By the way, Fischer at his peak was 125 points ahead of the second-rated player, Spassky.
It is absolutely true that the Elo model is a relative one and does not guarantee that a given rating number represents the same ability over time, but the belief that modern ratings are inflated is not unanimous. Ratings have certainly gone up over time, but computer analyses of games have indicated that intrinsic play quality has gone up over time as well. See the work of Ken Regan, for example (search for "ken regan ipr").
The difference between Elo and Bradley-Terry is that Bradley-Terry assumes to have "all" the data. So Bradley Terry is used in Psychology studies for that reason. (Eventually, you stop taking data).
Elo on the other hand, is mathematically equivalent to Bradley-Terry except with infinite data. Elo allows you to incrementally "add data" to an existing Bradley-Terry-esque model and make it more accurate.
BTW: Elo has been superceeded by superior models today, but all (good) ranking models are "interval properties" that have been derived from the Bradley Terry model from Psychology research.
See TrueSkill (which is based on Gaussian Curves, so they aren't technically Bradley-Terry but instead the Thurstone scale), Glicko, and Glicko2.
I would imagine many psychology studies are measuring something a great deal less well defined and more multidimensional in practice than "A will beat B at chess."
However, of course the Elo model might not be perfect, and thus a lot of other things contribute into the rating difference of players A and B, not only the expected result of the players playing only against each other.
More databases, more games played, internet giving opportunity to play many, many more games. Programs to analyze their play, coaching in the modern era, etc.
That is something that Anand didn't really benefit from when he was young.
Rating difference should be comparable, elo is designed so that a given rating difference is a given probability of beating your opponent.
but, at the same time, it's messy. and comparing the top two players only will probably not be as meaningful as looking at their games and their play.
the interesting question is not that you can be dominant against bad competition, but you can dominate over great competition. I think we can agree on that point.
Jordan was the best shooting guard in his time.
I think it's quite fair to call Carlsen the Lebron James of chess.
People will always gravitate toward recent greatness being greater than those in the past. But, it's frankly impossible to teller cause we don't have enough context and emotional separation. Being able to say that we saw the greatest ever play is appealing because some of that greatness can then pass over to us by association. It's better to enjoy the greatness we see now and leave the comparisons for history. It is fun to think about though.
[1] I never saw Jordan live, which is something I regret.
Obviously ppg is not the only metric, and championships are won by teams. LeBron is probably in the argument for best all time, and by the end of his career may have a legitimate argument, but he certainly isn't just obviously way better than everyone else. He's probably top 5 though.
In a specifically chosen 8 year period. There were 7 years before that where he didn't win a championship. LeBron's career is far from over, and titles won by a player is surely the least informative measure of an individual player's skill anyhow.
Fwiw Lebron didn't win a championship for his first 8 years. Perhaps he will win the next 6 and make Jordan look pedestrian. He's not there yet though.
I'm not saying Carlsen is the greatest ever. I'm just saying comparisons are totally valid.
[1] http://en.chessbase.com/post/the-greatest-che-player-of-all-... [2] http://www.chessgames.com/perl/chessplayer?pid=52948