arXiv subjects

Stephanie Kovalchik

Publications and source records attributed to Stephanie Kovalchik.

3 recordsLinked to original sources

arXiv2026

Stated, Realized, and Optimal Aiming Strategies for the Tennis Serve: Experimental Evidence from Collegiate Athletes

We study where, within a chosen Wide or T region, a tennis player should aim a serve. Aiming near a service-box boundary makes a serve harder to return but raises the probability of a fault, creating a trade-off that depends on the player's execution error. Ordinary match data provide limited information about execution error because players' intended targets are unobserved. We therefore conducted an experiment with members of the Brigham Young University men's tennis team. Each player identified targets they believed to be optimal, which we marked on the court. Players then served repeatedly toward each target while we recorded precise bounce locations. From these data, we estimate player-specific serve distributions while accounting for serves censored by net contact, then combine them with an estimated point-win reward surface in a Bayesian, two-period Markov decision process with a continuous spatial action space. We find that the estimated optimal second-serve target is more conservative than its first-serve counterpart in every player-region combination, consistent with prior theory. Also, while players' stated targets were generally more aggressive than optimal, their realized serve centers were more conservative than those targets and markedly closer to the estimated optima.

stat.AP↗

arXiv2021

A Markov process approach to untangling intention versus execution in tennis

Value functions are used in sports applications to determine the optimal action players should employ. However, most literature implicitly assumes that the player can perform the prescribed action with known and fixed probability of success. The effect of varying this probability or, equivalently, "execution error" in implementing an action (e.g., hitting a tennis ball to a specific location on the court) on the design of optimal strategies, has received limited attention. In this paper, we develop a novel modeling framework based on Markov reward processes and Markov decision processes to investigate how execution error impacts a player's value function and strategy in tennis. We power our models with hundreds of millions of simulated tennis shots with 3D ball and 2D player tracking data. We find that optimal shot selection strategies in tennis become more conservative as execution error grows, and that having perfect execution with the empirical shot selection strategy is roughly equivalent to choosing one or two optimal shots with average execution error. We find that execution error on backhand shots is more costly than on forehand shots, and that optimal shot selection on a serve return is more valuable than on any other shot, over all values of execution error.

math.OC↗

arXiv2020

Space-Time VON CRAMM: Evaluating Decision-Making in Tennis with Variational generatiON of Complete Resolution Arcs via Mixture Modeling

Sports tracking data are the high-resolution spatiotemporal observations of a competitive event. The growing collection of these data in professional sport allows us to address a fundamental problem of modern sport: how to attribute value to individual actions? Taking advantage of the smoothness of ball and player movement in tennis, we present a functional data framework for estimating expected shot value (ESV) in continuous time. Our approach is a three-step recipe: 1) a generative model for a full-resolution functional representation of ball and player trajectories using an infinite Bayesian Gaussian mixture model (GMM), 2) conditioning of the GMM on observed positional data, and 3) the prediction of shot outcomes given the functional encoding of a shot event. From the ESV we derive three metrics of central interest: value added with shot taking (VAST), Shot IQ, and value added with court coverage (VACC), which respectively attribute value to shot execution, shot selection and movement around the court. We rate player performance at the 2019 US Open on these advanced metrics and show how each adds a novel perspective to performance evaluation in tennis that goes beyond simple counts of outcomes by quantitatively assessing the decisions players make throughout a point.

stat.AP↗