Modelling player performance in basketball through mixed models

White men can't jump, but do they still get picked first? Race and player selection in the NBA draft, 1980-2021

Despite excelling at recruiting Black players, studies have repeatedly produced evidence of racial discrimination in the National Basketball Association (NBA). Through this study, we re-examine the topic of racial discrimination within the NBA through an analysis of the Association's annual entry draft. Using a novel dataset, we statistically model the relationship between player race and draft pick number using pooled data from 1980 to 2021. Overall, we find only limited evidence of racial discrimination. These findings are generally robust to sub-sample analyses, alternative specifications of our race variable, and alternate statistical modeling techniques. However, analyses performed on sub-samples of draft picks that participated in the NBA combine-and for whom we have measurements of player athleticism-produce some evidence of racial discrimination. Through such models we estimate that Black players are picked roughly three picks later in the draft. We consider the implications of these findings for contemporary theorizing about racial discrimination in the NBA and more mainstream labor markets.

Long-Term Trends in Shooting Performance in the NBA: An Analysis of Two- and Three-Point Shooting across 40 Consecutive Seasons

This study aims to depict two-point and three-point shooting trends and explore their influence on game outcomes in the NBA across 40 consecutive seasons. Therefore, the following game-related statistics were considered: total points per game (PPG), games played (GP), field goals made (FGM), field goal attempts (FGA), field goal percentage (FG%), two-point field goals made (2PM), two-point field goal attempts (2PA), two-point field goal percentage (2P%), three-point field goals made (3PM), three-point field goal attempts (3PA), three-point field goal percentage (3P%), and a three-point field goal to two-point field goal ratio (3P/2P). The fixed-base indexes and inter-decade ANOVAs or Friedman tests were used as the main statistical tools. The number of 3PA significantly increased over time, while the number of 2PA decreased. A significant increase in 3P% was also observed, whereas 2P% remained relatively stable over the analyzed period. This study also revealed a higher number of ball possessions and more points scored per game, especially in the last decade of NBA competition.

Bayesian GARCH modeling of functional sports data

The use of statistical methods in sport analytics has gained a rapidly growing interest over the last decade, and nowadays is common practice. In particular, the interest in understanding and predicting an athlete’s performance throughout his/her career is motivated by the need to evaluate the efficacy of training programs, anticipate fatigue to prevent injuries and detect unexpected of disproportionate increases in performance that might be indicative of doping. Moreover, fast evolving data gathering technologies require up to date modelling techniques that adapt to the distinctive features of sports data. In this work, we propose a hierarchical Bayesian model for describing and predicting the evolution of performance over time for shot put athletes. We rely both on a smooth functional contribution and on a linear mixed effect model with heteroskedastic errors to represent the athlete-specific trajectories. The resulting model provides an accurate description of the performance trajectories and helps specifying both the intra- and inter-seasonal variability of measurements. Further, the model allows for the prediction of athletes’ performance in future sport seasons. We apply our model to an extensive real world data set on performance data of professional shot put athletes recorded at elite competitions.

The underpinning factors of NBA game-play performance: a systematic review (2001-2020)

OBJECTIVE

Recognizing the high stakes associated with winning and losing in the National Basketball Association (NBA), a deep understanding of the underlying mechanisms of NBA game-play performance would provide substantial benefit to all stakeholders involved with preparing NBA players and teams for competitive success. To the best of the authors' knowledge, this systematic review presents the first attempt to systematically amalgamate and appraise the scientific literature published in the XXI Century, following a constraints-led approach (CLA). In particular, two underpinning factors of NBA game-play performance were investigated: (1) NBA player constraints (internal variables) and (2) NBA contextual constraints (external variables).

METHODS

Databases included PubMed (MEDLINE), Web of Science (WOS), ResearchGate, SPORTDiscus, SCOPUS, Google Scholar, and the World Association of Basketball Coaches' database (WABC). This review followed the Preferred Reporting Items for Systematic Review and Meta-Analyses (PRISMA) model and the Population, Intervention, Comparison and Outcomes (PICOS) guidelines.

RESULTS

Ultimately, 43 articles met the inclusion criteria (n = 43). Promisingly, the vast majority of studies were published in recent years (>2016; n = 28; 65.1%). Topics related to 'contextual constraints' (n = 25; 58.1%) received more attention than topics related to 'player constraints' (n = 18; 41.9%). Even though the importance of longitudinal-interventional approaches to applied sports science is well-documented, descriptive-observational research emerged as the most popular method of choice (n = 27; 62.8%); interventional studies were absent; and near all researchers merely utilized secondary data sources (n = 37; 86.0%).

CONCLUSIONS

Taking into account the total body of evidence (2001-2020), NBA practitioners may use this systematic review as a baseline reference to enrich their current knowledge about the nature, demands, and dynamics of the modern-day NBA ecosystem. Finally, adoption of an 'Applied Science Research Framework' is encouraged, fostering clearly outlined project incentives; standardizing taxonomies; sequencing follow-up studies; embracing holistic and cross-disciplinary viewpoints; and integrating longitudinal-interventional projects to increase the reproducibility of their findings.

Bounded Rationality and Heuristics: Do We Only Need to Score in Order to Win Individual Awards in Basketball?

In the game of basketball game-related statistics are utilised to help decision makers to evaluate players’ achievements. Previous research showed that in the case of individual awards, points are preferred over other indicators of effectiveness. Based on recent studies and following Simon’s bounded rationality, in our interpretation, decision-makers decide on nominations at the post-grant level according to points scoring which is the easiest aspect to assess and the most familiar to them. In this context we also hypothesise that youth all-star players have better overall performance than their not selected teammates. To test our hypotheses we selected all of the youth awarded male players and their teammates from 2004 to 2019. In our sample, we examined n = 3198 player statistics. Two groups were created with nominated and not selected players. We used a two-sample t-test, and correlation matrix to examine the relationship between the variables (p < 0.001). We found that scoring is the most important selection criteria for decision-makers (r = 0.605; p = 0.000) and the selected players had significantly better individual statistics. An important finding of our study is that although efficiency (EFF) is used to measure the players’ contribution to the game, it is not the primary selection factor and should therefore be redefined.

Regression Tree Model for Predicting Game Scores for the Golden State Warriors in the National Basketball Association

Data mining is becoming increasingly used in sports. Sport data analyses help fans to understand games and teams’ results. Information provided by such analyses is useful for game lovers. Specifically, the information can help fans to predict which team will win a game. Many scholars have devoted attention to predicting the results of various sporting events. In addition to predicting wins and losses, scholars have explored team scores. Most studies on score prediction have used linear regression models to predict the scores of ball games; nevertheless, studies have yet to use regression tree models to predict basketball scores. Therefore, the present study analyzed game data of the Golden State Warriors and their opponents in the 2017–2018 season of the National Basketball Association (NBA). Strong and weak symmetry requirements were identified for each team. We developed a regression tree model for score prediction. After predicting the scores of each player on two teams, we summed and compared the predicted total scores to obtain the predicted results (lose or win) of the team of interest. The results of this study revealed that the regression tree model can effectively predict the score of each player and the total score of the team. The model achieved a predictive accuracy of 87.5%.

Game-Related Performance Factors in four European Men's Professional Volleyball Championships

The present study was designed to assess the relevance of game-related performance factors as outcome predictors in high-level volleyball. To carry out the analysis, the official box scores of 399 matches played by 47 different teams in four different European male professional volleyball leagues (Italy, Poland, Germany and Turkey) during the 2013-14 regular season were analyzed. A logistic mixed model was performed to determine the effects of different variables in matches’ outcomes. According to the multivariate analysis the following factors were significantly associated with winning matches: the number of scorers (OR = 1.32; CI: 1.09 – 1.59), service errors (OR = 0.91; CI: 0.87 – 0.95), service points (OR = 1.25; CI: 1.15 -1.36), reception errors (OR = 0.79; CI: 0.74 – 0.84), the percentage of positive receptions (OR = 1.02; CI: 1.00 -1.04) and blocked balls (OR = 1.17; CI: 1.11 – 1.26). Team category 2 (OR = 0.39; CI: 0.24 – 0.63) and team category 3 (OR = 0.15; CI: 0.09 – 0.25) were significantly associated with losing matches. These findings can contribute to a better understanding of performance indicators in professional volleyball, helping coaches and decision makers to better determine the importance of particular game factors.