What are the ideas behind the 4.Qxd4 variation of Philidor's Defense? I recently learned that this is a valid way for White to play for advantage against the Philidor:
[FEN &quot;&quot;]

1.e4 e5 2.Nf3 d6 3.d4 exd4 4.Qxd4 Nc6 5.Bb5 Bd7 6.Bxc6 Bxc6

According to the Lichess database, White has won 59% of games from this position, while Black has only won 34%. The Masters database also heavily favors White, with 31% White wins / 17% Black wins.
What are the ideas behind White's 4.Qxd4 move, and why does it have such a high winrate? What is White's motivation for violating principles like bringing out his queen very early / giving up the bishop pair?
The principle is to not bring out the queen too early when it can be easily attacked.  In this situation there's no easy way for black to attack the queen on d4, so it's not too early.  So instead of being a weakness, the queen in a central square is a huge strength.
A very similar phenomenon happens in the following line of the Scotch game where white develops the queen early and gets a +.6 edge and 43%/21% winrate on lichess.
 [FEN &quot;&quot;]
 1. e4 e5 2.Nf3 Nc6, 3.d4 exd4, 4. Nxd4 Nxd4 5.Qxd4