Jeremy, Derek, I think you are arguing somewhat at cross-purposes here. You
are closer together on some positions than you believe, and you are
discussing 2 slightly different things. Further, Derek, you seem to not
like contrafactuals.
Derek is merely maintaining that the mere fact of moving first gives white
a 1/3 pawn advantage in the game. Jeremy is maintaining that it is
demonstrable in individual games there are higher-value moves than first
move. For example, checkmate is the highest value move outcome you can
have, and that never happens on the first turn. ;-)
Still, for the question of what the mechanism is by which white gains a
first turn advantage, can anyone come up with a better answer than
primarily mobility, and maybe some add-on from board size and possibly some
from pawn irreversibility?