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I think Gabriel is on the right track but needs an improved methodology.  I
would suggest using Betza's crowded board mobilty calculations.  To get
middle game figures, deflate the piece count by 40% and then calculate the
piece density.  For FIDE chess this gives a deflated piece density of 30%
and a square emptiness probability of 70%.  Then using these numbers
calculate the croweded board mobility of one army (for divergent pieces
such as pawns, just use the average of the mobility of the capturing and
non-capturing moves). As it happens this is quite close to 64 for FIDE
chess--so lets simplfy and say that that it is exactly 64 for a ratio of
mobility to number of squares of 1.0.

Having calculated the crowded board mobility of the army divide the square
of the number of squares by the mobitity. For FIDE chess, this is 64
squared divided by 64 = 64.  For a hypothetical 100 square game with a
whole army crowded board mobility of 125, this is 100 squared divided by
120 = 80, while an 81 square game with a whole army mobility of 72 = 91
1/8.  I would predict that the first hypothtical game would have a typical
number of moves close to FIDE chess than the second, even though it has
more squares. 

Final results significanlty greater than 64 indicate games that play
slower than FIDE Chess, results significantly less than 64 indicate games
that play faster than FIDE Chess.

Taking two real games as examples:

Betza's Tripunch Chess would play faster than FIDE Chess even if it were
played on a 10 by 10 board,

Feeble Los Alamos Chess will play slower than FIDE Chess even though it is
played on a 6 by 6 board.

There is no real need to do the actual calculations for purposes such as
time limits for tournaments--a good guess as to whether the game is faster
or slower than FIDE chess is adequate.  The relevant factors are number of
squares, piece density, and strength of pieces.