This post was made by legopiratesenior:
@Commander_Riker - just to be sure we're on the same page: nobody is advocating sending reports after losing a couple games. VKJ has stated a number of reasonable grounds for suspicion, and none of these suggest launching a report based on a couple of personal losses.
With experience, people become quite successful in correctly deciding whom to report. Taking myself for example (not to brag, but to protect the privacy of other cheat reporters): my most recent 42 reports resulted in 37 bans (including one titled player) -- that's about 88% success rate. Out of the 5 that did not get banned, one got a reprieve because his cheating happened up to about a year ago and then he stopped. Two did not get banned, despite stronger evidence than most of the 37 that got the boot (I know the reasons but cannot disclose them). Two remaining were highly suspicious, but not quite up to 99.99% confidence level that is needed for a ban -- but if they continue generating evidence at the current rate, they will get banned. I have also forwarded a number of reports on behalf of people who asked me for advice (and of those, which I decided had sufficient merit to be forwarded, all but one resulted in bans).
So, there is plenty that one can do to prevent cheating. Note that denying a group membership does not need to be supported by similar evidence (but it should not be justified by explicit accusations). I hope that denying engine users the satisfaction of gaining unearned respect may provide a significant damping factor.
This said, I have some more comments to VKJ's post:
"player whose rating keep increasing linearly" -- not necessarily. It is better to look for sudden and significant increase. Or for a linear-ish and significant increase in just one variant, with no gains made elsewhere. Big red flag. A recent example:
See that jump in the second half of 2014? About 600 point gain. Meanwhile, flat blitz results in the same time period, with plenty of games at about 1300 level. You see something like this, you're completely justified in keeping the guy out of the group. The guy above got banned soon after I passed the report on -- my decision here was done solely based on the rating charts + big rating discrepancy.
"Discrepanicies between online ratings" -- this needs a quantifier. If you see 800 points difference, with at least 100-150 games played in each chess variant, reporting a player is likely justified. With lower ranges, a bit more caution is needed until you get enough experience in weighting in other symptoms. Ideally, though, run analysis of the games (there are online sites that will do this for you). To get more advice, join the Cheating Forum and read the relevant threads. Get ChessAnalyse to evaluate games yourself (and buy it if you find it useful).
BTW, today in the morning, I reported a guy with < 1500 online rating and about 2200 blitz - a reversal of what one would normally consider suspicious. Of course the guy was running an engine in blitz -- playing closer to Houdini in 3|0 games than Carlsen and Anand in their title matches...
id u ever get turned in for cheating by a Fritz Pirate for beating his Fritz. i have. lol. ask agastyagoldy 
How to prevent obvious cheaters from getting into your group
"Open source recommendations, based on team feedback (Last updated 1/28/2020). Originally published in the ACTC club but posted here for this club's admin team to main and evolve this OP (post #1).
General strategy:
It is a good idea to only invite or accept players who have had minimum time on chess.com (say, 1,3 or 6 months). Many returning cheaters (or other trolls) are caught or banned early. Other new users stop being active and would time out if they joined your club and its matches.
What to look for:
1) A player who has a very high rating and mainly wins and extremely few losses/draws (and has played many games)
2) A player whoes rating keep increasing linearly, or jumps suddenly 400-600+ points, and who have played many games
3) Lots of short games involving very few opponents, one of which is always losing and another one winning (say fool's mate).
Below can raise some flags, but in themselves does not offer much evidence:
1) A player who does not have a title, but has 2300+ in online rating
2) A player who does not have a FIDE rating, but 2000+ in online rating
3) A player who is 2100+ and have 100+ concurrent online games (and no title or FIDE rating)
4) Discrepanicies between online ratings and other ratings (bullet/blitz/tactics)... when all ratings reflect many games played and not too many time out in fast games (which could be due to slow connections). An example would be a 800 points diffference with at least 100-150 games played.
None of this offer proof of cheating, but you can use it to determine whether to invite a new member. If you suspect cheating for someone who is already in your group, it may be best not to kick him/her out, but to file a support request with chess.com and let them determine if it is cheating or not.
From chess.com knowledge base:
How do I report someone I think is cheating?
More chess.com resources on cheating:
https://support.chess.com/search?query=cheating