arXiv subjects

Luke Bornn

Publications and source records attributed to Luke Bornn.

At least 19 recordsLinked to original sources

arXiv2021

Inverse Bayesian Optimization: Learning Human Acquisition Functions in an Exploration vs Exploitation Search Task

This paper introduces a probabilistic framework to estimate parameters of an acquisition function given observed human behavior that can be modeled as a collection of sample paths from a Bayesian optimization procedure. The methodology involves defining a likelihood on observed human behavior from an optimization task, where the likelihood is parameterized by a Bayesian optimization subroutine governed by an unknown acquisition function. This structure enables us to make inference on a subject's acquisition function while allowing their behavior to deviate around the solution to the Bayesian optimization subroutine. To test our methods, we designed a sequential optimization task which forced subjects to balance exploration and exploitation in search of an invisible target location. Applying our proposed methods to the resulting data, we find that many subjects tend to exhibit exploration preferences beyond that of standard acquisition functions to capture. Guided by the model discrepancies, we augment the candidate acquisition functions to yield a superior fit to the human behavior in this task.

cs.HC↗

arXiv2020

A framework for the fine-grained evaluation of the instantaneous expected value of soccer possessions

The expected possession value (EPV) of a soccer possession represents the likelihood of a team scoring or receiving the next goal at any time instance. By decomposing the EPV into a series of subcomponents that are estimated separately, we develop a comprehensive analysis framework providing soccer practitioners with the ability to evaluate the impact of both observed and potential actions. We show we can obtain calibrated models for all the components of EPV, including a set of yet-unexplored problems in soccer. We produce visually-interpretable probability surfaces for potential passes from a series of deep neural network architectures that learn from low-level spatiotemporal data. Additionally, we present a series of novel practical applications providing coaches with an enriched interpretation of specific game situations.

cs.LG↗

arXiv2020

SoccerMap: A Deep Learning Architecture for Visually-Interpretable Analysis in Soccer

We present a fully convolutional neural network architecture that is capable of estimating full probability surfaces of potential passes in soccer, derived from high-frequency spatiotemporal data. The network receives layers of low-level inputs and learns a feature hierarchy that produces predictions at different sampling levels, capturing both coarse and fine spatial details. By merging these predictions, we can produce visually-rich probability surfaces for any game situation that allows coaches to develop a fine-grained analysis of players' positioning and decision-making, an as-yet little-explored area in sports. We show the network can perform remarkably well in the estimation of pass success probability, and present how it can be adapted easily to approach two other challenging problems: the estimation of pass-selection likelihood and the prediction of the expected value of a pass. Our approach provides a novel solution for learning a full prediction surface when there is only a single-pixel correspondence between ground-truth outcomes and the predicted probability map. The flexibility of this architecture allows its adaptation to a great variety of practical problems in soccer. We also present a set of practical applications, including the evaluation of passing risk at a player level, the identification of the best potential passing options, and the differentiation of passing tendencies between teams.

cs.LG↗

arXiv2020

Estimating locomotor demands during team play from broadcast-derived tracking data

The introduction of optical tracking data across sports has given rise to the ability to dissect athletic performance at a level unfathomable a decade ago. One specific area that has seen substantial benefit is sports science, as high resolution coordinate data permits sports scientists to have to-the-second estimates of external load metrics, such as acceleration load and high speed running distance, traditionally used to understand the physical toll a game takes on an athlete. Unfortunately, collecting this data requires installation of expensive hardware and paying costly licensing fees to data providers, restricting its availability. Algorithms have been developed that allow a traditional broadcast feed to be converted to x-y coordinate data, making tracking data easier to acquire, but coordinates are available for an athlete only when that player is within the camera frame. Obviously, this leads to inaccuracies in player load estimates, limiting the usefulness of this data for sports scientists. In this research, we develop models that predict offscreen load metrics and demonstrate the viability of broadcast-derived tracking data for understanding external load in soccer.

stat.AP↗

arXiv2019

Measuring Spatial Allocative Efficiency in Basketball

Every shot in basketball has an opportunity cost; one player's shot eliminates all potential opportunities from their teammates for that play. For this reason, player-shot efficiency should ultimately be considered relative to the lineup. This aspect of efficiency---the optimal way to allocate shots within a lineup---is the focus of our paper. Allocative efficiency should be considered in a spatial context since the distribution of shot attempts within a lineup is highly dependent on court location. We propose a new metric for spatial allocative efficiency by comparing a player's field goal percentage (FG%) to their field goal attempt (FGA) rate in context of both their four teammates on the court and the spatial distribution of their shots. Leveraging publicly available data provided by the National Basketball Association (NBA), we estimate player FG% at every location in the offensive half court using a Bayesian hierarchical model. Then, by ordering a lineup's estimated FG%s and pairing these rankings with the lineup's empirical FGA rate rankings, we detect areas where the lineup exhibits inefficient shot allocation. Lastly, we analyze the impact that sub-optimal shot allocation has on a team's overall offensive potential, demonstrating that inefficient shot allocation correlates with reduced scoring.

stat.AP↗

arXiv2019

Home Sweet Home: Quantifying Home Court Advantages For NCAA Basketball Statistics

Box score statistics are the baseline measures of performance for National Collegiate Athletic Association (NCAA) basketball. Between the 2011-2012 and 2015-2016 seasons, NCAA teams performed better at home compared to on the road in nearly all box score statistics across both genders and all three divisions. Using box score data from over 100,000 games spanning the three divisions for both women and men, we examine the factors underlying this discrepancy. The prevalence of neutral location games in the NCAA provides an additional angle through which to examine the gaps in box score statistic performance, which we believe has been underutilized in existing literature. We also estimate a regression model to quantify the home court advantages for box score statistics after controlling for other factors such as number of possessions, and team strength. Additionally, we examine the biases of scorekeepers and referees. We present evidence that scorekeepers tend to have greater home team biases when observing men compared to women, higher divisions compared to lower divisions, and stronger teams compared to weaker teams. Finally, we present statistically significant results indicating referee decisions are impacted by attendance, with larger crowds resulting in greater bias in favor of the home team.

stat.AP↗

arXiv2019

Using In-Game Shot Trajectories to Better Understand Defensive Impact in the NBA

As 3-point shooting in the NBA continues to increase, the importance of perimeter defense has never been greater. Perimeter defenders are often evaluated by their ability to tightly contest shots, but how exactly does contesting a jump shot cause a decrease in expected shooting percentage, and can we use this insight to better assess perimeter defender ability? In this paper we analyze over 50,000 shot trajectories from the NBA to explain why, in terms of impact on shot trajectories, shooters tend to miss more when tightly contested. We present a variety of results derived from this shot trajectory data. Additionally, pairing trajectory data with features such as defender height, distance, and contest angle, we are able to evaluate not just perimeter defenders, but also shooters' resilience to defensive pressure. Utilizing shot trajectories and corresponding modeled shot-make probabilities, we are able to create perimeter defensive metrics that are more accurate and less variable than traditional metrics like opponent field goal percentage.

stat.AP↗

arXiv2019

Playing Fast Not Loose: Evaluating team-level pace of play in ice hockey using spatio-temporal possession data

Pace of play is an important characteristic in hockey as well as other team sports. We provide the first comprehensive study of pace within the sport of hockey, focusing on how teams and players impact pace in different regions of the ice, and the resultant effect on other aspects of the game. First we examined how pace of play varies across the surface of the rink, across different periods, at different manpower situations, between different professional leagues, and through time between seasons. Our analysis of pace by zone helps to explain some of the counter-intuitive results reported in prior studies. For instance, we show that the negative correlation between attacking speed and shots/goals is likely due to a large decline in attacking speed in the OZ. We also studied how pace impacts the outcomes of various events. We found that pace is positively-correlated with both high-danger zone entries (e.g. odd-man rushes) and higher shot quality. However, we find that passes with failed receptions occur at higher speeds than successful receptions. These findings suggest that increased pace is beneficial, but perhaps only up to a certain extent. Higher pace can create breakdowns in defensive structure and lead to better scoring chances but can also lead to more turnovers. Finally, we analyzed team and player-level pace in the NHL, highlighting the considerable variability in how teams and players attack and defend against pace. Taken together, our results demonstrate that measures of team-level pace derived from spatio-temporal data are informative metrics in hockey and should prove useful in other team sports.

stat.AP↗

arXiv2019

Winning Is Not Everything: A contextual analysis of hockey face-offs

This paper takes a different approach to evaluating face-offs in ice hockey. Instead of looking at win percentages, the de facto measure of successful face-off takers for decades, focuses on the game events following the face-off and how directionality, clean wins, and player handedness play a significant role in creating value. This will demonstrate how not all face-off wins are made equal: some players consistently create post-face-off value through clean wins and by directing the puck to high-value areas of the ice. As a result, we propose an expected events face-off model as well as a wins above expected model that take into account the value added on a face-off by targeting the puck to specific areas on the ice in various contexts, as well as the impact this has on subsequent game events.

stat.AP↗

arXiv2018

Markov Decision Processes with Dynamic Transition Probabilities: An Analysis of Shooting Strategies in Basketball

In this paper we model basketball plays as episodes from team-specific non-stationary Markov decision processes (MDPs) with shot clock dependent transition probabilities. Bayesian hierarchical models are employed in the modeling and parametrization of the transition probabilities to borrow strength across players and through time. To enable computational feasibility, we combine lineup-specific MDPs into team-average MDPs using a novel transition weighting scheme. Specifically, we derive the dynamics of the team-average process such that the expected transition count for an arbitrary state-pair is equal to the weighted sum of the expected counts of the separate lineup-specific MDPs. We then utilize these non-stationary MDPs in the creation of a basketball play simulator with uncertainty propagated via posterior samples of the model components. After calibration, we simulate seasons both on-policy and under altered policies and explore the net changes in efficiency and production under the alternate policies. Additionally, we discuss the game-theoretic ramifications of testing alternative decision policies.

stat.AP↗

arXiv2018

Rao-Blackwellizing Field Goal Percentage

Shooting skill in the NBA is typically measured by field goal percentage (FG%) - the number of makes out of the total number of shots. Even more advanced metrics like true shooting percentage are calculated by counting each player's 2-point, 3-point, and free throw makes and misses, ignoring the spatiotemporal data now available (Kubatko et al. 2007). In this paper we aim to better characterize player shooting skill by introducing a new estimator based on post-shot release shot-make probabilities. Via the Rao-Blackwell theorem, we propose a shot-make probability model that conditions probability estimates on shot trajectory information, thereby reducing the variance of the new estimator relative to standard FG%. We obtain shooting information by using optical tracking data to estimate three factors for each shot: entry angle, shot depth, and left-right accuracy. Next we use these factors to model shot-make probabilities for all shots in the 2014-15 season, and use these probabilities to produce a Rao-Blackwellized FG% estimator (RB-FG%) for each player. We demonstrate that RB-FG% is better than raw FG% at predicting 3-point shooting and true-shooting percentages. Overall, we find that conditioning shot-make probabilities on spatial trajectory information stabilizes inference of FG%, creating the potential to estimate shooting statistics earlier in a season than was previously possible.

stat.AP↗

arXiv2018

Time Perception Machine: Temporal Point Processes for the When, Where and What of Activity Prediction

Numerous powerful point process models have been developed to understand temporal patterns in sequential data from fields such as health-care, electronic commerce, social networks, and natural disaster forecasting. In this paper, we develop novel models for learning the temporal distribution of human activities in streaming data (e.g., videos and person trajectories). We propose an integrated framework of neural networks and temporal point processes for predicting when the next activity will happen. Because point processes are limited to taking event frames as input, we propose a simple yet effective mechanism to extract features at frames of interest while also preserving the rich information in the remaining frames. We evaluate our model on two challenging datasets. The results show that our model outperforms traditional statistical point process approaches significantly, demonstrating its effectiveness in capturing the underlying temporal dynamics as well as the correlation within sequential activities. Furthermore, we also extend our model to a joint estimation framework for predicting the timing, spatial location, and category of the activity simultaneously, to answer the when, where, and what of activity prediction.

cs.CV↗

arXiv2018

A Bayesian Nonparametric Approach to Geographic Regression Discontinuity Designs: Do School Districts Affect NYC House Prices?

Most research on regression discontinuity designs (RDDs) has focused on univariate cases, where only those units with a "forcing" variable on one side of a threshold value receive a treatment. Geographical regression discontinuity designs (GeoRDDs) extend the RDD to multivariate settings with spatial forcing variables. We propose a framework for analysing GeoRDDs, which we implement using Gaussian process regression. This yields a Bayesian posterior distribution of the treatment effect at every point along the border. We address nuances of having a functional estimand defind on a border with potentially intricate topology, particularly when defining and estimating causal estimands of the local average treatment effect (LATE). The Bayesian estimate of the LATE can also be used as a test statistic in a hypothesis test with good frequentist properties, which we validate using simulations and placebo tests. We demonstrate our methodology with a dataset of property sales in New York City, to assess whether there is a discontinuity in housing prices at the border between two school district. We find a statistically significant difference in price across the border between the districts with $p$=0.002, and estimate a 20% higher price on average for a house on the more desirable side.

stat.AP↗

arXiv2017

Learning Person Trajectory Representations for Team Activity Analysis

Activity analysis in which multiple people interact across a large space is challenging due to the interplay of individual actions and collective group dynamics. We propose an end-to-end approach for learning person trajectory representations for group activity analysis. The learned representations encode rich spatio-temporal dependencies and capture useful motion patterns for recognizing individual events, as well as characteristic group dynamics that can be used to identify groups from their trajectories alone. We develop our deep learning approach in the context of team sports, which provide well-defined sets of events (e.g. pass, shot) and groups of people (teams). Analysis of events and team formations using NHL hockey and NBA basketball datasets demonstrate the generality of our approach.

cs.CV↗

arXiv2017

A Nonparametric Bayesian Methodology for Regression Discontinuity Designs

One of the most popular methodologies for estimating the average treatment effect at the threshold in a regression discontinuity design is local linear regression (LLR), which places larger weight on units closer to the threshold. We propose a Gaussian process regression methodology that acts as a Bayesian analog to LLR for regression discontinuity designs. Our methodology provides a flexible fit for treatment and control responses by placing a general prior on the mean response functions. Furthermore, unlike LLR, our methodology can incorporate uncertainty in how units are weighted when estimating the treatment effect. We prove our method is consistent in estimating the average treatment effect at the threshold. Furthermore, we find via simulation that our method exhibits promising coverage, interval length, and mean squared error properties compared to standard LLR and state-of-the-art LLR methodologies. Finally, we explore the performance of our method on a real-world example by studying the impact of being a first-round draft pick on the performance and playing time of basketball players in the National Basketball Association.

stat.ME↗

arXiv2016

Meta-Analytics: Tools for Understanding the Statistical Properties of Sports Metrics

In sports, there is a constant effort to improve metrics which assess player ability, but there has been almost no effort to quantify and compare existing metrics. Any individual making a management, coaching, or gambling decision is quickly overwhelmed with hundreds of statistics. We address this problem by proposing a set of "meta-metrics" which can be used to identify the metrics that provide the most unique, reliable, and useful information for decision-makers. Specifically, we develop methods to evalute metrics based on three criteria: 1) stability: does the metric measure the same thing over time 2) discrimination: does the metric differentiate between players and 3) independence: does the metric provide new information? Our methods are easy to implement and widely applicable so they should be of interest to the broader sports community. We demonstrate our methods in analyses of both NBA and NHL metrics. Our results indicate the most reliable metrics and highlight how they should be used by sports analysts. The meta-metrics also provide useful insights about how to best construct new metrics which provide independent and reliable information about athletes.

stat.AP↗

arXiv2016

Nonparametric hierarchical Bayesian quantiles

Here we develop a method for performing nonparametric Bayesian inference on quantiles. Relying on geometric measure theory and employing a Hausdorff base measure, we are able to specify meaningful priors for the quantile while treating the distribution of the data otherwise nonparametrically. We further extend the method to a hierarchical model for quantiles of subpopulations, linking subgroups together solely through their quantiles. Our approach is computationally straightforward, allowing for censored and noisy data. We demonstrate the proposed methodology on simulated data and an applied problem from sports statistics, where it is observed to stabilize and improve inference and prediction.

stat.ME↗

arXiv2016

Adjusting for Scorekeeper Bias in NBA Box Scores

Box score statistics in the National Basketball Association are used to measure and evaluate player performance. Some of these statistics are subjective in nature and since box score statistics are recorded by scorekeepers hired by the home team for each game, there exists potential for inconsistency and bias. These inconsistencies can have far reaching consequences, particularly with the rise in popularity of daily fantasy sports. Using box score data, we estimate models able to quantify both the bias and the generosity of each scorekeeper for two of the most subjective statistics: assists and blocks. We then use optical player tracking data for the 2014-2015 season to improve the assist model by including other contextual spatio-temporal variables such as time of possession, player locations, and distance traveled. From this model, we present results measuring the impact of the scorekeeper and of the other contextual variables on the probability of a pass being recorded as an assist. Results for adjusting season assist totals to remove scorekeeper influence are also presented.

stat.AP↗