Creating the current position having the rest of the game It's a question a friend of mine brought up and I found intriguing.
Let's say you have the records of a game from a certain move to the end, using standard notation (i.e. Qf6).
Either assuming random play or strong play (which is really hard to define), how many more moves on average would you need to restore the current position?
I don't really know how to approach this question, but it seems to involve retrograde analysis. The factors I could come up with are these.

Knowing where a piece moved to tells you it's possible locations.
Knowing where a piece moves tells you about empty squares (on the piece's way). This of course depends on it's original location.
Checks give you information about both the location of the king and empty squares around it
Exchanges give you a lot of info, both about the exact position of a piece and about the squares around it.
Castlings give you info about 5-6 pieces.

Another variant to this question is where the starting square of a piece is also given in the notation, i.e. Nd5-e3 instead of Ne3. This is not the most popular notation but it's still usable. How much would it affect the result?
P.S. Why does CSE have no &quot;soft question&quot; tag?
Fascinating question! By definition, I can only come with a partial solution, or more accurately "elements" that will be part of the retro analysis. I know I'll be thinking about this more, but here are a few initial thoughts.

Just a few more 'factors' to add to your list:


We'd need a certain minimum number of moves (in the latter part of the game) to make any meaningful analysis.
If the game is played out (i.e.) ends in a mate, that would help in recreating the 'start' position.
If the starting square is given, then it will help immensely.
Knowing the move number would help. (Is it 19 Ne5 or 24 Ne5)
The idea of "candidate squares" for pieces. If Na1 was played, then the N must have been at b3 or c2. For a N to reach c2, it must have come from... In effect, we know there must have been a few moves to get the knight from b1 or g1.
Pawn moves give us 'definitive' information about the 'from' square (except for e2-e4 vs e3-e4 type double jumps) Bishop moves help because they stay in the same color. 


We could infer more, but these is a start.

Alt. solution If you were allowed to "cheat" (lateral thinking):


you could feed the moves to a good-sized database and see if it can match up a game.
Chessbase has advanced search features which let you search for positions by pieces occupying squares, and also by a sequence of moves.


We could even do try this out with an actual snippet of a game. Publish, say the last 20 moves of a 50 move game, and try to recreate the position at move #30, without cheating or referring to a chessDB.