arXiv subjects

Scott Powers

Publications and source records attributed to Scott Powers.

8 recordsLinked to original sources

arXiv2026

Strategies under a pickoff limit in baseball: A zero-sum sequential game with multilevel models

Recently, Major League Baseball (MLB) limited pitchers to three pickoff attempts, creating a cat-and-mouse game between pitcher and runner. Each failed attempt adds pressure on the pitcher to avoid using another, and the runner can intensify this pressure by extending their leadoff toward the next base. We model this dynamic as a two-player zero-sum sequential game in which the runner first chooses a lead distance, and then the pitcher chooses whether to attempt a pickoff. We establish optimality characterizations for the game and present variants of value iteration and policy iteration to solve the game. Using high-resolution lead distance data from optical player tracking, we estimate generalized linear mixed-effects models for pickoff and stolen base outcome probabilities given lead distance, context, and player skill. We compute the game-theoretic equilibria under the two-player model, as well as the optimal runner policy under a simplified one-player Markov decision process (MDP) model. In the one-player setting, our results establish an actionable rule of thumb: the Two-Foot Rule, which recommends that a runner increase their lead by two feet after each pickoff attempt.

math.OC↗

arXiv2025

Swinging, Fast and Slow: Interpreting variation in baseball swing tracking metrics

In 2024, Major League Baseball released new bat tracking data, reporting swing-by-swing bat speed and swing length measured at the point of contact. While exciting, the data present challenges for their interpretation. The timing of the batter's swing relative to the pitch determines the point of measurement relative to the full swing path. The relationship between swing metrics and swing outcomes is confounded by the batter's pitch recognition. We introduce a framework for interpreting bat tracking data in which we first estimate the batter's intention conditional on ball-strike count and pitch location using a Bayesian hierarchical skew-normal model with random intercept and random slopes for batter. This yields batter-specific effects of count on swing metrics, which we leverage via instrumental variables regression to estimate causal effects of bat speed and swing length on contact and power outcomes. Finally, we valuate the tradeoff between contact and power due to bat speed by modeling a plate appearance as a Markov chain. We conclude that batters can reduce their strikeout rate by reducing bat speed as strikes increase, but the tradeoff in reduced power approximately counteracts the benefit to the average batter.

stat.AP↗

arXiv2025

Ball path curvature and in-game free throw shooting proficiency in the National Basketball Association

Basketball shooting coaches agree that smoother shooting motions are better, but there is less agreement about what "smooth" means quantitatively or what part of the shooting motion needs to be smooth. Using ball tracking data from the 2023-2024 National Basketball Association regular season, we explore the relationship between ball path curvature and free throw shooting performance. We fit B\'ezier curves to the ball tracking data in the sagittal plane and test different methods of calculating path curvature. We find that both max curvature and terminal curvature are negatively associated with shooting performance, but terminal curvature explains much more of the between-player variance in free throw shooting performance. This suggests that shooting coaches would be better off focusing on the smoothness at the end of the shot rather than at the beginning of the forward motion of the ball.

physics.soc-ph↗

arXiv2024

Estimating individual contributions to team success in women's college volleyball

The progression of a single point in volleyball starts with a serve and then alternates between teams, each team allowed up to three contacts with the ball. Using charted data from the 2022 NCAA Division I women's volleyball season (4,147 matches, 600,000+ points, more than 5 million recorded contacts), we model the progression of a point as a Markov chain with the state space defined by the sequence of contacts in the current volley. We estimate the probability of each team winning the point, which changes on each contact. We attribute changes in point probability to the player(s) responsible for each contact, facilitating measurement of performance on the point scale for different skills. Traditional volleyball statistics do not allow apples-to-apples comparisons across skills, and they do not measure the impact of the performances on team success. For adversarial contacts (serve/receive and attack/block/dig), we estimate a hierarchical linear model for the outcome, with random effects for the players involved; and we adjust performance for strength of schedule not only on the conference/team level but on the individual player level. We can use the results to answer practical questions for volleyball coaches.

stat.AP↗

arXiv2017

Some methods for heterogeneous treatment effect estimation in high-dimensions

When devising a course of treatment for a patient, doctors often have little quantitative evidence on which to base their decisions, beyond their medical education and published clinical trials. Stanford Health Care alone has millions of electronic medical records (EMRs) that are only just recently being leveraged to inform better treatment recommendations. These data present a unique challenge because they are high-dimensional and observational. Our goal is to make personalized treatment recommendations based on the outcomes for past patients similar to a new patient. We propose and analyze three methods for estimating heterogeneous treatment effects using observational data. Our methods perform well in simulations using a wide variety of treatment effect functions, and we present results of applying the two most promising methods to data from The SPRINT Data Analysis Challenge, from a large randomized trial of a treatment for high blood pressure.

stat.ML↗

arXiv2017

Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball

We propose the nuclear norm penalty as an alternative to the ridge penalty for regularized multinomial regression. This convex relaxation of reduced-rank multinomial regression has the advantage of leveraging underlying structure among the response categories to make better predictions. We apply our method, nuclear penalized multinomial regression (NPMR), to Major League Baseball play-by-play data to predict outcome probabilities based on batter-pitcher matchups. The interpretation of the results meshes well with subject-area expertise and also suggests a novel understanding of what differentiates players.

stat.ML↗

arXiv2016

Customized training with an application to mass spectrometric imaging of cancer tissue

We introduce a simple, interpretable strategy for making predictions on test data when the features of the test data are available at the time of model fitting. Our proposal - customized training - clusters the data to find training points close to each test point and then fits an $\ell_1$-regularized model (lasso) separately in each training cluster. This approach combines the local adaptivity of $k$-nearest neighbors with the interpretability of the lasso. Although we use the lasso for the model fitting, any supervised learning method can be applied to the customized training sets. We apply the method to a mass-spectrometric imaging data set from an ongoing collaboration in gastric cancer detection which demonstrates the power and interpretability of the technique. Our idea is simple but potentially useful in situations where the data have some underlying structure.

stat.AP↗

arXiv2009

Mutually-Antagonistic Interactions in Baseball Networks

We formulate the head-to-head matchups between Major League Baseball pitchers and batters from 1954 to 2008 as a bipartite network of mutually-antagonistic interactions. We consider both the full network and single-season networks, which exhibit interesting structural changes over time. We find interesting structure in the network and examine their sensitivity to baseball's rule changes. We then study a biased random walk on the matchup networks as a simple and transparent way to compare the performance of players who competed under different conditions and to include information about which particular players a given player has faced. We find that a player's position in the network does not correlate with his success in the random walker ranking but instead has a substantial effect on its sensitivity to changes in his own aggregate performance.

physics.data-an↗