Last week we understood that a major battle in half guard is the battle for head positioning. If the bottom player wins this battle, she is in a more advantageous position than her opponent. This advantage reduces the amount of effort she needs to use to successfully sweep her opponent.
Winning the battle for head position means the bottom player has slightly more control than her opponent. Her goal is to increase this disparity and obtain the maximum amount of control possible. To do this, she will attempt to gain control of her opponent’s centre of mass.
Having her head positioned against her opponent’s chest means it is easy to gain a near side underhook on her opponent’s body. The bottom player uses this underhook to pull herself deeper underneath her opponent until her head is underneath her opponent’s belly. Now her arms can naturally wrap around her opponent’s belly/hips (his centre of mass).
Even with this control, the top player still has some freedom of movement. He can use his hands, and more importantly, feet to move himself around to find angles to create pressure. If the bottom player is able to snag his farside foot and pull it to his butt, his ability to move is severely restricted.
With control of his centre of mass, and with his movement restricted, the bottom player is in a good position to sweep and come on top.