Number of screen switches and speed of play are meaningless. If you use these to complain to the organizers of an online chess playing website they will laugh at you.
There are two ways to tell if someone is cheating. The first is the "smoking gun". Consider this game section -
[White "Allwermann,Clemens (1900) "]
[Black "Kalinitschev,Sergey (2505) Boeblingen (9), 30.12.1999"]
[FEN "r6k/1p3Rpp/p2p1bq1/3N4/2P5/1P6/P1b2QPP/5RK1 w - - 0 1"]
1.Qa7 Rg8 2.Qxb7 Be4 3.Nf4 Qf5 4.Qd7 Qe5 5.Kh1 g5 6.Nh3 g4 7.Nf2 Bf5 8.Nxg4 Be4 9. R7xf6 Bxg2+ 10. Kxg2 Qe4+ 11. Kh3
The question is what would you play in the that position? The situation is that a win in this, the last round of the competition, will win you the tournament ahead of a string of grandmasters. Not bad for a mere 1900. I suspect most of us would play something reasonably solid which keeps the win. Moves like Rxb7 or Rd7 or (for cowards like me ;-) Rxf6. Qa7 is a heart-stopper of a move, a smoking gun. Fritz rates as the best move in the position, a whopping 0.1 ahead of the next best move, Rd7.
Smoking gun #2 game at the end of the game when black resigned leaving the 1900 rated player as the tournament outright winner. What would you say to Kalinitschev in that position?
This is how the conversation went:
Allwermann: "It's mate in 8"
Kalinitschev: "I don't think so"
Allwermann: "“Check it out, you'll find I'm right"
Allwermann was right, of course. Can you find the mate in 8 in the final position? Without silicon assistance?
So, you have your smoking gun and you take it to the organizers. What will they do?
Well, then comes the second way of detecting and proving beyond reasonable doubt that cheating is going on.
They will need to collect at least 20 games each with at least 20 non-database moves and feed them into an engine for checking. Basically what they are looking for is the percentage of the time the suspect chooses a non-database move which matches the engine's first pick, one of first 2 picks, one of first 3 picks. The "proof" thresholds are -
Top 1 65%
Top 2 80%
Top 3 90%
A recent example is the furore over the performance of Borislav Ivanov.
Here are his statistics -
Zadar 19th:
Houdini 1.5a x64 Hash:256 Time:30s Max Depth:20ply
{ Borislav Ivanov (Games: 9) }
{ Top 1 Match: 210/314 ( 66.9% ) Opponents: 150/313 ( 47.9% )
{ Top 2 Match: 270/314 ( 86.0% ) Opponents: 207/313 ( 66.1% )
{ Top 3 Match: 285/314 ( 90.8% ) Opponents: 238/313 ( 76.0% )
{ Top 4 Match: 293/314 ( 93.3% ) Opponents: 267/313 ( 85.3% )
In the 8th round the live feed went down (it is suspected that this allowed his outside help get the moves) and he lost to GM Predojevic. If this result is removed then the new statistics are:
Zadar 19th:
Houdini 1.5a x64 Hash:256 Time:30s Max Depth:20ply
{ Borislav Ivanov (Games: ) }
{ Top 1 Match: 197/287 ( 68.6% ) Opponents: 135/286 ( 47.2% )
{ Top 2 Match: 252/287 ( 87.8% ) Opponents: 188/286 ( 65.7% )
{ Top 3 Match: 265/287 ( 92.3% ) Opponents: 218/286 ( 76.2% )
{ Top 4 Match: 272/287 ( 94.8% ) Opponents: 242/286 ( 84.6% )
As you see, both sets of statistics would get him thrown of a chess server.
For comparison here is the analysis for game 8 when the feed was down:
{ White: Borislav Ivanov }
{ Top 1 Match: 13/27 ( 48.1% )
{ Top 2 Match: 18/27 ( 66.7% )
{ Top 3 Match: 20/27 ( 74.1% )
{ Top 4 Match: 22/27 ( 81.5% )
{ Black: Borki Predojevic }
{ Top 1 Match: 15/27 ( 55.6% )
{ Top 2 Match: 19/27 ( 70.4% )
{ Top 3 Match: 20/27 ( 74.1% )
{ Top 4 Match: 25/27 ( 92.6% )
Note that FIDE has set up a commission to investigate ways to detect and combat computer cheating. Their guidelines are here. Note this section:
E. The FIDE Internet-Based Game Screening Tool
FIDE will supply an Internet-based Game Screening Tool, which will be
accessible to all authorized FIDE officials (IO, IA, ACC members) and
National Federations . It shall be hosted on a FIDE-dedicated webpage
and will enable authorized parties to upload games in PGN format for a
“fast test” that will identify potential outliers in a tournament . By
“screening” it is understood that this provides only a preliminary
test with no judgment value, except that it may be cited while
rejecting allegations and declining to proceed to a manual full test .