2026 SPECIAL EDITION: Featuring the Winning Team from the 2026 Wharton High School Data Science Competition

AUTHORS

Authors: Zach Zaslow, Lucas Greenwald, Max Li, Riley Wong, Aaron Wu, The Pingry School, Basking Ridge, NJ
Advisor: Mr. Bradford Poprik, The Pingry School, Basking Ridge, NJ

ABSTRACT

Traditional hockey stats such as win-loss record and raw goal differential fail to account for opponent strength, shot quality, and game state context, leading to systematically flawed team evaluations and rankings. We developed an analytical pipeline that used Bayesian mixed-effects modeling and Monte Carlo simulation to identify true team strength and predict tournament outcomes for the World Hockey League. In stage one of our model, we fit a Bayesian mixed-effects model on log expected goals per minute with team and opponent random effects estimated separately for even-strength, power-play, and penalty-kill phases and home/away settings. These estimates were back-transformed and converted into true expected goal differential per 60 for each phase, weighted by the distribution of each team’s actual ice time in each phase and converted to composite zscores.

We also studied how offensive line disparity impacts team performance by isolating the first offensive line’s and second offensive line’s performances and creating a ratio. In stage two, we generated win probabilities for each of the first-round tournament matchups. We used individual team penalty data to estimate the time spent in each phase, and then used the geometric mean of offense and defense to estimate scoring rates in each phase. This data was then run through 30,000 Monte Carlo simulations per matchup to produce our win probabilities. The model substantially reorders the standings: Mexico rises from 19th in points to 4th in true strength, while the Netherlands drops from 2nd to 7th. Offensive line disparity showed no relationship with team strength (r ≈ 0, p = 0.955), suggesting top-heavy offenses are not a competitive disadvantage.