all cheating players are caught, 50 cheats are banned, along with 1% of the remaining 950 honest players - say 10 honest players banned to keep the numbers round. That means that 60 players are banned in total, but 10 of then were honest, even if the algorithm is perfect at detecting cheats and has a small monthly probability of a false positive.
If the false positive rate is higher, or the number of actual cheats lower, then it is possible for the population of banned players to include more honest players than cheats.