I'm going to include Kasparov's games from Linares 1999 and compare it to Fischer's perfect 12-0 run, Karpov in Linares 1994 and Carlsen in Nanjing 2009 as an illustrative example to descripiton of my methodology.

Yes, Sonas' intention was to liquidate rating inflation. Quite successfully, I think. But he was unable to deal with the increasing quality of cless play.

<Why did you abandon % of best moves category in your rybka 3 analysis nimh?>

Because recording them was pointless,
the relation between good moves and the concurrences with engine top choices is not reciprocal.

If a move made by a player coincides with that of the engine, then in nearly all cases it can be considered a good move. But if a move is even outside of the top 3, it is by no means automatically bad.

<is it the same as the "difference" category?>

Difference is one of the parameters of difficulty of positions. It marks the average distance in eval figures between the first and the second best engine suggestions.

I was thinking to get a conclusion of rybkas playing style, but then again there could be other reasons to the actual results of such tests.. for instance a strong tactical player finding aloth of first choice moves in tactical positions but still such a player could still in theory play in a completely style to that of rybka in the early stages of the games.

1) Computer plays for accuracy in every type of positions - humans on the other hand tilt towards practical play, the more difficult positions, the more practical their play gets.

2) Computer strength lies in calculation - the strong point of humans is strategic vision and planning. The result of a game depends on making use of the weak points of the other side. Hence what matters in computer vs computer games is positional play, and human vs human games the crucial factor is tactics.

For what it's worth the four players you chose as geniuses are exactly the four I would choose, I couldn't agree more.

I chose the four players quite some time ago. Now I wonder whether I should count Lasker also among them, and instead of stating they're 'genuine geniuses' perhaps 'most remarkable among chess giants' would be a more suitable epithet

I found a free stats program you might be interested in. It takes data which doesn't agree with the central limit theorem and expresses it within the best-fit non-classical curve. The link goes to a demonstration video.

There are two programs for 30 day trial - Easy fit and Stat-assist, both Standard and Professional. It also lets you scroll back the date if your deadline expires, lol! So it's basically free.

I find your work to be particularly interesting! It's incredible that you've taken the time to analyze so many old time games from the great masters. I love this!!!

It's been said that we can't honestly compare the great players from the old days (Morphy, Philidor, Staunton) to the players of today. There is the issue of today's players standing on the shoulders of yesterday's players, which renders judgement to be almost impossible.

Having said that, your study is a great way to truly compare players across the ages. It's simple. The computer can easily tell us who blundered more: Morphy or Karpov for instance. With that alone we can make some pretty cool comparisons.

However, when we think about the "correct" (according to the computer) moves that were played, the computer can give us no insight in judging the creativity used to solve certain positions.

One more thing:

I was going through some of the old Labourdonnais - McDonell (spelling?) games. I was surprised at how accurate those guys played in most of the games. They made very few mistakes in a large number of games - comparable to some of today's players.

Actually I have to correct you on two points. The basis of the analysis is the average centipawn divergence between moves played and moves suggested by the engine. In mys study there are some graphs on blundering ratios, but these are just illustratory. Secondly, I must disagree with you on the LaBourdonnais and McDonnell match. It was by no means a display of accuracy, their play was simply awful by modern standards.

<However, when we think about the "correct" (according to the computer) moves that were played, the computer can give us no insight in judging the creativity used to solve certain positions.>

'Creativity' in chess is an arbitrarily created concept to encompass the ability to find regularily moves that are positionally unfounded and which usually surprise the opposition, but have sound tactical basis, and/or increase the difficulty of opponent's play, or is simply a mistake or a blunder. Often they are sacrifices of all kind, unless they're hackneyed cliches a la Greek gift Bxh7+, Sicilian Exchange sac Rxc3 etc. I believe this concept has no place in move-based playing strength analyses.

I think what you meant was the fact that sometimes players intentionally or unintentionally make objectively inferior moves in order to make it easier for the opponents to commit mistakes. It's indeed an important aspect of chess games. The engines cannot differentiate whether an inaccuracy was caused by miscalculation/misjudgement or was made intentionally to confuse the opponent. This is also the main reason why in such studies tactical players tend to be underrated.

<Please keep going with this fascinating study!>

Botvinnik vs Reshevsky, 1948

from move 15 until the game is lost some 20 moves later, botvinnik's play is simply quite awful, both strategically and tactically, but i have a hunch that it would be hard for the kind of machine analysis you do to really pick up how bad it actually was. (clear blunders will be spotted, of course, and i might be wrong - but i'd appreciate confirmation or the opposite!)

i was struck by the low quality going over the game <without an engine> first. even using houdini 1.5a x64 afterwards didn't reveal the crappy quality as well as my own "feeling" of botvinnik's aimless play.

note, the engine finds some tactically based counter-play that i assume current elite players would've found too, but which i'm incapable of getting right myself, of course. but the thing <i> am able to notice is that a perfectly equal but playable position detoriates quickly in ways it shouldn't if play is conducted by a strong player. so i started to wonder which features of the position that let a modern, weak master-level player "arrest" a past world champion's play (even during the tournament that made him world champion) in ways quick, superficial engine analysis might not.

I tried to prove whether keres actually threw his games to Botvinnik, but it seems there might have been some psychological factors too and it's nearly impossible to reach any definite conclusion by analysing the quality of moves only.

The game was indeed of quite low level of playing accuracy. Second worst after this one: Keres vs Botvinnik, 1948

The average error of Botvinik's moves was 0.273, prior to that, it was 0.195, which is also quite uncharacteristically low level of play. Note the evals of Rybka 2.3 are slightly lower than those of R3 or R4. White's advantage was highest on move 15 (0.61 d16). The only blunder occurred on move 35. where Bc2 (-1.46 d16) was preferred instead of Ke1 (-3.52 d16). As late as on move 30 the position was completely equal. Botvinnik needed to play either Rh1 or g4.

One thing that always intrigued me was how your analysis shows Anand's playing style as almost completely disjointed from every other player. Is this because of the sample size? Do you interpret it as an example of an extreme tactical player with little positional skill? One obviously can't argue with statistics but when it throws such glaring abberations, one is curious why it is so and rule out issues related to sample size, interpretation etc.