Is there any correlation between average rating and the time of the day?

Question

Crosspost to Stats.SE.

I play online bullet, mostly lichess, sometimes chess.com. Once I noticed that my average performance varies depending on the time of the day: e.g. at the morning I can lose 50 rating after a dozen of games, but I will easily regain it at the evening. One possible explanation is that my brain may work worse at the morning because of sleepyness or something. But can the reason be not me but my opponents?

Imagine two countries, A and B, in different time zones. Players from A and from B tend to play chess at the evening; let it be 00:00 UTC and 12:00 UTC respectively. And, for some reason, players from A are generally stronger than players from B. In the extreme example players from different countries never meet each other, so their ratings establish independently. So even if two players have similar strength, the player from B will have higher rating (because he is stronger among his population).

In this setting, if I play at 00:00 UTC I will meet opponents from A, and if I play at 12:00 UTC I will meet opponents from B. Players of my rating will have different absolute strength in these cases.

Another (imaginary) example about days of the week: it could be possible that on average stronger players tend to play on weekdays and weaker players on weekend, which leads to the similar effect.

Have anyone ever analyzed this kind of statistics and is the phenomenon in question possible, or it is believed that ratings are homogeneous in this sense?

Answer 1

I tried to calculate the day/night score rate on a couple of GMs with lichess account. Data is from the lichess bullet games. I use the UTCDate and UTCTime tag in the game header to classify day/night time.

It does not consider opponent's day/night, this is just a simple stats about the perf of the given player.

Here is the result.

The day is from 6am to 6pm in their respective local time given utc offset.
The rest of the hours are covered for the night. Game type is bullet.
        id  utc cty  dsrate  nsrate  dgames  ngames                              profile
  GMJOEY93    8  PH 0.74531 0.75417    2880    4674       https://lichess.org/@/GMJOEY93
 AnishGiri    1  NL 0.69815 0.70350     593    1199      https://lichess.org/@/AnishGiri

DrNykterstein    1  NO 0.74074 0.71805    1404    7583  https://lichess.org/@/DrNykterstein
gmwesleyso1993   -6  US 0.83078 0.86842     523      19 https://lichess.org/@/gmwesleyso1993
   alireza2003    1  FR 0.72139 0.60589     402    4802    https://lichess.org/@/alireza2003
  Azerichessss    4  AZ 0.62517 0.63803    1430    2543   https://lichess.org/@/Azerichessss
dgames = day games
ngames = night games
dsrate = day_score/day_games
nsrate = night_score/night_games
DrNykterstein = Magnus