arXiv subjects

Bailey Fosdick

Publications and source records attributed to Bailey Fosdick.

4 recordsLinked to original sources

arXiv2024

Expected Points Above Average: A Novel NBA Player Metric Based on Bayesian Hierarchical Modeling

In this paper, we propose two novel basketball metrics: ``expected points'' for team-based comparisons and ``expected points above average (EPAA)'' as a player-evaluation tool. Established within the Bayesian hierarchical model framework, teams and players are clustered based on their shooting propensities and abilities using posterior predictive distributions. We illustrate the concepts for the top 100 shot takers over the last decade and offer our metric as an additional metric for evaluating players. We compare our metrics to two traditional NBA player evaluation metrics: player efficiency rating and box plus/minus. Finally, we develop a Shiny web application that allows interested readers to make additional team and player comparisons.

stat.OT↗

arXiv2020

The causal effect of a timeout at stopping an opposing run in the NBA

In the summer of 2017, the National Basketball Association reduced the number of total timeouts, along with other rule changes, to regulate the flow of the game. With these rule changes, it becomes increasingly important for coaches to effectively manage their timeouts. Understanding the utility of a timeout under various game scenarios, e.g., during an opposing team's run, is of the utmost importance. There are two schools of thought when the opposition is on a run: (1) call a timeout and allow your team to rest and regroup, or (2) save a timeout and hope your team can make corrections during play. This paper investigates the credence of these tenets using the Rubin causal model framework to quantify the causal effect of a timeout in the presence of an opposing team's run. Too often overlooked, we carefully consider the stable unit-treatment-value assumption (SUTVA) in this context and use SUTVA to motivate our definition of units. To measure the effect of a timeout, we introduce a novel, interpretable outcome based on the score difference to describe broad changes in the scoring dynamics. This outcome is well-suited for situations where the quantity of interest fluctuates frequently, a commonality in many sports analytics applications. We conclude from our analysis that while comebacks frequently occur after a run, it is slightly disadvantageous to call a timeout during a run by the opposing team and further demonstrate that the magnitude of this effect varies by franchise.

stat.AP↗

arXiv2015

Women 1.5 Times More Likely to Leave STEM Pipeline After Calculus Compared to Men: Lack of Mathematical Confidence a Potential Culprit

The substantial gender gap in the science, technology, engineering, and mathematics (STEM) workforce can be traced back to the underrepresentation of women at various milestones in the career pathway. Calculus is a necessary step in this pathway and has been shown to often dissuade people from pursuing STEM fields. We examine the characteristics of students who begin college interested in STEM and either persist or switch out of the calculus sequence after taking Calculus I, and hence either continue to pursue a STEM major or are dissuaded from STEM disciplines. The data come from a unique, national survey focused on mainstream college calculus. Our analyses show that, while controlling for academic preparedness, career intentions, and instruction, the odds of a woman being dissuaded from continuing in calculus is 1.5 times greater than that for a man. Furthermore, women report they do not understand the course material well enough to continue significantly more often than men. When comparing women and men with above-average mathematical abilities and preparedness, we find women start and end the term with significantly lower mathematical confidence than men. This suggests a lack of mathematical confidence, rather than a lack of mathematically ability, may be responsible for the high departure rate of women. While it would be ideal to increase interest and participation of women in STEM at all stages of their careers, our findings indicate that simply increasing the retention of women starting in college calculus would almost double the number of women entering the STEM workforce.

math.HO↗

arXiv2012

Likelihoods for fixed rank nomination networks

Many studies that gather social network data use survey methods that lead to censored, missing or otherwise incomplete information. For example, the popular fixed rank nomination (FRN) scheme, often used in studies of schools and businesses, asks study participants to nominate and rank at most a small number of contacts or friends, leaving the existence other relations uncertain. However, most statistical models are formulated in terms of completely observed binary networks. Statistical analyses of FRN data with such models ignore the censored and ranked nature of the data and could potentially result in misleading statistical inference. To investigate this possibility, we compare parameter estimates obtained from a likelihood for complete binary networks to those from a likelihood that is derived from the FRN scheme, and therefore recognizes the ranked and censored nature of the data. We show analytically and via simulation that the binary likelihood can provide misleading inference, at least for certain model parameters that relate network ties to characteristics of individuals and pairs of individuals. We also compare these different likelihoods in a data analysis of several adolescent social networks. For some of these networks, the parameter estimates from the binary and FRN likelihoods lead to different conclusions, indicating the importance of analyzing FRN data with a method that accounts for the FRN survey design.

stat.ME↗