Top players always lose Elo in opens

Gibraltar 2015: Nakamura won with 2919 performance

Gibraltar 2016: Nakamura won with 2811 performance, ahead of MVL (2838)

Gibraltar 2017: Nakamura won with 2847 performance

Qatar 2014: Top seeds Giri and Kramnik scored 2870 and 2829 performances

Qatar 2015: Carlsen won with 2887 performance

Isle of Man 2016: Top seed Caruana scored 2908 performance

Isle of Man 2017: Carlsen won with 2903 performance, top six ranked players finished top six

And why shouldn't they? When you are on the top, there is nowhere to go but down.

The funny thing is that this has been repeated so often that it is no longer even discussed or questioned. After So declined playing Isle of Man Chessbase wrote that it was a wise decision since the top players generally lose Elo in opens. When I looked at other sites few or no one questioned the many times referred "truth" that the top players are overrated thanks to avoiding opens, where the opposition from underrated players is much harder compared to the opposition from supposedly overrated 2750+ opponents. But when you look at the actual results, the best players in general gain Elo in opens. And they even gain more than they "should", given that they always get at least 0.8 Elo for winning. So for all opponents rated more than 400 Elo lower than them they get more than they "deserve".

At Isle of Man the two top ranked players in all faced four opponents with a rating more than 400 Elo lower than them (and won all the games). Not that this in itself makes a huge extra Elo plus, maybe just one point in this specific case. But at the same time, I think this Elo gain in opens actually comes easier for the best players. They may have to prepare much harder for Sinquefield Cup or other top events, where the opposition is much more difficult (and you know who you will play). Then they can beat the 2500s a bit more on routine, being able to spend less time on preparation etc. Then it's another thing that there are few opens that are attractive enough for the best players to participate, but lately events like Gibraltar, Qatar and Isle of Man had a bunch of the best players. The World Champion hadn't played an open for 45 years, but now Carlsen has already played and won two.

In the two opens Carlsen has played since becoming World Champion he has in all gained 18.2 Elo. He scored +11-0=7 in the 18 games, so it has been on average one Elo plus per game. The opposition has been rather strong. Against 2730+ players the score has been +4-0=4 (two games being last round games where Carlsen played for quick draws as white).

AFAIK, there is a rule stating that if a player has won the event or shared 1st place, and his rating would go down, games from that event are excluded out of his personal ELO counts.

Another rule says in team matches a player is allowed to exclude victories (against low rated players) to increase average opposition.