It is not even disputable: Karpov would DEFINITELY WIN in 1975

I wish the year in the title was my rating xD

#80
Yes indeed, the Soviet players were far ahead in opening theory, but nevertheless Fischer just smashed Taimanov, Larsen, Petrosian and Spassky. Even so in the 2 examples I gave Botvinnik and Keres knew more about opening theory than Fischer, but Fischer refuted their home preparation over the board. All these examples provide evidence that being behind in opening theory would not have impeded Fischer in a 1975 match with Karpov.

Spassky was excellently prepared by Geller, but Fischer turned this opening preparation into a liability: ballast. Fischer avoided his usual King's Indian Defence and Grünfeld Indian Defence. After the 4th game you mention Fischer shifted to the surprising 1 c4, and later to the unusual 6 Bg5 avoiding his pet line 6 Bc4. After his loss with his pet 7...Qb6 in the Najdorf Fischer played Alekhine Defence twice careful to chose different variations, Pirc Defence and Taimanov Sicilian. Spassky got all of his preparation sidestepped.

#79
"Subtracting rating for no measurable public activity is ridiculous."
I think we can agree that inactivity and ageing impair ability. By how much is debatable. There is measurable public activity. We know the rating of Fischer after his 1972 Match with Spassky. We also know the tournament performance rating of Fischer in his 1992 revanche match against Spassky. The rating of Spassky was reliable, as he stayed active all the time. My first idea was linear interpolation between those two reference points to estimate Fischer's rating in 1975.

"All prior evidence actually points to Fischer retaining and/or increasing his playing strength during his sojourns from the public eye."
Fischer analysed for "My 60 Memorable Games" in 1969. There are no later books or chess articles of his that testify he analysed after 1972. Posts above indicate that Fischer was involved in other activities. He did comment on Karpov and Kasparov, so he followed chess, but he did not publish any analysis. Right after Fischer came back in 1970 he was not that strong immediately. For example at Siegen 1970 he lost to Spassky.
https://www.chessgames.com/perl/chessgame?gid=1044698
Fischer had never defeated Spassky prior to their 1972 match. So right after coming back Fischer was a bit rusty, but he regained his strength rapidly and in 1971 he was stronger than ever before.

- You are dodging the point.  Agreeing that aging has consequences does not mean a rating system should ever be allowed to assume a loss of rating that has not been demonstrated and measured.  It completely ceases to even *be* a real rating once you make that mistake.  The point of a rating system is to remove guesswork and speculation, not champion them.  You've lost his point, objectively, so you might as well move on.

- It's not a linear process, so why you would attempt to use linear interpolation is...baffling, to put it nicely.

- Your narrative is off.  In fact, Fischer made a big splash when talking about how he had extensively analyzed the matches between Kasparov and Karpov, so any fiction about him hanging up his boots after his book was released in 1969 is pure fantasy.

- You are contradicting yourself...Fischer either was not able to beat Spassky until 1972, or he "regained his strength rapidly in 1971".  Which is it?

#84
The question was if Karpov would have defeated Fischer in 1975. Only elo rating allows objective predictions. We know the rating of Karpov. We must estimate the rating of Fischer in 1975 with a discount for inactivity and ageing. Applying his 1972 rating in 1975 would be baffling. Chessmetrics applies some degradation. Linear interpolation between 1972 and 1992 is sensible too. If you do not approve linear degradation, then what degradation do you propose and on what grounds?

Fischer followed the games of Karpov and Kasparov and gave comments on these, but no analysis. If he had published analysis then that would have been proof of him being deeply involved. Some posts above provide evidence that Fischer was busy with other than chess.

Right after Fischer came back in 1970 he was not that strong yet: rusty from inactivity. He lost to Spassky in Siegen 1970. In 1971 and 1972 he was stronger than ever before.

Lol. 

- You said we must use elo ratings, when you are not using elo ratings at all.

- No "we" don't have to estimate anything.

- Name a single form of memory loss, atrophy, cognitive decline, etc. that follows a linear progression.

- You can't apply any degradation that is not demonstrated within the bounds of the rating system, so...no degradation on any grounds.

- "Some posts above" do not provide evidence of anything.  You entire argument is based on assumptions and guesses about information you do not have.

- A single data point (loss of a game vs. Spassky, in this case) cannot ever be proof of a trend or a static state (rusty due to inactivity).  This would seem to be quite obvious.

#86
Most decay processes are exponential, like

rating(t) = rating(oo) + (rating(0) - rating(oo))*exp(-t/T)

To a first approximation this is linear.
Exponential decays faster than linear.
So linear decay is a good approximation.
The error of linear is towards too high an estimate.

Of course its "disputable".  While my opinion is that Fischer was already spiraling downward into his paranoid craziness.  That is as a stated my opinion.  What I have always believed is that Fischer was so obsessed with winning the title, defeating the Russian chess machine, craving all the fame, money and popularity that goes with the title.  I also believe that once he won the title, I feel that poor man reached a point in his life where he honestly felt like there was nothing else to accomplish.  That has to be a terrible feeling to be 32 and to feel like life has nothing else to offer.  Throw that on top of his mental issues, and that's a recipe for disaster.

Thanks for admitting your flawed thinking, that was brave of you .  Using a linear estimate to determine such a decline overestimates the decline at the front end of the process significantly.

Fischer managed to survive their home preps due to his extensive hard-work and training but in 1975 he was not working on chess for 3 years.

But in those times he refuted the home-prep over-the-board, he was active. And when he defeated Taimanov and Petrosian even after their home prep, he was outplayed but the latters failed to convert those chances. Karpov too might have failed, I am not saying it is impossible. But What it shows is that this time Fischer would have needed to face an even bigger preperations and his opponent was not 40+ years old players he had faced in the past.

Spassky did not have his preps fail at his hands, in the second half of the match there were many novelties in which Spassky outplayed Fischer due to Spassky's prep but failed to convert them at the end.

That match in Siegen was not right after Fischer's return. Fischer's first games after his return were against Petrosian in the USSR vs Rest of the World match in which he defeated Petrosian with 2 wins and 2 draws. After that match, he played in Herceg Novi blitz, Buones Aires 1970, Zagreb tournament. He won all of these tourneys with noticeable gap and after than he faced Spassky and lost to him. After loss to Spassky, Fischer played in Palma De Mallorca interzonal and won again with notiecable gap

#89
"Using a linear estimate to determine such a decline overestimates the decline at the front end of the process significantly."
You seem unfamiliar with mathematics.
Exponential decay gives a concave curve: a positive second derivative.
d^2/dt^2(rating(oo) + (rating(0) - rating(oo))*exp(-t/T)) > 0
Hence linear decay underestimates the decline relative to exponential.

Rating_linear > rating_exponential.

It is not significant, the difference is small.

Linear decay is the only feasible approximation. You cannot estimate 2 parameters rating(oo) and T from 2 data points rating(1972) and rating(1992).
Hence linear is both quite accurate, feasible and gives too high an estimate for the rating.

Now be brave and admit your flawed thinking.

#91
Fischer lost to Spassky in 1970, but smashed him 12.5 - 8.5 in 1972.
Fischer lost to Larsen in 1970, but smashed him 6 - 0 in 1971.
https://www.chessgames.com/perl/chessgame?gid=1044314 

Fischer was still rusty in 1970 after inactivity during 1969 and came to full strength in 1971-1972.

#90
"his opponent was not 40+ years old players he had faced in the past."
Being more experienced is an asset, not a liability in match play.
In the first Karpov-Kasparov match the young Kasparov ferociously played to win as he was used to, but as a result he was down 0 - 4 after 9 games. Only after veteran Botvinnik adviced Kasparov to play for draws that Kasparov gradually came closer to 3 - 5 after 48 games when FIDE chairman Campomanes aborted the match.

So Fischer being older than Karpov is no disadvantage if he was physically fit.

You first asserted/implied the Spassky game was the game he played right after he returned, which is not. That game came after 3-4 tournaments Fischer won handily in 1970.

As for his loss to Larsen, that was in the same tournament Fischer won again handily: 3.5 points margin. No way to suggest he was rusty. A loss or two always occurs.

agreed.

also, fischer smashed him with a 4 point lead? how does that work? lol u guys need to read fischer's thoughts on interviews regarding the games he played against spassky. "smashed him", oof. i mean, kramnik and kasparov also disagree with that, but whatever.

"Fischer would have needed to face an even bigger preperations and his opponent was not 40+ years old players he had faced in the past."

To counter home prep of a young player at 24 is different than countering home prep of a 40+ years.

Fischer failed to counter both Petrosian and Taimanov's home preps, he was outplayed but the two failed to convert them: they were burning more fatigue and time. Karpov, being 24 years old, could avoid those problems and might have converted his home prep advantage.

Do not change the goal posts, "Fischer being older is a disadvantage" is an assertion you made up. Likewise, if I wanted I could have straw manned by stating "Karpov being younger was not a disadvantage."

Nope, you still lose .

The decay is not purely exponential either.  I'm sorry that you cannot seem to fathom that memory loss and cognitive decline will not follow simple mathematical formulas and curves, you have to actually use, you know, measurements?  You have no basis for your claims, at all.  You are just like the dweebs who try to diagnose Fischer's psychological maladies with him in the grave.  You don't have the information needed to make your assertions.

Neither does chessmetrics, in this case.  That is why chessmetrics' way of measuring chess ability will never become an officially sanctioned ranking system for chess players, anywhere, ever.  Not until they dump the idea of "estimating" to remove ratings points without any actual qualifying events/data to pull from.

As you can see from the chart, Fischer at 32 years old in 1975 would have had next to no decline in any of the most applicable metrics.  In fact he was entering the most stable period of cognitive function for an average person's life.

If you wish to try and extrapolate decline in chess ability from this (which is tenuous), then it would clearly be miniscule.