Yeah tbh it doesn't really go into chess-specific stats either
You could look at a bunch of other metrics to identify cheating: how many errors/perfect moves^ and whether that's within the usual range. How well were the opponents playing? Etc
If you consider that Nakamura might have been having a good day/week, was already stronger than his opponents, and some of them may have had bad games/days, you can change something from "extremely unlikely" to "about a dice roll"
not really. this may be true for the average player, but as Magnus has explained multiple times, all he or another top GM would need to be near-unbeatable would be to check an engine in 1 or 2 critical positions per game. this essentially impossible to detect statistically. even if a cheater were to use an engine on every move, it would be trivial to just vary the engine used for each turn, vary the number of moves picked, sometimes play a slightly worse move to evade detection, etc etc
What I was trying to say was that Hikaru can essentially predict the future given he has stockfish running in his head, while I don’t think Magnus has that ability, yet Hikaru is ranked lower
Magnus is widely regarded, including by Hikaru, as having the best chess intuition (i.e. subconscious understanding) of any player alive, by some distance. the times he's beaten are almost always when he's out-calculated on a very deep line that he had intuitively disregarded. at the same time though, Hikaru himself is also far better known for his intuition than his conscious calculation, explaining his much stronger performances in faster time controls. if you want a player that's more calculative and, ergo, more like stockfish or another traditional engine, perhaps look at Gukesh, who almost exclusively plays classical for that reason
Is that bit in The Queen’s Gambit about chess players coaching each other between matches complete bullshit? Or should one expect a player to occasionally play uncharacteristically when the stakes are high because they would seek out advice which skews their play?
Also psychological games fall neatly into the scenario you describe. I play better and you play worse because I got into your head, or sent the noisy people to be across the hall from you instead of from me, so I slept like a baby and you didn’t.
The adjournments in The Queen's Gambit were rendered obsolete after chess engines became strong enough to be useful in analysis. The last year that they were permitted was 1996.
Match play at the World Championship (where the two players play each other repeatedly for many games) involves a ton of inter-game coaching and work as each player's team goes over what went well, what went wrong, and how the next game should be approached.
Round robin play in small fields also has a significant amount of preparation because the schedule is known in advance, so players will know whom they have to play the following morning and will prepare accordingly.
I'm not comfortable saying that Hikaru does exactly 0 preparation for 3-minute Chess.com blitz games, but it's probably pretty close to 0.
You could look at a bunch of other metrics to identify cheating: how many errors/perfect moves^ and whether that's within the usual range. How well were the opponents playing? Etc
If you consider that Nakamura might have been having a good day/week, was already stronger than his opponents, and some of them may have had bad games/days, you can change something from "extremely unlikely" to "about a dice roll"
^ according to stockfish