How Are Chess Rankings Determined?

My understanding is that Grandmaster So-n-So, with an FIDE ranking of 2431, got that ranking based on analysis of his play, presumably by other chess players.

But for someone to evaluate another’s chess play, the evaluator would, by necessity, have to be better than the evaluateee, so as to identify blunders, good moves, brilliant moves, etc.

This being the case, then, how is anybody, anywhere, in any kind of position to evaluate Garry Kasparov’s play and thus assign a rating to it?* By most accounts he is, if not the best, then definitely one of the top three players to ever live. How can anyone else judge his play? It is, presumably, beyond the skill of anyone else to even analyze.

Am I missing something here? Is there more to the FIDE rating system than analysis of one’s play?

*I know that Kasparov doesn’t really play anymore, but he’s still a good example.

Rating would seem to me to depend on how many times they won, drew or lost against other opponents, not on detailed analysis of each game, because you would want the rating to be as objective as possible, and to be calculated fairly easily from game statistics.

The rankings are derived from your number of wins, loses, and draws against other ranked players in USCF* sanctioned chess tournaments, not by the quality of the individual games. These scores aren’t always representative of the player’s actual ability. When a player first joins the USCF, they start with a rating of 1000. If they play in a very limited enviroment, it’s easy to end up with over-inflated scores. For example, my Jr. High chess club was the best in the nation, and we had a lot of stiff competition from other Northern Californian chess teams. I wasn’t a particularly strong player myself, and was consistently ranked around 900 or so, which is a below average score. The best player on our team was ranked (IIRC) around 1500 or 1600. The second year my team went to the national championship, midway through the tournament I was paired against a player who was ranked around 1450. And I mopped the floor with the guy, because he’d only ever played tournaments against the same small pool of opponents, all people he could easily beat. Consequently, his rating was vastly overinflated. On the other hand, my own rating, in a much more competitive enviroment, was likely somewhat suppressed.