We present a model for rating college football (NCAA) teams that takes into account the score of each game at every point in time. Unlike pure margin-of-victory models, our methodology does not reward unnecessarily lopsided victories. This approach is of special interest for the NCAA FBS national championship, which is contested by two teams chosen after a regular season in which most teams never play each other. Ranking systems based on win-loss results, such as those used by the BCS, can have difficulty evaluating undefeated teams with weak schedules because of the limitations of these data. Alternative rating systems based on margin of victory can be strongly in influenced by extreme results and may incentivize poor sportsmanship. Instead, our model considers the entire history of within-game scoring plays to infer the relative abilities of all teams. RUSH treats the score difference throughout each game (visitor minus home) as a stochastic process in order to model the evolution of the visiting team’s probability of winning the game. Thus meaningless scoring plays, those that occur when the probability of winning is near 0 or 1, have little effect on the teams’ ratings.