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The arrival of strong chess engines as Stockfish, Houdini or Rybka allow top players to deeply prepare lines in openings or to study better endgames.

I would expect a rating increase of top players. However, Kasparov's top score from 1999 is still the second best rating score of all time and Karpov and Fischer are still in the top twenty historical rated players.

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Source: Wikipedia

If those engines have a 3600 Elo, shouldn't top players have profited from it to leave Kasparov's 2851 score in 1999 far away?

And shouldn't more than 18 players surpass Fischer's 2785 in 1972?

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I think they certainly have increased their ELO, but more importantly, their overall chess strength. ELO is only a rating relative to others in the pool so it may tend to go up more slowly if everyone in the pool gets better, which they have collectively.

First, you need to take an average of the top players, rather than look at just two incredibly special players, Kasparov, and Carlsen, and their peak ratings. Fischer was a total anomaly for his time, and again, you cannot base a lot on one person. Humans probably have a limit mentally much the way runners will eventually hit a speed wall that they cannot break. It is the Bell Curve in action: Easy to make progress in the middle, but harder on the end.

ChessBase, and the first strong engine, KnightStalker (aka Fritz 1.0, renamed at version 2.0) came out in 1990, and the Internet was still in its infancy. In January of 1990, there were only two players over 2700, Karpov at 2730, and Kasparov at 2800. Today, there are 37 players over 2700, and of those, three are over 2800.

I have been playing for a long time, and anyone, who knows my handle, has seen me watching relays of the top tournaments on ICC for more than 20 years, and I can say that it is not just inflation from having actually watched the level of play improve over the years. Players at the Master-level, including even normal Masters, are MUCH better now due to the tools available today than the tools available when I first became a Master.

When I first started playing, all we had was books, and a local club. Today, I can logon virtually any day, and play a GM. I was also a ranked tennis player as a teenager, and I can tell you from that experience, playing better competition makes you better, so being able to logon and play stronger players than ever has increased the overall level of play. In addition, we now have ChessBase, and a database of about 8.3M games that can be sorted efficiently and studied. We also have engines, as noted in the question, and they certainly have also added to our chess knowledge, and fundamentally changed how the top players prepare. Lastly, I mentioned books, and as an avid collector (I had 1800 at my peak), I can tell you that even the quality of the material in books is on another level since when I started.

I cannot tell you what proportion of all these advances have played toward X-number of rating points increase, but I can tell you that without a doubt, they all have lead to players at the top levels, and even down some, being much better overall.

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The question is apparently based on a misunderstanding of how ELO ratings work. There is absolutely no mechanism by which the overall increase in players' strength would lead to increase in their ELO. The actual value of the ELO rating bears no meaning; nor does the comparison of ELO at distant times. The only thing that has direct relevance is the difference in simultaneous rating between players.

If tomorrow FIDE decided to add a constant, say, 500 points, to every player's rating, essentially nothing would change - the outcomes of games would lead to the same increments in ratings, so the rating dynamics would be the same, just at +500 points level. And the computers will provide no basepoint - their ELO is relative to human players, so they will play at 3600 rather than 3100.

The same applies if such a constant were somehow added or subtracted gradually due to natural processes - e. g., expansion of rated players' base, players becoming inactive with higher rating than they started with, etc. And this, apparently, did happen as we witnessed rating inflation until recently.

Similarly, if all the players suddenly, or gradually, start playing stronger, without a change of their relative strength, there is no reason to expect a change in rating dynamics.

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If those engines have a 3600 Elo, shouldn't top players have profited from it to leave Kasparov's 2851 score in 1999 far away?

No. The main effect of engines and also the internet has been to democratise chess. The top players have always had access to top level evaluation and knowledge. For lower level players that kind of knowledge, analysis, position evaluation, endgame knowledge was very difficult to acquire.

This is important because higher level players gain rating points by beating lower level players. If those lower level players are harder to beat because of increased access to the analysis and knowledge that engines and the internet provide then it actually becomes harder to reach higher levels as measured by rating.

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A few things:

1) Ratings overall tend to rise due to inflation of more players entering the pool, rather than the average playing strength of players increasing. If everyone becomes better by some factor due to engines, why would top players' ratings increase? They're now playing opponents who have also gotten stronger by roughly the same amount.

2) Kasparov, Karpov, and Fischer are anomalies of a sort (Kasparov especially), considering they are all world champions. And still, they only occupy 3/20 spots on the list - all other ratings were achieved in the modern era.

3) Engines are making people stronger, but not to a huge extent. People aren't able to extract all the strength out of an engine, we just see the moves it recommends.

In summary, engines make people somewhat stronger, but in any case this wouldn't be reflected in the ratings. The pool of players is a closed system: everyone getting stronger doesn't benefit one player/group of players in particular. The way the ratings rise (at all levels) is from more people joining the system.

EDIT: one way you would see some increase purely due to engines is in a hypothetical scenario where we played against another group of people who didn't have access to our engines.

EDIT 2: Point 1 may not be entirely correct (see the discussion in the comments).

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    1) That's a common misconception: pure ELO rating actually deflates due to new players entering the pool. They enter at low rating, then progress, taking the points away from the others. As they become inactive, a vast majority of players are higher rated than at entry. This means they take points away from the system.
    – Kostya_I
    Dec 27, 2019 at 11:20
  • @Kostya_I But new players bring more points into the system via their initial rating. Even if one's starting rating is only 1000, they still brought 1000 points in by basically taking nothing away. Dec 27, 2019 at 14:08
  • @Inertial_Ignorance, imagine a new player who gets initial rating of 1000 points and never plays again. By your logic, he or she "brought 1000 points in", but in fact nothing changed for other players. And if they do play, they will typically progress - say, to 1500. That's 500 points taken away from other players, so, their rating will decrease by that amount while their strength has not diminished. That's deflation. Of course, someone could drop below their inital level, which is the only case they really "bring points in", but that's a rare case
    – Kostya_I
    Dec 27, 2019 at 14:36
  • @Kostya_I That's a good point. But inflation is happening with ratings, so how do you explain that? Dec 28, 2019 at 2:52
  • @Inertial_Ignorance, the inflation is no longer happening - the top-N averages are steady for about 7-10 years. The inflation in 1990s and 2000s might have been due to lowering the rating floor, where a lot of established players were added, who no longer progressed from that point on, but aged and declined in strength, giving away the rating points. Or it may be that the deflation counter-measures (different coefficient K for new players) were not properly adjusted.
    – Kostya_I
    Dec 28, 2019 at 9:21
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People are not computers. They learn and memorize as much as possible but they can not do as much as a computer can nor as fast. The top players are doing everything they can but they can not do it all like the computer does.

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  • Well I think Carlsen has sometimes played a 25 moves Stockfish line that wasn't on books. I agree with your answer and it gives a point but I was not asking why GM don't reach engines level, I was asking why they don't increase a bit more his rating, saying all top ten players at 2900.
    – user18196
    Dec 26, 2019 at 20:17
  • I suspect that all the top players are using as much as they can whether printed or online to improve. So if nobody improves more than the others and they only keep playing themselves then their ratings will stay the same. The top GMs need to play wider competition and take some of their points from lower rated players for the top to improve.
    – yobamamama
    Dec 26, 2019 at 21:01
  • That's the point of my question. Allbody have engines, but top rated players may prepare better games than said, the 2600. Caruana says his point is game preparation. Doesn't engines help 2800 to beat lazy 2600 more easy than Bobby, Gary or Anatoly faced to?
    – user18196
    Dec 26, 2019 at 21:34
  • Maybe, but that won't affect the ratings.
    – yobamamama
    Dec 26, 2019 at 21:43

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