Play Calling Strategy in American Football: A Game-Theoretic Stochastic Dynamic Programming Approach

1999 ◽  
Vol 13 (2) ◽  
pp. 103-113 ◽  
Author(s):  
Jess S. Boronico ◽  
Scott L. Newbert
Keyword(s):  
Dynamic Programming ◽  
Stochastic Dynamic Programming ◽  
Quantitative Methods ◽  
American Football ◽  
Programming Approach ◽  
Stochastic Dynamic ◽  
Theoretic Approach ◽  
Dynamic Programming Approach ◽  
Game Theoretic

This manuscript presents a model to assist in the determination of optimal American football play selection for first down and goal situations. A game theoretic approach is embedded within a stochastic dynamic programming formulation, resulting in a mixed strategy satisfying the ex-ante declared objective of maximizing the probability of scoring a touchdown. The methodology provides a quantitative framework to a problem that impacts on team performance and addresses a gap in the literature concerning the application of quantitative methods to sports.

A Decoupled and Prioritized Stochastic Dynamic Programming Approach for Automated Transport of Multiple Particles Using Optical Tweezers

2009 ◽  
Author(s):  
Ashis Gopal Banerjee ◽  
Wolfgang Losert ◽  
Satyandra K. Gupta
Keyword(s):  
Dynamic Programming ◽  
Motion Planning ◽  
Optical Tweezers ◽  
Stochastic Dynamic Programming ◽  
Graph Matching ◽  
Programming Approach ◽  
Stochastic Dynamic ◽  
Step Method ◽  
Dynamic Programming Approach ◽  
Multiple Particles

Automated transport of multiple particles using optical tweezers requires the use of motion planning to move them simultaneously while avoiding collisions amongst themselves and with randomly moving obstacles. This paper develops a decoupled and prioritized stochastic dynamic programming based motion planning framework by sequentially applying a partially observable Markov decision process algorithm on every particle that needs to be transported. An iterative version of a maximum bipartite graph matching algorithm is used to assign given goal locations to such particles. The algorithm for individual particle transport is validated using silica beads in a holographic tweezer set-up. Once the individual plans are computed, a three-step method consisting of clustering, classification, and branch and bound optimization is employed to determine the final collision-free paths. Simulation results in the form of sample trajectories and performance characterization plots are presented to illustrate the usefulness of the developed approach.

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