Do Behavioral Considerations Cloud Penalty-Kick Location Optimization in Professional Soccer? Classical/Statistical Game Theory & Empirical Testing using Polynomial and ML Regularized Lasso Regression

For penalty kicks in soccer, the classical and statistical game-theoretic models developed herein predict a non-negative relationship between goal area partition-conditional shot-volume and conversion-rate for a goal-optimizing penalty kick taker in soccer. However, we find a strong negative relationship between goal area partition subsets of the study data, which considers 536 penalty kicks from the 2020 UEFA Champions and Europa Leagues. The estimated indifference sets and underlying inferential statistics of linear, polynomial, and ML-regularized Lasso regression models indicate that penalty-takers (significantly) value both conversion-rate and on-target rate when locating PK-shots. While partial optimizers, PK-takers in soccer deviate from optimal PK-locating strategies in a manner consistent with the behavioral valuation of keeping up appearances of highly-skilled play, in this case by limiting the likelihood of missing the goal entirely, as might a novice player. That is, players are revealed to value the optics of performance rather than strictly performance optimization. The result is consistent with stated and revealed aversion to underhanded free-throw shooting among large-handed NBA and EuroLeague Centers despite evidence of performance benefits for this group. The result is also consistent with evidence that corner three-point shooters are twice as likely to hit the front of the rim as compared to the side of the backboard. The optics of the latter causes players to bias their shot and decrease the overall conversion rate. Optimization utility is estimated to be 3.12 times as important to the representative PK-taker on the margin as is behavioral utility. The models are highly-explanatory, indicating that optimization and behavioral factors explain approximately 85.2% of PK-shot locating variation for top professional players. The negative estimated slope of the indifference sets provides visual evidence that players are revealed to value both conversion-rate and on-target rate. They trade-off between these interests when selecting penalty-shot locations. We conclude strong statistical evidence that suggests penalty-takers represent hybrid decision-makers: part rational-optimizers and part behavioral-agents seeking to keep up appearances of highly-skilled play. Our polynomial regression also suggests that PK-takers are risk averse, as their partition-dependent shot-volume increases at a decreasing rate in conversion-rate. As the purpose of a PK-attempt is to maximize expected goal (likelihood) directly, the presence of risk-aversion here represents another behavioral factor on the part of the PK-taker.

Shane Sanders is Professor of Economics & Sport Analytics at Syracuse University. He conducts research in the areas of player performance analytics with emphasis on team and player (sub-)optimization. He also studies issues of player valuation and league design. Sanders has consulted on basketball roster construction for teams in the EuroLeague and NCAA and has advised NBA teams on cross-league player projections. Sanders 88 academic journal articles, many in top journals of economics, statistics, finance, and sport (J of Business & Economic Statistics, J of Behavioral & Experimental Finance, Economics Letters, J of Sport Management, J of Sports Economics, Social Indicators Research, and J of Quantitative Analysis in Sport among them). His research has been supported by research grants from FIFA, PARCC, and the Mercatus Center Policy Analytics Program. Sanders’ research has been cited in a U.S. Supreme Court sport antitrust case (American Needle, Inc. v NFL), as well as in leading media outlets such as USA Today, NPR Here and Now, MSNBC, Globe and Mail, Fox Sports, TrueHoop, and The Late Show with Stephen Colbert. Last year, Sanders was a Research Finalist at MIT SSAC for his joint work (with Justin Ehrlich) on NBA advanced shot charts and the increasing 3PA dispremium in the League. He also also presented his work at Carnegie Mellon Sport Analytics Conference, the Harvard New England Symposium on Statistics in Sport, and the SABR Analytics Conference. Institution page: https://falk.syr.edu/people/sandersshane/

Ava Uribe is a current senior Sport Management and Sport Analytics student at Syracuse University. Uribe recently completed her second season with the Syracuse University Women’s Soccer team, and in her youth career has represented the U.S. Youth National Team from Under-14 to Under-18. With the U.S National Team, she competed internationally in tournaments such as the UEFA competition in England as well as international friendlies across Europe. She aspires to play professionally post-graduation and has focused her academic and athletic experiences on performance analysis in a variety of sports, especially soccer. As a primary penalty kick taker for the Syracuse Orange, Uribe developed a research interest in penalty kick trends at the professional level, particularly as major international tournaments increasingly see matches decided by shootouts. Her analysis has provided valuable insights into goal conversion strategies, which she has shared with her coaches and teammates to enhance performance in the highly competitive ACC. Syracuse University player page: https://cuse.com/sports/womens-soccer/roster/Ava-Uribe/24409

Dr. Justin Ehrlich is an Associate Professor in Sports Management at Syracuse University, specializing in sport analytics, machine learning, and computer science. His diverse research portfolio spans virtual reality, 3D human pose estimation, advanced visualization, sports rating and ranking, the business of sport, risk analysis for CTE in football players, and biomechanical assessment. As a faculty member in Syracuse University's Big Data Cluster, Dr. Ehrlich focuses on big data applications, performance analytics, and advanced visualization tools such as shot charts.His innovative work has been showcased at the MIT Sloan Sports Analytics Conference and published in journals including the Journal of Behavioral & Experimental Finance, JAMA, Public Choice, and PLOS ONE. Dr. Ehrlich has also conducted extensive golf research in collaboration with the University of Nevada, Las Vegas, exploring topics like the effects of weather on performance, optimizations in swing sequencing, and the impact of swing consistency on course outcomes. Institution page: https://falk.syr.edu/people/ehrlich-justin/