Getting over the advantage line

Anyone who watches Rugby on TV would be familiar with the term "Getting over the advantage line". Basically the team with the ball gets further up the field each time they run at the opponents defence.
In chess terms this equates with having move space (assuming you treat both sets of forwards as pawns!), although in endings it also means having your pawns over the halfway line on the board.
An example of the latter definition occurred during a game at my chess club this evening. In the diagram it was Black to move, and he was playing for a win, not so much because he knew his position was better, but simply because he had 10 minutes on the clock to his opponents 1. At first he tried to gain the opposition by luring the white king onto the wrong square, but seeing this didn't work, he hit upon the temporary sacrifice of a pawn (5. ... g4+). It was this idea that worked, especially as his opponent lost on time playing 8.Kf1, although it wasn't noticed for another move. This was somewhat fortunate for Black as Kg3 makes the win a lot harder than Kf4.

1...Kf5 2.Kf3 Kf6 3.Kf2 Kg6 4.Ke3 Kf5 5.Kf3 g4+ 6.hxg4+ Kg5 7.Kf2 Kxg4 8.Kf1 Kg3 9.Kg1 0-1 (time)

It is important to note that if you move the kingside pawns up one rank (so they are in their own half of the board), then the position is drawn.