A Multiresolution Stochastic Process Model for Predicting Basketball Possession Outcomes

Basketball 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 paper, 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 \textit{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 estimating EPV, these models reveal novel insights on players' decision-making tendencies as a function of their spatial strategy.Comment: 31 pages, 9 figure

Factorized Point Process Intensities: A Spatial Analysis of Professional Basketball

We develop a machine learning approach to represent and analyze the underlying spatial structure that governs shot selection among professional basketball players in the NBA. Typically, NBA players are discussed and compared in an heuristic, imprecise manner that relies on unmeasured intuitions about player behavior. This makes it difficult to draw comparisons between players and make accurate player specific predictions. Modeling shot attempt data as a point process, we create a low dimensional representation of offensive player types in the NBA. Using non-negative matrix factorization (NMF), an unsupervised dimensionality reduction technique, we show that a low-rank spatial decomposition summarizes the shooting habits of NBA players. The spatial representations discovered by the algorithm correspond to intuitive descriptions of NBA player types, and can be used to model other spatial effects, such as shooting accuracy.Engineering and Applied Science

Real-Time Traffic Maps

This dissertation summarizes research investigating the design of real-time traffic maps. As traffic congestion continues to burden our largest cities, and as the Internet continues to grow at a rapid pace, real-time traffic maps have the potential to be among the world’s most popular maps. Furthermore, as mobile devices and in-car-navigationsystems begin to connect to the Internet, millions of drivers will access and read these maps on an array of media. This dissertation reports on research aimed to understand as well as enhance the design of real-time traffic maps. The dissertation includes reviews of previous scientific research, as well as several online traffic maps from around the world. The dissertation also introduces new methods to design and empirically evaluate the performance of real-time traffic maps. The design methods are guided by established cartographic principles, as well as the findings of human subjects studies that reveal more intuitive cartographic strategies. The investigation pays particular attention to the influences of cartographic classification, and cartographic symbolization; the findings suggest that both classification and symbolization significantly influence how map readers perceive and respond to graphical depictions of traffic conditions. With this in mind, the research suggests it is imperative to not only understand the influence of design variables on map perception, but also to, as best as possible, link map design with map-readers’ perceptual preconceptions, and preferences. This idea of cognitive congruence represents a new challenge for all kinds of cartographers

Thematic relevance and perceptual salience of dynamic geovisualization displays

We propose a research agenda for empirically assessing the effectiveness of dynamic displays with the eye-movement data collection method. The proposed framework is based on the relationship between perceptual salience and thematic relevance in static (e.g., visual variables: color hue, color value and orientation) and animated displays (e.g., dynamicvariables including transitions). The proposed empirical studies adhere to experimental design standards in cognitivepsychology, but are additionally grounded on a solid dynamic design framework borrowed from cartography, computer graphics and cinematography, to investigate how different dynamic and visual variables, and various levels of interactivity affect people’s knowledge construction processes from dynamic displays as compared to static displays

Considerations in Design of Transition Behaviors for Dynamic Thematic Maps

Maps provide a means for visual communication of spatial information. The success of this communication process largely rests on the design and symbolization choices made by the cartographer. For static mapmaking we have seen substantial research in how our design decisions can influence the legibility of the map’s message, however, we have limited knowledge about how dynamic maps communicate most effectively. Commonly, dynamic maps communicate spatiotemporal information by 1) displaying known data at discrete points in time and 2) employing cartographic transitions that depict changes that occur between these points. Since these transitions are a part of the communication process, we investigate how three common principles of static map design (visual variables, level of measurement, and classed vs. unclassed data representations) relate to cartographic transitions and their abilities to congruently and coherently represent temporal change in dynamic phenomena. In this review we find that many principles for static map design are less than reliable in a dynamic environment; the principles of static map symbolization and design do not always appear to be effective or congruent graphical representations of change. Through the review it becomes apparent that we are in need of additional research in the communication effectiveness of dynamic thematic maps. We conclude by identifying several research areas that we believe are key to developing research-based best practices for communicating about dynamic geographic processes