Volume 20, Issue 3

Plus-minus is a widely used performance metric in sports. Players with high plus-minus ratings are often considered more efficient than others. While numerous plus-minus models have emerged since the introduction of adjusted plus-minus in 2004, most of these metrics focus on evaluating player performance at the individual level. In the present study, we follow the plus-minus framework and adopt a hierarchical Bayesian linear model to estimate plus-minus at the position level in the NBA from 2015–16 to 2021–22. Results show that players with versatile offensive skills and big players who defend the paint area are the most valuable offensive and defensive contributors respectively. We also find that the gaps in offensive plus-minus between offensive position groups have decreased over time. Overall, our analysis offers valuable information regarding average positional values in the NBA, allowing more objective player comparisons within position groups. We also show improved prediction accuracy in player plus-minus when factoring in player positions.

The COVID-19 pandemic has led to a global shutdown of sporting activities. While professional sports competitions restarted in mid-2020, spectators were usually not allowed. This paper investigates the effect of absent fans and reduced social pressure on performance in professional darts – a setting where individual player performances can be well observed. Considering almost five years of tournament data, we use Bayesian multilevel models to investigate potential heterogeneity across players concerning reduced social pressure. For our analysis, we consider the two main performance measures in darts: the three-dart average and the checkout performance. Our results indicate that the effect of reduced social pressure on performance varies substantially across players. We further find experienced players to be less affected by social pressure compared to relatively inexperienced players.

Special teams (i.e. power play and penalty kill) situations play an outsized role in determining the outcome of ice hockey games. Yet, quantitative methods for characterizing special teams tactics are limited. This work focuses on team structure and player deployment during in-zone special teams possessions. Leveraging player and puck tracking data from the National Hockey League (NHL), a framework is developed for describing player positioning during 5-on-4 power play and 4-on-5 penalty kill possessions. More specifically, player roles are defined directly from the player tracking data using non-negative matrix factorization, and every player is allocated a unique role at every frame of tracking data by solving a linear assignment problem. Team formations naturally arise through the combination of roles occupied in a frame. Roles that vary on a per-frame basis allow for a fine-grained analysis of team structure. This property of the roles-based representation is used to group together similar power play possessions using latent Dirichlet allocation, a topic modelling technique. The concept of assignments, which remain constant over an entire possession, is also introduced. Assignments provide a more stable measure of player positioning, which may be preferable when assessing deployment over longer periods of time.

Prior clustering approaches of soccer players have employed a variety of methods based on various data categories, but none of them have focused on clustering by career paths characterized through a time series analysis of yearly performance quality. Therefore, this study aims to propose a methodology how a career path can be represented as a time series of a player’s seasonal qualities and then be clustered with players that have a similar career path. The underlying data focuses on soccer players from the five largest European soccer nations (Big-5). This allows for the identification of different types of career paths of players and the investigation of significant disparities between career paths among the Big-5 nations. In line with our proposed methodological approach, we identified and interpreted 13 different clusters of player career paths. These range from the cluster with the highest player quality scores to the pattern comprising players with the weakest scores. Further, the detected clusters show significant differences regarding variables of soccer players’ early career phase in adolescence (e.g., age of debut in professional soccer, years spent in a youth academy). The presented approach might represent a first step for stakeholders in soccer to get an objective insight in players’ career by utilizing mainly freely available data sources.

The tournament rules for long jump competitions have changed in recent years. Today, only the three athletes with the best jumps from the five initial attempts are qualified to make an additional sixth jump – a format called The Final Three. In the first implemented version of The Final Three, the top athletes sequentially make one final jump, starting with the athlete ranked third place from the initial attempts. The athlete with the longest jump in this sixth attempt wins the competition, irrespective of achieved results in previous attempts. In this study, we analyze the effect of the athletes’ jump order on the probability of winning the competition within this first implemented version of The Final Three. We derive the final’s symmetric subgame perfect equilibrium and compute the corresponding equilibrium winning probabilities, given estimated distributional parameters from the Olympic long jumping final in Tokyo 2021. The modeling of the game is preceded by a development of a stochastic model for the outcome in long jumping. Our results indicate a last mover advantage, albeit small. Our model also reveals the importance of having a low variation in the approach run length and thinking strategically in this tournament format.