Dan Cervone
September 26, 2015
NESSIS 2015
Work in collaboration with: Luke Bornn, Alex D'Amour, Alex Franks, Kirk Goldsberry, Andrew Miller
Installed in 2013, tracks:
About 1 billion space-time points per season
Think of locations as stocks, players as shareholders:
Think of locations as stocks, players as shareholders:
Specifically: divide the court into \( m \) equally sized cells
\[ x^i_j(t) = \begin{cases} \frac{1}{1 + w^i_j(t)} & i = \text{argmin}_h w^h_j(t) \\ 0 & \text{otherwise} \end{cases} \]
Portfolio value differential: \[ V_t \beta = \left(\sum_{i: \text{ offense}} X^i(t) - \sum_{i: \text{ defense}} X^i(t)\right)\beta \]
Market capitalization: \[ M_t \beta = \left(\sum_{i: \text{ offense}} X^i(t) + \sum_{i: \text{ defense}} X^i(t)\right)\beta \]
Minimize \[ \sum_t \frac{1}{2}\beta'(V_t - V_{t - 1})'(V_t - V_{t-1})\beta + \lambda_1 \frac{1}{M_t} \beta + \lambda_2\beta'\Omega_{\kappa}\beta \]
subject to:
Free parameters: \( \lambda_1, \lambda_2, \kappa \).
\[ \begin{array}{c} \lambda_2 \\ \downarrow \end{array} \]
\( \lambda_1 \rightarrow \)
Choose \( \lambda_1, \lambda_2, \ell \) that best classify possession outcomes based on portfolio value differential.