Let's look at this quote:

<The reason Fischer's overall 3 year peak includes an inactive year, is simply because he had no other sustained periods of brilliance in his career, unlike most of the other greats. And that's nobody's fault but Fischer's.>

This brings up another point which I've made, but not as forcefully and directly.

There is a difference between a player travelled on unlimited money, sponsored by the USSR, and a player who was poor (and that was what Fischer was before 1972) who only has the resources to compete directly for the world championship itself, plus occasional overseas tournaments.

In fact, going back to your earlier list, this is a criticism of punishing some of the great champions of the past for not travelling to so many tournaments. They are being punished for the fact that

a) not so many of these tournaments even existed as they do today

b) for players such as Lasker - travelling to these tournaments could take a significant amount of time and expense which they sometimes couldn't afford

c) some players felt it best to simply concentrate on the road to the championship itself.

1) Every rated game of chess played under professional tournament conditions should be 'weighted' the same as any other. (This is not to say that due to differences in ratings, some wins may not be more helpful to a player than others).

2) Only the games played matter - there is no mystical 'padding' factor. More games in and of itself is not better.

3) The player should have played at least a minimal number of games. We don't take a guy who won 1 game and didn't play against for 5 years and call him the greatest ever.

44 games is an awful lot, really. It's not some aberattion - Fischer is playing the very best players availble, taking the quickest yet toughest road to the world championship.

Why is there a need to dilute 44 games
with 7 non-existant draws?

Match vs Petrosian: Fischer wins 3 to 1

Rovinj/Zabreb tournament Fischer 1st place +10 -1 =6
Buenos Aires Fischer 1st place +13 -0 =4

Siegen Olympiad Fischer +8 -1 = 4

Palma Interzonal: Fischer 1st place +15 -1 =7

(Not included is Fischer winning Herceg Novi with +17 -1 =4)

For example :

Lasker after St. Petersburg 1914

Capablanca after London 1922 or

Alyekhin after Bled 1931.>

Expected consequence: Fischer fans are so out of it that they'll be the only people not to have noticed or understood what has just transpired on this page. Fischer @#$%*&!# will continue to pollute chess's legends and general pyschosphere.

Elo, the guy who really invented these rating systems, was able to predict future results. For example, Elo called the result of Spassky vs. Fischer correctly, before the match was played.

I see the problem with rating systems as one of combatting rating inflation. As mentioned before, in large part, the players of the past get punished because rating systems such as Sonas's start with the assumption that all players are on a level playing field - therefore more games is 'better' and should be 'rewarded'.

These systems do not consider that in the past:

a) not so many of these tournaments even existed as they do today

b) for players such as Lasker - travelling to these tournaments could take a significant amount of time and expense which they sometimes couldn't afford

c) some players felt it best to simply concentrate on the road to the championship itself, given the small resources they had.

This approach to the game could go terribly wrong when facing the best of the best:

Burn vs Rubinstein, 1912

To judge whether (to quote rook) <Fischer's run from 1970 to 1972 was the best there was>, you would need to calculate performance ratings for three -year intervals. That might be interesting; but it's not the question Sonas is asking.

Sonas is asking roughly this: who, - on average, over a 3-year period, and based on the statistical information at the date of the game, was the strongest player ? - i.e. the player likely to score highest against his strongest contemporaries ?

You can argue the merits of padding either way. <what the fat>'s numbers suggest that <rook>'s nasty insinuations about Sonas' motives - <To give sombody else a higher place in the standings, that's why> - are out of place. (Strictly, however, one should be looking at the number of games played in the 4-year window before the date of the rating). If Sonas found that the quality of his results (probably judged by the likelihood of the results based on the model) was improved by the padding, then it makes sense to do it.

I was looking at Petrosian, and there is something interesting. At one time, Zukertort used to be more highly rated than Petrosian, which can't be right because all Zukertort did was lose when it mattered. But in the latest revision by Sonas, Petrosian emerges ahead. I was encouraged to see this.

What still remains are issues like Maroczy being rated higher than Petrosian, despite the fact that none of the tournaments Maroczy were as stacked as any of the 4 USSR championships Petrosian won. (To say nothing of the World Championship itself for which Petrosian won two matches).

If you want to talk about 'weight's:
how's this for a common sense system:

Comes to think of it, here is what Nimzovich has to say on the topic: <The number of great defenders is small. Author knows only the following names: Steinitz, Dr. Emanuel Lasker, Amos Burn, Dr. O.S. Bernstein, Duras, and not last Louis Paulsen ...> 'Praxis' (1928).

Meanwhile, Kasparov's highest rating is 2886, in March, 1993. This is derived (along with the padding games) from 94.4 weighted rated games, against a weighted average opponent of 2722.

What I did now, is I took Sonas' formulae, and recalculated the ratings as they would be <WITHOUT padding>.

That is, the padded formula:
Rating = 43+[(PR*n)+(AR*4)+(2300*3)]/(n+7), is replaced by Rating=PR.

Calculating this, we yield:

<Fischer>
Padded rating: 2895
Unpadded rating: 2885

<Kasparov>
Padded rating: 2886
Unpadded rating: 2864

To quote Sonas directly:
"Before I go any further I just want to emphasize a very important point here. This system rewards players who play a lot of games. That's because there are always 7 "fake" games that provide the padding. If you play a lot of games, the 7 games don't have much effect on your rating. If you only play a few games, they can play a dominant role in your rating, as they should!"

Both Fischer, and Kasparov (as well as basically any top active player), played enough games for the padding to become near irrelevant.