Using United States National Football League play-by-play data for the 2002-2012 seasons, we train a neural network to predict win probability, based on measures of the game state. This predictor's performance is comparable to the point spread at the start of the game and improves thereafter with little bias. We define a measure of success as the change in a team's win probability over the course of a possession, and show that streaks in this measure are highly unlikely to be random. Further, this finding holds when controlling for the effects of clock management in the fourth quarter of football games, when win probability can increase incrementally for the leading team as the game continues. By defining momentum as an increase in win probability over the course of at least three successive changes in possession, we show some ability to anticipate its emergence, based on game state, using a second neural network. The possibility of using this knowledge for strategic advantage is discussed. We consider these results in the context of examples from National Football League games, including that from Super Bowl LI (Atlanta Falcons versus the New England Patriots), and end with some discussion of future extensions to this work.