Using an ultra-high ELO chess engine to score each possible move, then reversing through the players moves and seeing how often it would have been a positive move (one that shifts the balance of the game in your favor) - or perfect move (not sure which). It is extremely rare to make 100% perfect moves in a game, let alone a series of games. Typical gameplay for high level chess player doesn't peak over 72-75% for a given series of N games. Niemann has several tournaments over this and several games with 100% perfect moves. The inconsistency is also a concern since he goes from mid-60's to 78/79 in a span of one tournament.

His games against Magnus were exceedingly high.

FM Yosha puts forward a fairly convincing argument about odds and engine correlation, but another commenter rightly pointed out that these statistics are not seen as incriminating in and of themselves. Unfortunately, even when the preponderance of evidence seems to be against a player - best example is Sebastian Feller (https://en.wikipedia.org/wiki/S%C3%A9bastien_Feller) playing with superhuman accuracy at crucial moments, and whose team captain later admitted to helping him cheat - they can still cast enough doubt to be allowed to continue playing at the highest level.

Here is a blunder that Feller played on move 13 just over a month ago (https://new.chess24.com/wall/news/grandmaster-blunders-mate-...) - this same guy managed to draw against Magnus Carlsen in 2008, in a game where Carlsen also found the moves/mannerisms of his opponent highly unusual.

It's been talked to death. The consensus is you cannot just cherry-pick some games and claim he's cheating.

Everyone has games that are perfect. Everyone. Not just GMs or Super GMs. I have at least a few perfect games and I'm half the rating Hans is.

The games analyzed also have crazy blunders by his opponents.

the gist seems to be that he has unrealistically high correlation with game-engine recommendations, often all the way up to 100%, but only when playing "tough" opponents, and far lower / realistic correlation scores (around 50%) in other games.

for reference, magnus carlsen's correlation score at his peak averages around 70% (according to the video)

Ai written summary https://www.summarize.tech/youtu.be/jfPzUgzrOcQ

He played several games with 100% correlation with what chess engines considered to be the best move, and also played in 5 consecutive tournaments with such a high fraction of engine-preferred moves that his performance rivals the best players in history at the pinnacle of their careers.

It would be nice to get an ELI5 on this too. I used to play chess and have an understanding of the significance... but I don't think I can fully appreciate it as well as someone with a solid background in both.