Hikaru cheating allegations is the last thing his peers need

Good. It's not wise to push the guy. Remember, desperate people do desperate things. I think Kramnik has moved on to Fabi now.

I note the case is made for chess.com ratings to be very inaccurate.

In the old days, on ICC, there were bullet blitz and rapid, but there was also the 3 minute pool (which didn't affect your blitz rating).

The "pool" ratings were always lower because:

1) Pairings were random (no rematches or challenges).
2) "No escape" was always on (in the old days, when internet was poor, if you disconnected the game was adjourn, meaning paused indefinitely, and you didn't lose).
3) It was only the single time control.

If you actually bother to pay attention you'll realize ALL (except for one that may have slipped through the cracks) discussion of politics were removed, regardless of who said what.

This guy made some random political statements that had nothing to do with the situation, and so they were removed.

They are a statistic calculated from your actual results, using an Elo-based formula, like most other ratings. They can't be "inaccurate" without starting with the assumption that they are meant to be calculating something different to what they are.

A meaningful question would be "How good is [some specified] chess.com rating at predicting the statistics of [some specified] results?". chess.com ratings are surely very good at predicting results in games similar to the ones they were calculated from (time control, mainly).

I was referring to the video I linked.

I'm not knowledgeable enough to know if the case was sound or not.

lol - @alexlehrersh is also currently getting away with an explicitly political avatar - will be interesting to see how long that survives here on Chess.com, at which point he will no doubt yell "Censorship!", much like Elon Musk.

ELO difference (difference is all that matters in the formula, not value) predicts how likely one player is to beat another on a given game, given no other information. So if the ELO difference is 400, the stronger player needs 10 points for every one point of the weaker player to maintain ELO. That's the predicted result. If the difference is 200, the ratio is close to 3:1. 120 points is 2:1.
If you want to predict the odds of winning multiple games, you now need to make further assumptions. One common assumptions is the results are uncorrelated: after the first game, the odds are essentially the same no matter which player won the prior game.
But I can tell you from personal experience I have better days and worse days. My games are not uncorrelated. If I'm on a good day, and being on a win streak is a good sign I'm on a good day, then I'm playing above my rating that day. Similarly, a match opponent might be playing below their rating. Or maybe our particular playing styles tend to favor one player over the other, because players are more complex than a simple ELO number. Or maybe they're playing a particular time control, like increment vs no increment, and one or both players are better on a particular type of time control. I'm much better at 5+5 than 3+0 for example (both blitz). This is all different from a coin-flip model where no matter how many times a coin comes up heads, I have no information about whether it's likely to be heads or tails next flip.
This is the problem with analyzing streaks on a purely "statistical" basis.
Hikaru plays a huge number of games. Sometimes he's more focused, sometimes less. This is true of all streamers. You can't expect they will play to an exact ELO every game, against every opponent, at every time control variant, something assumed in the modeling.

Fabi is a rational guy... they might structure the show to set him up for these little speeches, but even in interviews this is how he talks, so yeah, a pretty good source of information. On top of that he also has insights only professonal players have.

Ratings don't literally mean "nothing" of course, since they are (relatively) stable. They're just not stable in the way he's accustomed to (FIDE classical ratings). For example if Hikaru bounces between 3100 and 3300 in a predictable way, it means it's a good system.

More specifically he's correct about, for example, how there are many time controls wrapped up under a single banner of blitz or rapid or bullet. That's why when I was looking at Hikaru's streaks, and running some numbers, I filtered them so that only 3+0 games were considered. He's also correct that rematching and playing infrequently makes ratings less reliable... he's also right that you can "make the numbers say anything" which is why a real mathematician would never release a statement like "Nakamura is cheating." They would release a PDF that meticulously detailed their methods, assumption, conclusions, and stipulations... this is why it kills me to see Kramnik use the word "mathematics" and "statistics" a dozen times in a single post without a single freakin' equation, calculation, graph... nothing... ok back on topic...

I always like going back to the analogy of an economy where currency is rating points, and intrinsically valuable things like gold represent skill. In this case we'd stretch the metaphor and say if I have something intrinsically valuable (maybe I manufacture chairs) in order to set the right price (i.e. establish the correct rating) I would have to interact with lots of different places in the market. I wouldn't just sell them all to the first person I came across, because I might be getting a good (or bad) deal. Similarly, to be correctly evaluated, people should play a wide variety of opponents.

Now... is the market "meaningless" if I find a sucker who gives me a little too much for my latest batch of chairs? No, of course not. It just "artificially" makes my chairs seem more valuable. The rest of the market doesn't agree, and so next time I probably won't be able to sell them that high.

Caruana is accustomed to highly regulated markets, so in a street market, when someone is getting 10% more than they should, he thinks it's preposterous, but they're both robust and reliable systems (both chess.com's rating environment and FIDE's). And a professional mathematician (or let's say Ken Regan) would certainly be able to make correct statements about online cheating, if they had access to all of chess.com's data.

Oh, I missed this post before typing my long one

https://twitter.com/i/status/1728769857666122209