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 .
Although aforementioned basketball work did not have access to raw trajectory data, , use the same dataset provided by STATS for some of their work involving basketball. They explore how to get an open shot in basketball using trajectory data to find that the number of times defensive players swapped roles positions was predictive of scoring. However, they explore open versus pressured shots (rather than shot making prediction), do not represent the data as an image, and do not implement neural networks for their findings. Other trajectory work includes using Conditional Random Fields to predict ball ownership from only player positions ( @cite_6 ), as well as predicting the next action of the ball owner via pass, shot, or dribble @cite_0 . use non-negative matrix factorization to identify different types of shooters using trajectory data. Because of a lack of defensive statistics in the sport, A. Franks et. al. create counterpoints (defensive points) to better quantify , defensive plays ( @cite_1 @cite_4 ). make use of trajectory data by segmenting a game of basketball into phases (offense, defense, and time-outs) to then analyze team behavior during these phases.
@cite_0 @cite_4 @cite_1 @cite_6
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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... We present a model that uses a single first-person image to generate an egocentric basketball motion sequence in the form of a 12D camera configuration trajectory, which encodes a player's 3D location and 3D head orientation throughout the sequence. To do this, we first introduce a future convolutional neural network (CNN) that predicts an initial sequence of 12D camera configurations, aiming to capture how real players move during a one-on-one basketball game. We also introduce a goal verifier network, which is trained to verify that a given camera configuration is consistent with the final goals of real one-on-one basketball players. Next, we propose an inverse synthesis procedure to synthesize a refined sequence of 12D camera configurations that (1) sufficiently matches the initial configurations predicted by the future CNN, while (2) maximizing the output of the goal verifier network. Finally, by following the trajectory resulting from the refined camera configuration sequence, we obtain the complete 12D motion sequence. Our model generates realistic basketball motion sequences that capture the goals of real players, outperforming standard deep learning approaches such as recurrent neural networks (RNNs), long short-term memory networks (LSTMs), and generative adversarial networks (GANs). 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. In this paper, we describe a method to represent and discover adversarial group behavior in a continuous domain. In comparison to other types of behavior, adversarial behavior is heavily structured as the location of a player (or agent) is dependent both on their teammates and adversaries, in addition to the tactics or strategies of the team. We present a method which can exploit this relationship through the use of a spatiotemporal basis model. As players constantly change roles during a match, we show that employing a "role-based" representation instead of one based on player "identity" can best exploit the playing structure. As vision-based systems currently do not provide perfect detection tracking (e.g. missed or false detections), we show that our compact representation can effectively "denoise" erroneous detections as well as enabling temporal analysis, which was previously prohibitive due to the dimensionality of the signal. To evaluate our approach, we used a fully instrumented field-hockey pitch with 8 fixed high-definition (HD) cameras and evaluated our approach on approximately 200,000 frames of data from a state-of-the-art real-time player detector and compare it to manually labelled data.