Someone posted some basic analysis with mild QC on elo vs age for FIDE rated players as of 2014: https://www.chess.com/blog/LionChessLtd/age-vs-elo---your-ba...

I think there are a lot of confounders to consider. Though GMs like Anand show a drop in standard rating (https://ratings.fide.com/profile/5000017/chart), his blitz rating is near his all-time-high (ie. is his standard rating drop due to decreased mental performance or a shift in interest/focus to blitz?). Similarly, I suspect a lot of strong players who fall in the `2000<FIDE rating<2300` realize they may not be the next magnus and shift focus when/if they make the decision to pursue a career outside of professional chess.

> I wonder when Magnus will stop being able to "beat" Magnus of 1 year ago.

While this doesn't answer your question, it's interesting to note Magnus's peak rating was actually 7 and a half years ago, when he was only 23.

Then again with how ELO works it doesn’t necessary mean that it was Magnus’s peak only that that the point when the gap between him and the rest of the chess world was the largest. I think others became stronger and he had more competition. Still Magnus himself seems to think he is past his peak in interviews.

I mean, he himself wouldn't necessarily be able to tell the difference of him getting worse or the rest getting better. To him it's just getting harder to beat people. At his level how can you judge yourself unless you played against a fixed-version AI chess program?

Here's some data for your question. A list of the world's top players (over 2700 Elo) is maintained here: https://2700chess.com/.

With the exception of Anand at 51, they're all quite young.

Hey, I'm not 51 yet!

I watched a YouTube video recently that talked about how difficult it is to go from 2350 FIDE to 2500. It seemed to imply if you don’t make 2500 by age 20, you will probably won’t ever get there or it will require years of study. The video was just an opinion, no data to support it was presented.

Hikaru claims it's 25 when he and many others peaked.

It's worth noting that chess grandmasters can burn up to 6000 calories per day while competing in tournaments. It's an absolutely exhausting endeavor, and I imagine sheer endurance can play a huge role.

So yes, performance does fall off with age, though not as intensely as something like hockey.

Is that true? I thought that the difference between deep thinking energy expenditure and rest expenditure of the brain was not a huge % of the rest energy expenditure. I couldn’t find any source to the 6000 calorie figure, and this article seems to support that the chess player’s calorie deficit was likely due to skipping meals and stress https://www.livescience.com/burn-calories-brain.html

The brain is an organ like any other and gets fatigued more easily with age.