In this paper, we predict the likelihood of a player making a shot in basketball from multiagent trajectories. Previous approaches to similar problems center on hand-crafting features to capture domain specific knowledge. Although intuitive, recent work in deep learning has shown this approach is prone to missing important predictive features. To circumvent this issue, we present a convolutional neural network (CNN) approach where we initially represent the multiagent behavior as an image. To encode the adversarial nature of basketball, we use a multi-channel image which we then feed into a CNN. Additionally, to capture the temporal aspect of the trajectories we "fade" the player trajectories. We find that this approach is superior to a traditional FFN model. By using gradient ascent to create images using an already trained CNN, we discover what features the CNN filters learn. Last, we find that a combined CNN+FFN is the best performing network with an error rate of 39 .
Previous work on Recursive Neural Networks (RNNs) shows that these models can produce compositional feature vectors for accurately representing and classifying sentences or images. However, the sentence vectors of previous models cannot accurately represent visually grounded meaning. We introduce the DT-RNN model which uses dependency trees to embed sentences into a vector space in order to retrieve images that are described by those sentences. Unlike previous RNN-based models which use constituency trees, DT-RNNs naturally focus on the action and agents in a sentence. They are better able to abstract from the details of word order and syntactic expression. DT-RNNs outperform other recursive and recurrent neural networks, kernelized CCA and a bag-of-words baseline on the tasks of finding an image that fits a sentence description and vice versa. They also give more similar representations to sentences that describe the same image. ABSTRACTBasketball games evolve continuously in space and time as players constantly interact with their teammates, the opposing team, and the ball. However, current analyses of basketball outcomes rely on discretized summaries of the game that reduce such interactions to tallies of points, assists, and similar events. In this article, we propose a framework for using optical player tracking data to estimate, in real time, the expected number of points obtained by the end of a possession. This quantity, called expected possession value (EPV), derives from a stochastic process model for the evolution of a basketball possession. We model this process at multiple levels of resolution, differentiating between continuous, infinitesimal movements of players, and discrete events such as shot attempts and turnovers. Transition kernels are estimated using hierarchical spatiotemporal models that share information across players while remaining computationally tractable on very large data sets. In addition to estima... Although basketball is a dualistic sport, with all players competing on both offense and defense, almost all of the sport's conventional metrics are designed to summarize offensive play. As a result, player valuations are largely based on offensive performances and to a much lesser degree on defensive ones. Steals, blocks and defensive rebounds provide only a limited summary of defensive effectiveness, yet they persist because they summarize salient events that are easy to observe. Due to the inefficacy of traditional defensive statistics, the state of the art in defensive analytics remains qualitative, based on expert intuition and analysis that can be prone to human biases and imprecision. Fortunately, emerging optical player tracking systems have the potential to enable a richer quantitative characterization of basketball performance, particularly defensive performance. Unfortunately, due to computational and methodological complexities, that potential remains unmet. This paper attempts to fill this void, combining spatial and spatio-temporal processes, matrix factorization techniques and hierarchical regression models with player tracking data to advance the state of defensive analytics in the NBA. Our approach detects, characterizes and quantifies multiple aspects of defensive play in basketball, supporting some common understandings of defensive effectiveness, challenging others and opening up many new insights into the defensive elements of basketball. Tracking objects like a basketball from a monocular view is challenging due to its small size, potential to move at high velocities as well as the high frequency of occlusion. However, humans with a deep knowledge of a game like basketball can predict with high accuracy the location of the ball even without seeing it due to the location and motion of nearby objects, as well as information of where it was last seen. Learning from tracking data is problematic however, due to the high variance in player locations. In this paper, we show that by simply "permuting" the multi-agent data we obtain a compact role-ordered feature which accurately predict the ball owner. We also show that our formulation can incorporate other information sources such as a vision-based ball detector to improve prediction accuracy.