Our algorithmic research focuses on the development and understanding of algorithms that can be used in sports analytics. These activities are sometimes purely theoretical, sometimes purely empirical, and sometimes a mix of the two.
Unlike most other efforts in sports analytics, we do not focus on the development of machine learning algorithms. Instead, we focus on the development of network optimization algorithms, network equilibrium algorithms, and algorithms for "classical" spatial statistics.
A variety of systems exist for determining the location of
players on the field/court. In graph-theoretic terms, these
systems provide information about the location of the
vertices of the graph. This part of the project is looking
at algorithms for determining the edges of the graph from
the locations of the players and the coverage areas of the
defenders.
We have to solve instances of the same problem repeatedly (e.g., 25 times per second) with parameters that change very little from instance to instance. We intend to explore the use of sensitivity analysis and duality theory to improve the performance of our solution techniques.
To data, all of our models and algorithms have assumed that all movement is on the plane (i.e., the field, court, or ice). However, all of the sports we are interested in allow passes along the ground and through the air. We intend to explore how we can efficiently incorporate a third spatial dimension into our models and algorithms.
Most research on solving graph-theoretic problems considers the development of algorithms that are appropriate for large problems (e.g., street networks, communication networks). The problems we are concerned with, however, are naturally very small. Hence, we intent to consider whether there are algorithms that are appropriate for small problems.
