This question baffled me for sometime once, I was disparate trying to comprehend the elo rating e.g. how far certain rating is compared to more higher or less rating. Personally, the answer I was looking for is comprehensive one, i.e. to comprehend what it takes to move from certain chess elo to another.
The best way to understand this is by borrowing an analogy. The best analogy I can think of is Richter scale. Richter scale, for those who don't know, is a mathematical way (a formula) to quantify or measure how powerful an earthquake is (same as elo measures how powerful chess player is).
Unlike elo rating, Richter scale is calculated using 10 based algorithm, which means that 8 grades (gs) earthquake is 10 times powerful than 7 gs, and and 9 gs is 10 times powerful than 8 gs, so that 9 gs is 100 more powerful than 7 gs and 10 gs is 1000 times than 7 gs and so one.
The difference is that in chess Elo; the number of times calculating power (or creativity or what ever you call) a 2800 chess player have compared to 2700 one, is not very obvious like in Richer scale, but generally, it increases exponentially as the rating increases, for example, if we started like: 1800 chess player has a double calculating ability of 1600 player, 2000 player is 6 times 1600, 2200 is 12 times of 1600, and so on, if we continued like this, it will unfortunately get weird at the top levels, this abnormality is due to the exponential increment at the ultimate end of the rating spectrum.
So, I guess, unlike the uniformity in the lower levels, a 2700 chess player, for example, would have 50 times calculating ability of 2600 player, and 2800 player, have let's say 200 times calculating ability of 2600 player and could be more which is insane. I am not statistics expert, so the general theme should be understood not the precise numbers.
Nevertheless, this can be supported by many historical facts such as:
i) Only about 20 players have breached 2800 rating and about 100 breached the 2700 in the entire history of chess Elo rating.
ii) The ranking fixation e.g. some great iconic players were unable to become world champions no matter how much they try, the reason is that top candidates out calculate their ability by ridiculously multiplicity times, and also because calculating ability can't be increased after a certain age.
Finally, there are good lessons here for chess player such as:
i) In order for someone to have a high level chess future career, s/he should have undergone a hard consistent long term brain burning practicing activities (e.g. blindfold chess, bullet chess).
ii) Chess career level = prodigy+(training period and consistency x practice hardship level) / starting age, i.e. the higher level the practice is, the more brilliant future, the less starting age is, the more brilliant future, and the more consistency in training, the more brilliant future. This is applies not only on prodigies, but also on any normal human being. Additionally, I also believe that all the above also applies on IQ levels.
Hi. What is the key difference between players ranging between 2600-2700 and 2700-2800. Is it pure calculation ability? Ability to avoid blunders? Opening preparation and work ethic? Positional understanding? Endgame ability? All of the above?
I read somewhere that GM Timur Gareev played over 30 blindfold games simultaneously, and that many Super GM's considered this unhuman and ridiculously impressive. Yet, these players are higher rated than Timur.
In the case of Nakamura, you have a player that is an absolute tactical genius, but who sometimes makes big inaccuracies. Carlsen on the other hand is known for super precision, his positional genius and an almost inability to make huge blunders. Anand is mostly known for his amazing preparation. All of these players are over 2800, so I find it hard to believe that there is a "true" answer to this question.