agree with shoe. one thing to add, the situation in terms of it being a battle, or if you were the only viable school, as far as i can tell, that has no impact on whether the guy signs or not. i think the way to think of it is, there is a cycle where the player is programmed to sign, if there is an eligible school. before this time, the player will not sign no matter what. after this time, the player will sign the first cycle there is an eligible signer.
so basically, like shoe said, the 0 ship team would stay very high. if the player hits the signing cycle, they'll immediately sign with you on a 100% basis (no roll). but if before that signing cycle hits, the other team opens a spot, or another team gets to high or very high, you'll be back to a roll.