#28
You hope to extract more information from the data base than you can.
The strongest correlation with win/loss is by the rating difference.
Sometimes the stronger player voluntarily refrains from castling.
https://www.chessgames.com/perl/chessgame?gid=1044179
Sometimes the weaker player voluntarily refrains from castling.
https://www.chessgames.com/perl/chessgame?gid=2135056
Relationship between castling first and win rate

Castling late (move 36):
The black king held at gunpoint by the white king's men and wife was forced to walk in shame to their territory only to be greeted by the white king himself who executes him with his rook bazooka. A tragic tale.

Not there yet but getting closer.
In did Scid vs PC searches in a huge referencebase (Caisabase) for four positions. That doesn't give a clear answer yet but I think you might be able to go from here with logical thinking and counting.
win White % | draw % | ||||
all | 4.574.978 | 54 | 30 | ||
Castles first*: | |||||
white O-O | 2.022.944 | 54 | 31 | ||
white O-O-O | 248.976 | 56 | 26 | ||
black O-O | 1.719.919 | 54 | 30 | ||
black O-O-O | 68.170 | 52 | 25 | ||
*search on King and Rook for the castler and K, R, R on the original position for the non castler |

@AtaChess68 Thank you! What is the rating range of the players in the Caisabase?
The way I read the numbers is that White castling short before Black has minimal impact on win rate as only 1% goes from a draw to a win for Black when Black castles short first.
There seems to be a bigger effect when the castler castles long although there might be more variance due to the lower numbers.

BTW, there is a separate topic https://www.chess.com/forum/view/general/when-not-to-castle-as-soon-as-possible for discussing examples of when castling is a bad idea.

... What is the rating range of the players in the Caisabase? ...
I think it's official games, rating starts around 1300. http://caissabase.co.uk/

The chess master said the advice especially applies to players below 1500 but also applies to stronger players when they find themselves out of book and therefore do not know what the engines would say what the best opening moves are.
Kotov in 'Think Like a Grandmaster" recommended to prepare castling, but to postpone castling when a more active move is available.

@KevinOSh, why do you want to know? Is it general interest or are you reconsidering your play style? If it's about your play style you could go for the general advise (castle asap <1500) but if you want more then your own game data seems as least as relevant as the caisabase figures (and if you find a significant result then you could have a look at the games themselves and find out why. That's were my real learning starts ).
If you want I can have a look at your games in december and november.

@KevinOSh, why do you want to know? Is it general interest or are you reconsidering your play style? If it's about your play style you could go for the general advise (castle asap <1500) but if you want more then your own game data seems as least as relevant as the caisabase figures (and if you find a significant result then you could have a look at the games themselves and find out why. That's were my real learning starts ).
If you want I can have a look at your games in december and november.
A bit of both. Over the last few months on average I have been castling later. Some games I get all my pieces out and if the king is safe I wait to decide which way I want to castle. Occasionally letting your opponent castle first is useful because it tells you which way you should castle.
I am below 1500 in all time controls, however there is a huge difference between daily games and rapid and blitz games. In daily games it is usually pretty easy to know when to castle. In rapid games and especially in blitz games I am a much weaker player and am much more inclined to follow the advice on castling as soon as possible in at least the majority of openings.
If you discover anything interesting in my games I'd appreciate it, thanks.

Yeah, i think I am more or less at the same stage: I am starting to realize that it's sometimes usefull to delay castling.
From your games from september till now:
win White % | draw % | ||||
all | 248 | 54 | 30 | ||
Castles first*: | |||||
white O-O | 108 | 62 | 6 | ||
white O-O-O | 9 | 33 | 22 | ||
black O-O | 60 | 41 | 12 | ||
black O-O-O | 4 | 75 | 0 | ||
*search on King and Rook for the castler and K, R, R on the original position for the non castler |

https://www.chess.com/game/live/28729186205?username=annamaria4465

There is no single rule in chess that you can follow blindly, atleast I haven't heard one yet. Same goes with this one. Statistics wont show you anything crucial. You can castle right into M1, it doesn't matter were you first one to castle or not. Sometimes players even wait to see what their opponent is going to do and decide by that wheter they will castle kingside, queenside or not castle at all. It depends on so many things

https://www.chess.com/game/live/28729186205?username=annamaria4465
Thanks. According to Stockfish the opponent's O-O-O move was a mistake and I should have castled two moves earlier, but Ne7 was almost as good, and O-O was the best move when I made it.
I recently heard a chess master say you should be the first player to castle and if you castle first you will win more games.
Has anyone done a study over millions of games to see what the win rates are when one or the other player castles first?
When it comes to stronger players, they all castle on time (except in the rare occasion when they misjudge the situation and get crushed or when they play an opening where you don't castle). Master said that to you because beginners tend to castle later than when it is optimal to castle. When it comes to below who are rated below 1000 rapid (below 800 blitz, for those who only play blitz), a lot of them castle way too late in most of their games.
#23 I can't tell the answer to my OP question from insights feature as it is but chess.com and I think also developers with access to the API should be able to calculate the answer from the large number of games in the database.