# Going Deep: Models for Continuous-Time Within-Play Valuation of Game Outcomes in American Football with Tracking Data

## TL;DR

This paper introduces a novel continuous-time framework using tracking data and neural networks to evaluate American football play outcomes dynamically during plays, enabling more precise and granular game analysis.

## Contribution

It presents a modular framework for within-play valuation and develops a recurrent neural network model for yardage estimation, extending the analysis to continuous-time expected play value.

## Key findings

- Developed a continuous-time valuation framework for football plays.
- Created a neural network model for yardage prediction during plays.
- Enabled calculation of play value expectations in real-time.

## Abstract

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.