If you review his games over time, you'll noticed he's become a much more balanced player, capable of playing both extremely dangerous and tactical positions filled with traps, but also more quiet positions that aren't as sharp, but rich with strategic possibilities.

Many players tend to lean towards a specific "style" of play, but Carlsen has a rare gift to be able to adapt a variety of styles depending on his position and opponent.

Strategic play is much more subtle, but becomes more important as you get stronger. Strategic play generally involves more long term planning with the goal of creating a lasting advantage for yourself. Some examples of strategic concepts are creating more space for yourself (and at the same time constricting your opponent), having a better pawn structure (e.g your opponents pawns are isolated and vulnerable to attack), having your minor pieces better positioned(e.g your bishops rake open diagonals while your opponent's are trapped behind pawns)

  Tactics - winning pieces or losing fewer than your opponent
  Strategy - putting yourself in a position where the above is more likely to happen or be possible

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Strategery: knowing what to do when there's nothing obvious to do, aka vision, planning.

Strategy concerns more of theoretical ideas, long term possibilities. 10+ moves ahead. This involves pawn structure, where your king is positioned, how your pieces are developed, which side of the board left or right you might launch an attack, end game considerations, etc. How you intend to defend or win the game. This type of play is usually called positional. Whereby the placement of your pieces gives you an overall advantage. In GM level play this is very subtle and 15+ moves ahead. Positional vs. tactical.

As an analogy tactics are like cobra strikes and positional play is like a boa constrictor where tiny shifts strangle the opponent in the end. Both are lethal.

strategical: I wonder if I can machinate to end up mostly on white squares by the end-game, then I could let his black bishop take this pawn for free, while I work on getting my pawn structure to become invincible on the other side, effectively nullifying his bishop by the end-game while opening my position for greater pressure.

tactical: how can I protect this pawn, together with the rest of my pieces, so that all lines in the next 15 moves have all pieces protected, so that he can't take anything, and defensive enough that he can't force a 'better position' in any of them, while remaining offensive enough to open up for a future attack.

IE - Knowing your opponent is aggressive with their queen and having plans in place to quickly neutralize her, or being good at manipulating your opponents pieces util it gets to a point where you can gain a strong advantage by castling.

All these objectives form the basis of what you're trying to accomplish with the ideal being that successfully executing your major objectives will gain you victory.

Tactics refers to how well one reacts to and overcomes changes on the board.

IE - Based on the current board layout you notice that a certain move(s) will heavily fortify a section of the board that you previously were not focused on, or seeing your opponent set up for a particular pattern of play you feint a reaction only to hit them somewhere else.

As a tactical player he focuses more on evolving his strategy(larger objectives) to fit the board rather than trying to manipulate the board to fit his strategy more so than the average chess player.

this is a good example of both tactics and positional play: https://www.youtube.com/watch?v=NEcRQXN2dbg

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