Relationship between castling first and win rate

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?

You would be well advised to listen to him.  If you can't refute this piece of advice, then you should certainly heed it.

At the point in time you have enough experience to articulate the exceptions, then you'll know when you are safe to ignore it.

So moving more knights and bishops out before your opponent (letting you castle), would be a good castle opening.

Right?

It’s an interesting discussion. I also don’t have an answer to the initial question but “castling first” and “not castling” are two different questions. My view would be that keeping a tempo can mean it is ok to castle after your opponent if the tempo is significantly improving your position and not leaving yourself open. Also, once the queens come off the board then castling becomes less important as well. 

castling is usually very useful and good thing to do...
but every rule has some exceptions... and in some specific moments and variations is just better stay with the king in the center...

When I'm white I don't care who castles first, when I'm black I prefer to castle second.

There are certain types of positions in which castling first is disadvantageous, and also types of positions in which it is advantageous to leave the King in the center permanently.

Sicilian Najdorfs figure prominently in both of these types of positions.

very true

Castling late (move 36):

It depends on the position.

1)There's also this tension where you wait for your opponent to castle while preparing  a pawn storm and manoeuvering the pieces where your opponent will castle, planning to castle on the opposite side later on.

2)However, if your opponent is having a good grip on the centre and development, you must be weary of your king safety. 

*The first point is more applicable on the situation where your opponent castled too soon;  Castles before even the development is completed. 

@blueemu. Made me laugh. Well done

My insights shows I win more games when I castle in the middlegame. This is only a sample of a few hundred games though.

Castling is a powerful move: it brings the king to safety and connects the rooks, so it is like 3 moves Kf2 Rf1 Kg1 in one and it wins 2 tempi.

If one side castles and the other does not castle, then the side that castles has a definite advantage of 2 tempi. The side that castles is then the side that castles first.

If both sides castle, then none has any advantage over the other in that respect. In that case it does not matter who castles first. Usually it is white who castles first as white plays first and white is 1 tempo ahead anyway, regardless of castling so white enjoys an advantage of 1 tempo and is likely to castle first, but is is rather the tempo advantage that leads to castling first than castling first leading to an advantage.

Castling first is prudent as it brings your king to safety and avoids tactics against the uncastled king. Castling first also leads to connecting rooks first and thus often to occupying an open file with a rook first.

#24 yes that is why I am interested to see a study of millions of games, so that advantages of one player over another are averaged away (in layman's terms).

What you say is correct, the other player might have been forced to move the king or rook for example. If that is the case then that player may have been too slow in the opening.