Statistically speaking, for white and black, what is the last piece moved from its starting position, and why?
I think a good approach to this is to see what pieces most likely move first.
Central pawns normally always come out.
The bishops and knights come out early
If you castle early, one of the rooks plus the king will have moved
The other rook is sometimes left stationary unless there is an open file.
The queen normally gets into play.
Since you want to keep the king safeguarded, especially if castled, I would say most players would try to move the pawns in front of the castled king last or leave them on their original squares.
There are so many factors that would affect that. Player strength, for one, as weaker players tend to play heavy pieces first (beginners always have to be told not to push their rook pawns and bring their rooks out in front of their pawns).
Next, the opening choice affects it strongly, because that can dictate both castling and pawn structure.
What's the purpose of the question, aside from idle curiosity? Is there a principle you're aiming for?
The rook or the queen. Typically
Knights & Bishops should be developed early Queen should be out after the minor pieces are out The rooks are out last and usually come out via castling. Sometimes, it stays there and attacks from there (e.g. in the sicilian yugoslav attack, white players usually castle queenside and push the h-pawn, with the rook staying on h1)
We can remove a few unlikely contenders:
That leaves us with the queens, the queen's rooks, and the a-, b-, f-, g-, and h-pawns. Among the pawns, I think the b- and g-pawns are most likely to move first, since the fianchetto is a relatively common maneuver. Among the two remaining pieces, the queen is generally developed earlier in the game than the queen's rook, so we can rule her out.
Now, we're down to the queen's rook and three pawns. Even though I initially thought the f-pawn was going to be the most frequent last piece developed, a quick look at my games says otherwise. The vast popularity of the Bird's opening, as well as frequent kingside attacks, ensures that the f-pawn is rarely the last piece developed.
I'm also going to rule out the a-pawn, since it is moved frequently in openings such as the Sicilian (e.g. the Najdorf) and the Ruy Lopez (e.g. main line).
With only the h-pawn and the queen's rook remaining, it is hard to make a comparison without statistics. While, in most games, the last piece to be developed will be a pawn, the large number of pawns relative to the number of likely pieces makes it possible that the queen's rook is the single, most statistically likely piece to be developed last.
I'd say the queen for the very reason she isn't moved much early on - because she is more susceptible to attack!
Also, isn't knights before bishops a rule for the opening that holds true under most circumstances? I say this because that would nearly eliminate the knight from contention, or would in tournaments anyway.