If the race metaphor is accurate, I would expect the head-start to be
compared not to the length of the runner's stride, but to the length of
the entire race. I would guess that a 10m head-start would be much more
likely to be decisive in a 100m sprint than in a marathon.
Perhaps we should not be looking at the mobility of individual pieces, but
the length of the overall game? Piece mobility would likely be a factor in
game length, but board size, number of pieces, and several other factors
could also be highly significant.