Applying Deep Bidirectional LSTM and Mixture Density Network for Basketball Trajectory Prediction

Data analytics helps basketball teams to create tactics. However, manual data collection and analytics are costly and ineffective. Therefore, we applied a deep bidirectional long short-term memory (BLSTM) and mixture density network (MDN) approach. This model is not only capable of predicting a basketball trajectory based on real data, but it also can generate new trajectory samples. It is an excellent application to help coaches and players decide when and where to shoot. Its structure is particularly suitable for dealing with time series problems. BLSTM receives forward and backward information at the same time, while stacking multiple BLSTMs further increases the learning ability of the model. Combined with BLSTMs, MDN is used to generate a multi-modal distribution of outputs. Thus, the proposed model can, in principle, represent arbitrary conditional probability distributions of output variables. We tested our model with two experiments on three-pointer datasets from NBA SportVu data. In the hit-or-miss classification experiment, the proposed model outperformed other models in terms of the convergence speed and accuracy. In the trajectory generation experiment, eight model-generated trajectories at a given time closely matched real trajectories

INTELLIGENT COMPUTER VISION SYSTEM FOR SCORE DETECTION IN BASKETBALL

Development of an intelligent computer vision system for Smart IoT basketball training and entertainment includes the development of a range of various subsystems, where score detection subsystem is playing a crucial role. This paper proposes the architecture of such a score detection subsystem to improve reliability and accuracy of the RFID technology used primarily for verification purposes. Challenges encompass both hardware-software interdependencies, optimal camera selection, and cost-effectiveness considerations. Leveraging machine learning algorithms, the vision-based subsystem aims not only to detect scores but also to facilitate online video streaming. Although the use of multiple cameras offers expanded field coverage and heightened precision, it concurrently introduces technical intricacies and increased costs due to image fusion and escalated processing requirements. This research navigates the intricate balance between achieving precise score detection and pragmatic system development. Through precise camera configuration optimization, the proposed system harmonizes hardware and software components

Multi-agent statistical discriminative sub-trajectory mining and an application to NBA basketball

Improvements in tracking technology through optical and computer vision systems have enabled a greater understanding of the movement-based behaviour of multiple agents, including in team sports. In this study, a Multi-Agent Statistically Discriminative Sub-Trajectory Mining (MA-Stat-DSM) method is proposed that takes a set of binary-labelled agent trajectory matrices as input and incorporates Hausdorff distance to identify sub-matrices that statistically significantly discriminate between the two groups of labelled trajectory matrices. Utilizing 2015/16 SportVU NBA tracking data, agent trajectory matrices representing attacks consisting of the trajectories of five agents (the ball, shooter, last passer, shooter defender, and last passer defender), were truncated to correspond to the time interval following the receipt of the ball by the last passer, and labelled as effective or ineffective based on a definition of attack effectiveness that we devise in the current study. After identifying appropriate parameters for MA-Stat-DSM by iteratively applying it to all matches involving the two top- and two bottom-placed teams from the 2015/16 NBA season, the method was then applied to selected matches and could identify and visualize the portions of plays, e.g., involving passing, on-, and/or off-the-ball movements, which were most relevant in rendering attacks effective or ineffective

FRMDN: Flow-based Recurrent Mixture Density Network

Recurrent Mixture Density Networks (RMDNs) are consisted of two main parts: a Recurrent Neural Network (RNN) and a Gaussian Mixture Model (GMM), in which a kind of RNN (almost LSTM) is used to find the parameters of a GMM in every time step. While available RMDNs have been faced with different difficulties. The most important of them is high$-$dimensional problems. Since estimating the covariance matrix for the high$-$dimensional problems is more difficult, due to existing correlation between dimensions and satisfying the positive definition condition. Consequently, the available methods have usually used RMDN with a diagonal covariance matrix for high$-$dimensional problems by supposing independence among dimensions. Hence, in this paper with inspiring a common approach in the literature of GMM, we consider a tied configuration for each precision matrix (inverse of the covariance matrix) in RMDN as (\(\Sigma _k^{ - 1} = U{D_k}U\)) to enrich GMM rather than considering a diagonal form for it. But due to simplicity, we assume \(U\) be an Identity matrix and \(D_k\) is a specific diagonal matrix for \(k^{th}\) component. Until now, we only have a diagonal matrix and it does not differ with available diagonal RMDNs. Besides, Flow$-$based neural networks are a new group of generative models that are able to transform a distribution to a simpler distribution and vice versa, through a sequence of invertible functions. Therefore, we applied a diagonal GMM on transformed observations. At every time step, the next observation, \({y_{t + 1}}\), has been passed through a flow$-$based neural network to obtain a much simpler distribution. Experimental results for a reinforcement learning problem verify the superiority of the proposed method to the base$-$line method in terms of Negative Log$-$Likelihood (NLL) for RMDN and the cumulative reward for a controller with fewer population size

Integrating machine learning and decision support in tactical decision-making in rugby union

Funding: National Research Foundation of South Africa andthe Department of Higher Education and Training via the Teaching and Development Grant (IRMA:29113).Rugby union, like many sports, is based around sequences of play, yet this sequential nature is often overlooked, for example in analyses that aggregate performance measures over a fixed time interval. We use recent developments in convolutional and recurrent neural networks to predict the outcomes of sequences of play, based on the ordered sequence of actions they contain and where on the field these actions occur. The outcomes considered are gaining territory, retaining possession, scoring a try, and being awarded or conceding a penalty. We consider several artificial neural network architectures and compare their performance against baseline models. Accounting for sequential data and using field location improved classification accuracy over the baseline for some outcomes. We then investigate how these prediction models can provide tactical decision support to coaches. We demonstrate that tactical insight can be gained by conducting scenario analyses with data visualisations to investigate which strategies yield the highest probability of achieving the desired outcome.PostprintPeer reviewe

Dynamic Switching State Systems for Visual Tracking

This work addresses the problem of how to capture the dynamics of maneuvering objects for visual tracking. Towards this end, the perspective of recursive Bayesian filters and the perspective of deep learning approaches for state estimation are considered and their functional viewpoints are brought together

Essays in Basketball Analytics

With the increasing popularity and competition in professional basketball in the past decade, data driven decision has emerged as a big competitive edge. The advent of high frequency player tracking data from SportVU has enabled a rigorous analysis of player abilities and interactions that was not possible before. The tracking data records two-dimensional x-y coordinates of 10 players on the court as well as the x-y-z coordinates of the ball at a resolution of 25 frames per second, yielding over 1 billion space-time observations over the course of a full season. This dissertation offers a collection of spatio-temporal models and player evaluation metrics that provide insight into the player interactions and their performance, hence allowing the teams to make better decisions. Conventional approaches to simulate matches have ignored that in basketball the dynamics of ball movement is very sensitive to the lineups on the court and unique identities of players on both offense and defense sides. In chapter 2, we propose the simulation infrastructure that can bridge the gap between player identity and team level network. We model the progression of a basketball match using a probabilistic graphical model. We model every touch event in a game as a sequence of transitions between discrete states. We treat the progression of a match as a graph, where each node represents the network structure of players on the court, their actions, events, etc., and edges denote possible moves in the game flow. Our results show that either changes in the team lineup or changes in the opponent team lineup significantly affects the dynamics of a match progression. Evaluation on the match data for the 2013-16 NBA season suggests that the graphical model approach is appropriate for modeling a basketball match. NBA teams value players who can ``stretch'' the floor, i.e. create space on the court by drawing their defender(s) closer to themselves. Clearly, this ability to attract defenders varies across players, and furthermore, this effect may also vary by the court location of the offensive player, and whether or not the player is the ball handler. For instance, a ball-handler near the basket attracts a defender more when compared to a non ball-handler at the 3 point line. This has a significant effect on the defensive assignment. This is particularly important because defensive assignment has become the cornerstone of all tracking data based player evaluation models. In chapter 3, we propose a new model to learn player and court location specific offensive attraction. We show that offensive players indeed have varying ability to attract the defender in different parts of the court. Using this metric, teams can evaluate players to construct a roster or lineup which maximizes spacing. We also improve upon the existing defensive matchup inference algorithm for SportVU data. While the ultimate goal of the offense is to shoot the ball, the strategy lies in creating good shot opportunities. Offensive play event detection has been a topic of research interest. Current research in this area have used a supervised learning approach to detect and classify such events. We took an unsupervised learning approach to detect these events. This has two inherent benefits: first, there is no need for pretagged data to learn identifying these events which is a lobor intensive and error prone task; second, an unsupervised approach allows us to detect events that has not been tagged yet i.e. novel events. We use a HMM based approach to detect these events at any point in the time during a possession by specifying the functional form of the prior distribution on the player movement data. We test our framework on detecting ball screen, post up, and drive. However, it can be easily extended to events like isolation or a new event that has certain distinct defensive matchup or player movement feature compared to a non event. This is the topic for chapter 4. Accurate estimation of the offensive and the defensive abilities of players in the NBA plays a crucial role in player selection and ranking. A typical approach to estimate players' defensive and offensive abilities is to learn the defensive assignment for each shot and then use a random effects model to estimate the offensive and defensive abilities for each player. The scalar estimate from the random effects model can then be used to rank player. In this approach, a shot has a binary outcome, either it is made or it is a miss. This approach is not able to take advantage of the “quality” of the shot trajectory. In chapter 5, we propose a new method for ranking players that infers the quality of a shot trajectory using a deep recurrent neural network, and then uses this quality measure in a random effects model to rank players taking defensive matchup into account. We show that the quality information significantly improves the player ranking. We also show that including the quality of shots increases the separation between the learned random effect coefficients, and thus, allows for a better differentiation of player abilities. Further, we show that we are able to infer changes in the player's ability on a game-by-game basis when using a trajectory based model. A shot based model does not have enough information to detect changes in player's ability on a game-by-game basis. A good defensive player prevents its opponent from making a shot, attempting a good shot, making an easy pass, or scoring events, eventually leading to wasted shot clock time. The salient feature here is that a good defender prevents events. Consequently, event driven metrics, such as box scores, cannot measure defensive abilities. Conventional wisdom in basketball is that ``pesky'' defenders continuously maintain a close distance to the ball handler. A closely guarded offensive player is less likely to take or make a shot, less likely to pass, and more likely to lose the ball. In chapter 6, we introduce Defensive Efficiency Rating (DER), a new statistic that measures the defensive effectiveness of a player. DER is the effective distance a defender maintains with the ball handler during an interaction where we control for the identity and wingspan of the the defender, the shot efficiency of the ball handler, and the zone on the court. DER allows us to quantify the quality of defensive interaction without being limited by the occurrence of discrete and infrequent events like shots and rebounds. We show that the ranking from this statistic naturally picks out defenders known to perform well in particular zones

Dynamic Switching State Systems for Visual Tracking

This work addresses the problem of how to capture the dynamics of maneuvering objects for visual tracking. Towards this end, the perspective of recursive Bayesian filters and the perspective of deep learning approaches for state estimation are considered and their functional viewpoints are brought together