  Continuous-time assessments of game outcomes in sports have become
increasingly common in the last decade. In American football, only
discrete-time estimates of play value were possible, since the most advanced
public football datasets were recorded at the play-by-play level. While
measures such as expected points and win probability are useful for evaluating
football plays and game situations, there has been no research into how these
values change throughout the course of a play. In this work, we make two main
contributions: First, we introduce a general framework for continuous-time
within-play valuation in the National Football League using player-tracking
data. Our modular framework incorporates several modular sub-models, to easily
incorporate recent work involving player tracking data in football. Second, we
use a long short-term memory recurrent neural network to construct a
ball-carrier model to estimate how many yards the ball-carrier is expected to
gain from their current position, conditional on the locations and trajectories
of the ball-carrier, their teammates and opponents. Additionally, we
demonstrate an extension with conditional density estimation so that the
expectation of any measure of play value can be calculated in continuous-time,
which was never before possible at such a granular level.
