FIDE published its September 2026 rating list on the first of the month, and the top of the open list looks familiar in one way and fresh in another. Magnus Carlsen still sits at number one with 2823, a spot he has held for years. Behind him, though, the order keeps shifting. Hikaru Nakamura moved back to second on 2792, Fabiano Caruana slipped to third on 2789, and Javokhir Sindarov holds fourth at 2778.
The month's real headline is Rameshbabu Praggnanandhaa. The Indian grandmaster jumped from 12th to 8th, gaining eleven points to reach 2761 and entering the world's top ten for the first time. His rise was powered by a strong Grand Chess Tour season, capped by winning the tour. Wesley So also made news, returning to the top five after nearly four years away, helped by his Sinquefield Cup victory. On the women's list, Hou Yifan remains the world's top-rated player, and Tan Zhongyi climbed back into the top five after winning the Cairns Cup.
The list was shaped mostly by the Sinquefield Cup, the Grand Chess Tour Finals, the Cairns Cup, and a handful of open tournaments across Europe. That is how these lists always work: every month, results from rated events get folded in, and the numbers move.
Which brings us to the question behind the list. What does a rating like 2823 actually mean?
The Elo system, named for the Hungarian-American physics professor Arpad Elo, was adopted by the US Chess Federation in 1960 and by FIDE in 1970. It does not try to measure how "good" a player is in some absolute sense. It measures one thing: how likely a player is to beat another player. A rating is a forecast, not a verdict.
The math is simpler than it looks. Each player has an expected score against any opponent, worked out from the gap between their ratings. A 200-point gap means the stronger player is expected to score about 0.75 — roughly three wins out of four. A 400-point gap multiplies the expected score tenfold. When the ratings are equal, the expectation is a coin flip.
After each game, the system compares what you were expected to score with what you actually scored. A win counts as 1, a draw as 0.5, a loss as 0. Score better than expected and your rating rises; score worse and it falls. The size of the change is set by the K-factor, which controls how fast a rating moves. New players use a higher K so their numbers settle quickly; established players above 2400 use a lower one, which is why Carlsen's rating barely budges even when he wins a big event. Beating a much weaker opponent earns almost nothing, because you were expected to win anyway. Upsetting a much stronger one pays handsomely.
That is why a single result rarely tells you much. Elo is built for averages over many games, and it is why the September list — with its tiny gaps at the top, where just a few points separate second from third — is best read as a snapshot of a long, slow conversation between players, one game at a time.
For more on the players behind these numbers, our sister site Hermes News keeps a running look at the tour.