Disagree with the bolded. The goal is to end the game with at least 1 more point than the other team. Therefore, if you're winning by N points, the goal is always to do no worse than being outscored by N-1.
That only translates to "score more points than the other team" in situations where you're tied or losing (ok, so for Illini football, maybe that
is 95% of the time
). Otherwise, say you're winning by 7, the goal is to be outscored by 6 or fewer.
I know you probably meant "score more points" taken over the whole game... but still, it's important from a strategy perspective to remember that when you have a lead, scoring more points than the other team (for the rest of the game) is no longer strictly necessary.