Statistical analysis of the games of Hans Niemann

by ChessBase
10/4/2022 – The cheating accusations against Hans Niemann continue to make waves. To check these accusations, a number of chess players have statistically analysed Niemann's games with the help of computer programmes. The latest research comes from the Brazilian streamer, programmer and data analyst "Rafaelvleite". He comes to the conclusion that Niemann's play "after 2018 shows unexpected" results "not compatible with" a rating of 2700. Here are excerpts from his article about his research.

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According to himself "Rafaelvleite" has

"a bachelor in Production Engineering at the University of Sao Paulo (POLI-USP), and [is] also a Programmer and Data Scientist. Besides that, [he has] a YouTube channel about chess in Brazil, called “Xadrez Brasil”, with almost 300k subscribers and more than 80 million views.

"Rafaelvleite" published his finding on his YouTube channel and in an article, in which he claims to have found the "perfect correlation between ... rating and ACPL (Average Centipawn Loss) and STDCPL (Standard Deviation Centipawn Loss)".

ACPL and STDCPL provide data that allow to estimate the playing strength of a whole range of players by comparing their games with engine programs:

"Basically, Centipawn Loss is a measure of how distant the evaluation of the move a player made in a game is from the suggested computer best move. It is reasonable to think that as a chess player gets better and more professional, the lower will be the Average of the Centipawn Loss.

And Standard Deviation Centipawn Loss is a measure of how consistent the moves are. Amateur players tend to do some good moves, then bad moves, but a professional player is more consistent on the quality of his moves. It is reasonable to think that there is some correlation between Rating and STDCPL then."

The Brazilian had the idea to take a closer look at the games of Hans Niemann and other strong players after "after seeing a video from FIDE Master Yosha, a player that was trying to find some evidence by comparing Niemann’s moves with the ones suggested by the computers".

Here's the video by Yosha Iglesias

To pursue this idea, "Rafaelvleite" built a database of 7568 games from players that "included ... top GMs like Andrey Esipenko, Gukesh, Firouzja, Keymer, Praggnanandha, Erigaisi, Carlsen, Niemann, Caruana, Bobby Fischer and others". He then analysed all games with Stockfish 15 and writes about his results:

"With these studies, I made 2 huge findings: there is an established correlation between a player Rating and the ACPL (Average Centipawn Loss) and STDCPL (Standard Deviation Centipawn Loss).

And when I took the Centipawn Loss averages from all players in the database and grouped by Rating Tiers, and the same to the standard deviations, I found this:

According to the Brazilian statistician there is a marked "correlation between Rating, ACPL and STDCPL". To illustrate his claim, he lists the ACPL and STDCPL values of a number of players:

  • * GM Gukesh (ACPL 22, STDCPL 40)
  • * GM Vincent Keymer (ACPL 21, STDCPL 40)
  • * GM Praggnanandha (ACPL 22, STDCPL 37)
  • * GM Erigaisi (ACPL 22, STDCPL 38)
  • * GM Magnus Carlsen (ACPL 17, STDCPL 32)
  • * GM Fabiano Caruana (ACPL 17, STDCPL 33)

However, the ACPL and STDCPL values of Hans Niemann differ from the ACPL and STDCPL values of these players:

  • * GM Hans Niemann (ACPL 25, STDCPL 48)

"Rafaelvleite" then details the numbers of Hans Niemann:

  1. ACPL stopped to go down at 25 value even when Hans acchieved 2700 rating. According to our expected curves, 25 should stand for a 2500–2550 rated player. A 2700 rated player should have gone down to 22, as all 2700 players above did.
  2. STDCPL is at 48. The lowest value he achieved was 44, again, those are values found in a 2500–2550 player. A 2700 rated player is expected to go down to value 38. This level of 48 shows a high variation regarding the quality of his moves for a 2700 rated player.

Moreover, according to "Rafaelvleite", the data of Niemann changed dramatically after 2018:

"The years before 2018 shows an expected curve: linear, with decay on ACPL and STDCPL, expected values. But the years after 2018 shows unexpected behavior. Low correlations and ACPL and STDCPL not compatible with 2700 rating.

After listing all these data, the Brazilian streamer asks the "Big Question":

"The big question is: What can possibly explain a 2500 strength player acchieve 2700 rating?" and concludes:

"I have pointed a new direction showing the perfect correlation between ACPL, STDCPL and Rating. I have explained the steps that I took, anyone can easily replicate it.

My contribution is done. If FIDE wants to use it as a complementary method to use in the ongoing investigations, it may be helpful. It may not be. I don’t know. I just feel happy with what I found and thankful to have the opportunity to spread it to the world."

The video...

The article...

<< FIDE ratings October 2022
Garry Kasparov on Magnus Carlsen: "his behavior was unacceptable" >>
Topics: Hans Niemann, Magnus Carlsen
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60m van Wely Anti Sicilian

Tired of spending hours and hours on the boring theory of your favourite opening? Then here is your solution, play an Anti-Sicilian with 3.Bb5 against 2...d6 or 2...Nc6, and 3.d3 against 2...e6. In 60 minutes you will get a crash course in how to avoid mainstream theory and in understanding the ideas of this Anti-Sicilian setup. After these 60 minutes you should be able to survive the Sicilian for a long time, without being bothered by new developments found by engine x supported by an x-core machine. Now that it finally comes down to understanding, let's play chess!

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tauno tauno 10/20/2022 06:17
@martinmoore

There are many world-class chess players who are somewhere on the autism spectrum (a couple of them even in the top ten), but it's rude to call them "mad". These types of beliefs are mostly based on lack of knowledge and prejudice, which unfortunately can lead to contempt and hatred in some people who struggle with low self-esteem (or have the same type of diagnosis).

We should understand that these people on the spectrum have certain non-normative abilities, which while they may be limiting in some areas (such as social interaction), may be highly functional in others, to the point that in some cases they may even give you some kind of "superpowers", as Greta Thunberg has put it.
martinmoore martinmoore 10/16/2022 07:51
I do know if Hans cheated or not - it is impossible to prove at any rate but two observation I make

1. How 'mad; would I be to be accused of this if I were completely innocent - Hans is pretty quite really don't you think?
2. In March this year, in an interview, he said that is he did not reach 2700 he would consider his chess career 'a failure' - he also was at pains to point out (same interview) that he has no social life and that he spends most of his rest time in chess training.
mstefa mstefa 10/12/2022 11:21
we'll see how his rating slowly goes down since new security measures.. 2.5 out of 7 for a 2588 performance rating..
Could be due to pressure and accusations.. so we'll have to see next 6 months or a year. My bet - he's never going to be 2700 on official rating list. and not too long on 2600 list either
Thomas Richter Thomas Richter 10/12/2022 06:55
As I quipped years ago (based on a different dataset kindly provided by Ken Regan): To win in chess you don't need to play well, you just need to play better than your opponent. Several people already pointed out that high ACPL (for both players!) can occur in tactical positions, comparisons with players from the past - Tal, Shirov, Morozevich, ... - were proposed. But there's also one player from the current crop of teenagers aiming for complex tactical positions: Alireza Firouzja. I really wonder why data for him aren't shown - maybe because his pattern would be similar to Niemann's?
mc1483 mc1483 10/8/2022 02:46
@jacob: thank you for the link.
Jacob woge Jacob woge 10/8/2022 02:30
You are welcome! Ramirez covers a lot of angles, confirming some opinions I and others, y'all included, may have vented on this site while dismissing others. So, that is nice. As I see it, until now these C-squared podcasts present the highest quality of discussion. These guys have been up and close, they actually know stuff - and recall the JW 1st Law of Conservation:

Opinions times Knowledge = Constant.

The less you know, the more you opine. And vice versa.
tauno tauno 10/8/2022 02:09
@Jacob woge, thanks for the link from me too.
lajosarpad lajosarpad 10/8/2022 01:45
Interesting interview, Alejandro presents a balanced position, expresses his suspicion that Niemann has "likely" cheated, shares that many GMs also believe that. Yet, he adds that he is not sure about it and he did not look into the games. Yet, the circumstantial evidence that you may find when you look into the games only tells you with a probability of 0 < p < 1 (somewhere in the "unsure" zone) that Niemann has cheated (or not). If p is reasonably high, then it is desirable to investigate the case further. But, in order to validly condemn him, I think he needs to be caught in some unmistakable way, like being caught while using a device, or receiving moves invalidly during the game, etc.
lajosarpad lajosarpad 10/8/2022 12:55
@Jacob Woge thanks for the link, looking into it.
Jacob woge Jacob woge 10/8/2022 07:55
This potcast with commentator Ramirez giving his opinion on the whole debacle seems very informative and level-headed to me.

https://youtu.be/NmHyqiKl7GM

Begin at 39:45, and enjoy. Takes more than a lunch break.
Jacob woge Jacob woge 10/6/2022 09:32
“I did not watch the video transmission, I await those who find something interesting in it to point out where and how we can watch it. It is the accusers who need to do the actual work and dig out the proof/evidence, not skeptics.”

I see.

Apart from accusers and sceptics, both of which by the way come in two colours, there is a third option: Genuine interest.

My curiosity got thebetter of me -was great enough to make me want to go see for myself. Clean slate - Avoid other people’s cherry picking. Yours wasn’t, Fair enough.
lajosarpad lajosarpad 10/6/2022 07:56
@Jacob Woge I did not watch the video transmission, I await those who find something interesting in it to point out where and how we can watch it. It is the accusers who need to do the actual work and dig out the proof/evidence, not skeptics. I'm aware you are not an accuser, but you are essentially saying that there is something interesting at some point in the video transmission. I would be willing to invest a short amount of time if this is easily available, but I do not intend to invest 5-6 hours into finding out what moments were suspicious for you. I'm sure that if the accusers (Carlsen & co) find the transmission to be backing their narrative, then they will come up with such a compilation sooner or later.
Jacob woge Jacob woge 10/6/2022 07:19
"Can you point out the timestamp of one or more relevant moments?"

Sorry, no. Segments are scattered thruout the 5h broadcast, putting in the effort once was enough. I pretty much assumed anyone debating the issue had already done the same. How else would you form an opinion?

"Niemann may look very casual, or he may indeed be very casual even in critical moments. This is strange, I grant you that, but does not suggest he is cheating."

Playing against a Mr Nobody, like myself, I would not find absent-mindedness odd. The win comes with no effort at all. The same lack of effort appears in the first face-to-face with the World Champ:

Suggests cheating, yes. Implies, no.

"I do not say that 29... Nc4 disproves the cheating allegations, but it is a serious question and it deserves a serious answer from those who accuse Niemann."

I don’t know about accusers, but think I have given a few options one may or may not regard as serious, that’s not for me to decide. Obviously a definite answer is elusive, otherwise the whole matter would have been settled long ago. Suffice it to say that the dangers of accepting too much advice are apparent, and by their experience with cheating, more apparent to some players than others.

By the way, given the chess.com report, Nepomniachtchi’s smirk makes sense. He played a blitz match with Niemann during that player’s covid lock-down on-line cheating rampage, summer of 2020.

To be fair, I think Niemann in a side remark added the lockdown as an admitted not kosher period, to the aged 12, aged 16 ones. Not being willing to re-re-review, perhaps someone else has noticed.
lajosarpad lajosarpad 10/6/2022 12:11
@Jacob Woge

I do not say that 29... Nc4 disproves the cheating allegations, but it is a serious question and it deserves a serious answer from those who accuse Niemann. Yet, I have seen no explanation about how exactly Niemann cheated in that game and I have seen no explanation of this critical mistake. I have seen many errors from Carlsen in that game, much more than he usually does and I do not see any wonder in the fact that a GM is beating an imprecise champion. Carlsen is the champion because if he play precisely. Once his precision drops, he will no longer be a champion. So, if his precision drops in a game, he will be deservedly beaten. If Niemann used outside assistance to achieve that, then this needs to be proven, Niemann needs to be punished. But none of this is proven so far and I find it deeply troubling that without proof such a campaign of defamation is used against Niemann. Do we want to live in a world where GMs would be afraid to beat Carlsen in view of his large financial and corporative empire? I surely do not. If Carlsen has suspicions, then he needs to back those up with factual proof. If not, then this is simply slander.

"I think a theory needs to be formed about a possible OTB cheating method. Then, somebody has to volunteer to conduct the experiment of applying that method without being detected by security. If successful, then we know it can be done. "

Agreed. But if we find such a method, then that's not proving yet that Niemann was using it. However, we would be more informed about what to focus on when watching him play.

@Tauno

"I'm not sure I understood you correctly, but there are some problems when for-profit companies become courts and judges with their own laws and rules. It can be compared to authoritarian regimes with mock trials and arbitrary punishments. We've seen it on Twitter and Facebook and even Chess.com."

Well said!
lajosarpad lajosarpad 10/6/2022 12:11
@Jacob Woge

"The round 3 video is public, there is ample footage of that particular game. It does take some hours of watching, though. When done, with an open mind, one has a bit more than Carlsen’s gut feeling to judge from."

Can you point out the timestamp of one or more relevant moments? I would be interested to watch those, but I'm less interested to watch the full transmission in order to understand what you suggested. So, I would be happy to look into it if you are making the argument above more specific.

"One could compare with, say Kasparov- Deep Blue. The concentration level of the operator vs. that of opponent."

Everyone is different. Niemann may look very casual, or he may indeed be very casual even in critical moments. This is strange, I grant you that, but does not suggest he is cheating.

"Only if one is out to demonstrate every single move is computer-generated, does this constitute a possible problem. Is that the claim?"

The exact claim was not specific-enough to determine whether that's the case, but it's a bit unfair to attribute Niemann's good moves to the engine and his bad moves to himself. When we have a claim (here it is his supposed cheating), then we need a falsifiable claim, that is, we need to be able to put the claim to the test and, if it's false, then to detect the falsehood. 29... Nc4 is a serious error. We know that Carlsen strongly implied that Niemann was not even concentrating in the game even at critical times (and the 29th move was of critical importance), in other words that he cheated against Carlsen at the Sinquefield Cup. So, if Niemann did not concentrate in the critical moments, because he had outside assistance, then 29... Nc4 does not fit into the pattern.
lajosarpad lajosarpad 10/6/2022 12:10
@Arzi

"Maybe we are not so different?"

We are certainly like-minded in this topic.

@reddawg07

"This "Rafaelvleite" analysis doesn't allow for exceptional chess players who engaged in practices that allow them a spurt in chess abilities."

He is asking a fallacious question:

"The big question is: What can possibly explain a 2500 strength player acchieve 2700 rating?"

Since Niemann has a rating around 2700, the premise that his strength is 2500 is fallacious. It is something Rafaelvleite would like to reach as a conclusion. This is a circular argument ("I'm right because I think I'm right") and also this premise is provably wrong. Niemann played like a 2700 player, this is why he reached his Élő. The accusation against him is that he used outside assistance in order to reach that level.

@Allray15 "about Hans's massive and unprecedent OTB rating gain raise lot of suspicions"

It's certainly not unprecedented. Gukesh and Firouzja also gained Élő points in a very quick fashion and Firouzja climbed from < 2600 to > 2700 quicklier than Niemann. Is Firouzja's performance suspicious to you? If not, then why Niemann's slower rise than Firouzja is suspicious while Firouzja's quicker rise is not? Please explain your suspicion.
tauno tauno 10/6/2022 11:03
@SKAcz, I'm not sure I understood you correctly, but there are some problems when for-profit companies become courts and judges with their own laws and rules. It can be compared to authoritarian regimes with mock trials and arbitrary punishments. We've seen it on Twitter and Facebook and even Chess.com.

User agreement
https://www.chess.com/legal/user-agreement

"TERMINATION
You agree that Chess.com may, without reason and without notice, immediately terminate your Chess.com account, associated email address and access to the Service. ..."

Of course, it is up to Chess.com how they run their own business. However, since Chess.com is an official FIDE partner, I wonder what will happen if it is revealed that Chess.com has violated the FIDE Ethics and Disciplinary Code or the fundamental principles of law and fair trial in handling this current matter.
SKAcz SKAcz 10/6/2022 02:32
Btw. in article

https://en.chessbase.com/post/is-hans-niemann-cheating-world-renowned-expert-ken-regan-analyzes

also is explained (what give big sense) that Kasparov lost to deep blue because started playing it as computer instead of trying continue playing best chess and so he played under his standard more like 2600 than like 2800.
SKAcz SKAcz 10/6/2022 02:18
Science maybe has no proof that Niemann has cheated, but in real as pointed out in bigest czech tv today was presented that he is cheater beacause cheated in more than 100 games! Dot. Checkmate to Niemann. Commercial companies become courts and judges in present and who in real cares about truth, simply be careful to win over Carlsen who has good relationships or is owner of chess server :) Who owns media owns world! :)
Jacob woge Jacob woge 10/6/2022 01:29
“Carlsen strongly indicated that Niemann has cheated, based on Carlsen's gut feelings about how much concentration Niemann did (not) invest into the game. ”

The round 3 video is public, there is ample footage of that particular game. It does take some hours of watching, though. When done, with an open mind, one has a bit more than Carlsen’s gut feeling to judge from.

One could compare with, say Kasparov- Deep Blue. The concentration level of the operator vs. that of opponent.



“It seems strange that the accusers always conveniently ignore 29... Nc4, a mistake that makes a draw far more achievable. ”

Only if one is out to demonstrate every single move is computer-generated, does this constitute a possible problem. Is that the claim?

There is a similar slip in the Firouzja game.


I think a theory needs to be formed about a possible OTB cheating method. Then, somebody has to volunteer to conduct the experiment of applying that method without being detected by security. If successful, then we know it can be done.

The future state of competetive chess may rely upon it.
romainardes romainardes 10/5/2022 05:59
People who are calling this study number cruching forget one crucial factor: How strong the correlation found is. We are not talking about something debatable, but about a .98/.99 correlation. That is HELLA reliable. Cant be simply ignored on a whim.
romainardes romainardes 10/5/2022 05:56
People are dismissing these numbers too quickly. Even IF being an aggressive player that took risks could change Hans' results somewhat, his path toward his current rating still should have shown a somewhat linear progression. His std. deviation could be higher than expected due to play style? Maybe. But he wouldnt fall so completely out of the progression pattern of all other players.
allray15 allray15 10/5/2022 05:26
@Arzi , yes i read it, have you read that 72 page? i bet you you didnt. about Hans's massive and unprecedent OTB rating gain raise lot of suspicions. read page 11 you will know what im talking about. and i bet you have not read appendix x2 chart showing strength by age compared to nordibek , firouzja ,gukesh carlsen, keymer its just straight diagonal up not even a curve explain that to me? its either he is genius or just cheater. Danny gave him a chance and look what he's been up to say publicly that he has cheated only twice.
reddawg07 reddawg07 10/5/2022 04:21
I think I will just rely on Karpov's analysis of the game where Magnus lost to Nieman. To paraphrase Karpov, Magnus played poorly in certain positions in the game. And Kasparov's comment about inappropriate behavior coming from a champion. This "Rafaelvleite" analysis doesn't allow for exceptional chess players who engaged in practices that allow them a spurt in chess abilities. Just like what Nieman did when he went out to Europe and played several tournaments in over the board games and did nothing but study chess. There is even a book in 2012
that touts 'How did Jonathan Hawkins manage to go from being an average tournament competitor to a player on the brink of clinching the Grandmaster title?
PatChessFan PatChessFan 10/5/2022 03:45
Unconvinced...so far.
1.Lets STOP labeling a 12 year old kid a cheat...its always a 12 yr old kid.
2. Cheating "100 times"-means cheating maybe 10 times at 10 games a time (mostly blitz?).
3. Chess.com have a bias to contend with-if they came out and said no cheating other than that admitted to they could have a 7 figure $ liability. Maybe.
4. How much money...if any...did he gain by these 100 games? Anybody know?
5.NOTHING about OTB. NOTHING.
arzi arzi 10/5/2022 01:39
allray15, did you read the chess.com -raport?
arzi arzi 10/5/2022 01:38
Lajosarpad:"@Arzi I was going to describe the witch tests, but you have beat me to it! :)"

Maybe we are not so different?
allray15 allray15 10/5/2022 01:15
Guys Just watch Niemann's analysis of his game against Firouzja in the recent Sinquefield cup, this is not something 2700 analyzes games according to Naka. and I believe him. Just look at his face and the way he explains

https://www.youtube.com/watch?v=-sfb6o1oWBU
lajosarpad lajosarpad 10/5/2022 01:01
@Arzi I was going to describe the witch tests, but you have beat me to it! :)
lajosarpad lajosarpad 10/5/2022 12:59
Our main topic, as Arzi pointed out is the Carlsen - Niemann game, about which Carlsen strongly indicated that Niemann has cheated, based on Carlsen's gut feelings about how much concentration Niemann did (not) invest into the game. Analyzing all of Niemann's games to validate (or invalidate) a suspicion does indicate information about Niemann's play (when the analysis is done correctly), but does not answer the main question: has Niemann cheated in his game against Carlsen? If yes, then the main point of his accusers is correct. If not, then Carlsen is factually wrong about that game. It seems strange that the accusers always conveniently ignore 29... Nc4, a mistake that makes a draw far more achievable.

Now, on a broader spectrum, analyzing Niemann's games in his career to find possible cheating, a valid analysis would include all the games of players ever achieving 2700 and apply the same metric. Doing the analysis for only a few people can easily lead to premature, unsubstantiated conclusions (take a glass of whater from the sea... Now, do you see any whales in it?). However, even if such analysis is correctly done and even if it is enforcing the suspicion, it is by far not enough to factually know that a player has cheated. Such analysis can only validate a suspicion and serve as an argument for an investigation to start. But we all agree, if I'm not mistaken that an investigation is most welcome.
arzi arzi 10/5/2022 12:36
In Sinquefiled Cup he had elo 2688. His performance number in that same tournament was 2722. His current Elo is 2699. Do we count 2700 as a 2700 group or when the number is 2701?
Revealingknighty Revealingknighty 10/5/2022 12:15
Has anybody pointed out that Niemann has not yet actually reached a 2700 rating on any fide classical rating list? Why does he keep getting referred to as a 2700?
arzi arzi 10/5/2022 12:02
satman, it is not so simple. Those certain people want Niemann to play these testgames forever. In the old days, in a witch test, the suspect was tied to a chain and thrown into a pond. If he/she survived, then the suspect was a witch, he/she had to be burned to death, and if the suspect drowned, then he/she was innocent and went to heaven. Hallelujah!
mc1483 mc1483 10/5/2022 11:58
@satman: what if his rating drops but he claims that's because the spotlights are on him, and he cannot focus on chess anymore?
satman satman 10/5/2022 11:41
The answer to all this is simple - just let him play.
With the spotlight firmly on him, cheating will be out of the question.
If he can maintain his 2700 rating under these conditions then certain people will have to eat their words.
mc1483 mc1483 10/5/2022 10:09
@Sigmasan: "Seems logical to do it when playing significantly higher rated players to maximize the rating gain and trusting your skills when playing lower rated players".
I think it is the opposite: playing bad against strong opponents, playing good against weak ones. Because this way a possible cheating would be more difficult to notice; also only a minimum assistance would be required, making the cheating even more difficult to notice.
arzi arzi 10/5/2022 07:24
littlefish:"I'm not necessarily saying Niemann didn't cheat, just that so far noone has found anything in statistical analysis of his OTB games that indicates cheating. Of course a 2500 who cheats in a smart way could be virtually undistinguishable from a real 2700."

In fact that is the point! Did Niemann cheat in Carlsen-Niemann otb-game? If Niemann has cheated in the past, that's a separate case. This whole thing started from that otb-game. Carlsen has not given any proves for his mystic claims.
WildKid WildKid 10/5/2022 07:07
As a data analyst and statistician I'm a bit sceptical of this analysis. Several questions:
1. Average values of centipawn loss etc are quoted for different ELO values. But how much variation is there among players in this statistic? What for instance is the standard deviation?
2. A strange thing about this analysis is that if true it seems to show, not that Niemann uses some illegal technique to find good moves, but that the MOVES THEMSELVES are not good enough for his rating. But if he makes so many bad moves, how come he gets good results? Cheating may help you find good moves. It doesn't help you get good results with bad moves, no method can do that.
3. If anything, the fact that he (according to this analysis) makes so many bad moves, would seem to indicate that he DOESN'T cheat!
littlefish littlefish 10/5/2022 06:12
On the influence of playing style, me and other posters from the ChessNinja message board did analysis on this about 15 years ago and found a clear correlation between ACPL and playing style. Some examples for ACPL of top players and their opponents: Kramnik 5.46:6.21, Anand 6.12:7.55, Leko 5.91:5.76, Adams 6.97:7.33, Morozevich 7.77:8.74, Topalov 6.01:8.10, Shirov 6.64:7.79, Grischuk 6.72:7.94. The opponent ACPL values in particular are pretty much what you'd intuitively expect from the players' styles.

So yes, it's very much possible that Niemann's high ACPL is caused by a tactical style. That should be easy to verify by looking at the average ACPL of his opponents. If it's higher than you'd expect from their ratings that points to a tactical style.

As has been mentioned, the only plausible alternative is that Niemann raked up a high ACPL in games he lost to compensate for an unusually low one in his wins, but that too should be easy to check.

In fact Chess.com did more detailed analysis and concluded that "there is nothing in our statistical investigation to raise any red flags regarding Hans’ OTB play and rise". (I'm not necessarily saying Niemann didn't cheat, just that so far noone has found anything in statistical analysis of his OTB games that indicates cheating. Of course a 2500 who cheats in a smart way could be virtually undistinguishable from a real 2700.)
SigmaSan SigmaSan 10/5/2022 03:27
Difficult to assess the trustworthyness of this analysis but let's assume it's OK for the time being. Let's try to answer the question: "How can a 2500 strength player have a rating of 2700?"
Well, it seems obvious that IF hans was cheating, he wouldn't be cheating all the time, right? When would you cheat and take the risks? Seems logical to do it when playing significantly higher rated players to maximize the rating gain and trusting your skills when playing lower rated players. So I would be interested now to see an analysis of the ACPL in function of rating difference with his opponents.
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