Spatial analyses of basketball shot charts: An application to Michael Jordan's 2001-2002 NBA season
Abstract
Michael Jordan, one of the greatest sports celebrities of modern times, returned to the game of professional basketball during the 2001-2002 season. Sports commentators suggest that Jordan settles for jump shots instead of penetrating the defense for a lay-up. We utilize spatial point process methods to determine patterns in his shot selection, i.e., where he is most likely to shoot the basketball and/or make the shot. Data were obtained from "shot charts" or maps of the location of each shot taken. Non-parametric kernel smoothing methods allow us to estimate the spatial intensity function of made and missed shots and we compare these intensity functions for each game Jordan played. Michael Jordan's shooting patterns suggest fairly consistent results throughout the season with areas of better performance (probability of making a shot) on the left side of the court (from the baseline to the free throw line) and around the right portion of the free throw line. Areas of poor performance appear in the lane (between the goal and foul line), on the right side of the court (from the baseline to the free throw line) and around the three point arc. Furthermore, he is more likely to make lay-ups/slam dunks and shots 14-18 feet from the goal and miss shots within 1-9 and beyond 20 feet from the goal (including three point shots). This statistical analysis provides insight into Jordan's shooting patterns, the variation in such patterns across games, and illustrates a tool for the analysis of "shot chart" data in general.
... Another commonly employed rating is known as Player Efficiency Rating, which was developed by John Hollinger (4). Hollinger claims thats "PER sums up all a player's positive accomplishments, 1 In this paper, we define a field goal as a basket scored on any shot or tap other than a free throw, layup, or dunk. 2 We verified this assumption empirically by observing the shot success percentage curves for the entire NBA. ...
... Previous studies have done similar work that quantify shooting and offensive ability using spatial data. The first such study analyzed the performance of Michael Jordan (1). Their model considered each shot chart as an instance of some Poisson process and estimated the corresponding nonparametric functions relating to each event. ...
We propose two new measures for evaluating offensive ability of NBA players, using one-dimensional shooting data from three seasons beginning with the 2004-05 season. These measures improve upon currently employed shooting statistics by accounting for the varying shooting patterns of players over different distances from the basket. This variance also provides us with an intuitive metric for clustering players, wherein performance of players is calculated and compared to his cluster center as a baseline. To further improve the accuracy of our measures, we develop our own variation of smoothing and shrinkage, reducing any small sample biases and abnormalities.
The first measure, SCAB or, Scoring Ability Above Baseline, measures a player's ability to score as a function of time on court. The second metric, SHTAB or Shooting Ability, calculates a player's propensity to score on a per-shot basis. Our results show that a combination of SCAB and SHTAB can be used to separate out players based on their offensive game. We observe that players who are highly ranked according to our measures are regularly considered as top performers on offense by experts, with the notable exception of LeBron James; the same claim holds for the offensive dregs. We suggest possible explanations for our findings and explore possibilities of future work with regard to player defense.
... The quest to understand basketball shooting behaviors through spatial analysis dates back to the 1940s. Research on this topic [21,39], however, was scattered, until Goldsberry's CourtVision technique paper [18] popularized the technology in both academia and industry, with his signature shot map paving the way for basketball spatial analytics. Ensuing research has emphasized developing and improving models [6,22,23,32] to either reduce dimension or provide estimations/evaluations. ...
Data visualization has the power to revolutionize sports. For example, the rise of shot maps has changed basketball strategy by visually illustrating where “good/bad” shots are taken from. As a result, professional basketball teams today take shots from very different positions on the court than they did 20 years ago. Although the shot map has transformed many facets of the game, there is still much room for improvement to support richer and more complex analytical tasks. More specifically, we believe that the lack of sufficient interactivity to support various analytical queries and the inability to visually compare differences across situations are significant limitations of current shot maps. To address these limitations and showcase new possibilities, we designed and developed HoopInSight, an interactive visualization system that centers around a novel spatial comparison visual technique, enhancing the capabilities of shot maps in basketball analytics. This article presents the system, with a focus on our proposed visual technique and its accompanying interactions, all designed to promote comparison of two different scenarios. Furthermore, we provide reflections on and a discussion of relevant issues, including considerations for designing spatial comparison techniques, the scalability and transferability of this approach, and the benefits and pitfalls of designing as domain experts.
... In any case, other researchers have also reached conclusions on the impact of field goal efficiency on the final score in women's basketball (Gómez et al., 2006;Čižauskas, 2007, 2010;Leicht et al., 2017), as well as the efficiency of free throws (Gómez et al., 2006;Milanović et al., 2016;Nakić, 2004). At the same time, FG% or its variants are one of the most commonly used measurements in basketball when assessing offensive capability (Hickson and Waller, 2003;Piette et al., 2010), and, in all collective sports, shot precision is an indicator of the highest level of competence and a guarantee for achieving great results in sports (Milanović et al., 2016). Studies have shown that FG% is a key factor of team success for young female basketball players as well (Koh et al., 2012). ...
Evaluation in women's basketball is keeping up with developments in evaluation in men’s basketball, and although the number of studies in women's basketball has seen a positive trend in the past decade, it is still at a low level. This paper observed 38 games and sixteen variables of standard efficiency during the FIBA EuroBasket Women 2019. Two regression models were obtained, a set of relative percentage and relative rating variables, which are used in the NBA league, where the dependent variable was the number of points scored. The obtained results show that in the first model, the difference between winning and losing teams was made by three variables: true shooting percentage, turnover percentage of inefficiency and efficiency percentage of defensive rebounds, which explain 97.3%, while for the second model, the distinguishing variables was offensive efficiency, explaining for 96.1% of the observed phenomenon. There is a continuity of the obtained results with the previous championship, played in 2017. Of all the technical elements of basketball, it is still the shots made, assists and defensive rebounds that have the most significant impact on the final score in European women’s basketball. It can be noted that, unlike with the previous championship, inside play is no longer dominant, but there is a balance between inside and outside play, which has already been established as a developing trend in men’s basketball. The emergence of the offensive efficiency variable indicates that it is becoming significant in top-tier competitions as well but is still a challenge for coaches to grasp the causes of this multicomplex issue based on this indicator.
... The progressive inclusion of shot-location coordinates in play-by-play data in the most important basketball competitions around the world (seeMartínez, 2010) facilitates data analysis using spatial statistics. Nevertheless, as far as we know,a few studies, such asHickson & Waller (2003) andReich, Hodges, Carlin & Reich (2006)have used this perspective. Both studies only analysed the performance of a single player (Michael Jordan and Sam Cassell, respectively). ...
The importance of quantitative analysis in sports using objective data (such as game statistics), has been had prominent in recent years. In this paper we have shown an application of spatial statistics to understand more thoroughly the game of basketball. This methodology has been rarely used in sports research, specifically in basketball. We have depicted how a spatial clustering technique, such as the Kulldroff test, which is widely employed in epidemiology, can be applied to analyze basketball data. This test detects low and high incidence clusters of shots, and therefore it better characterizes the game of teams and individual players. In addition, we have also used a test based on entropy, the V-test, which serves to statistically compare shooting maps. We illustrate the interesting contribution of this methodological perspective in the case of the analysis of the Lakers� performance, showing the transformation of this team from a medium-level NBA franchise into a champion team, because of, among other factors, the incorporation of two key players in the 2007-08 season: Pau Gasol and Derek Fisher.
Streakiness is an important measure in many sports data for individual players or teams in which the success rate is not a constant over time. That is, there are many successes/failures during some periods and few or no successes/failures during other periods. In this paper we propose a Bayesian binary segmentation procedure using a bivariate binomial distribution to locate the changepoints and estimate the associated success rates. The proposed method consists of a series of nested hypothesis tests based on the Bayes factors or posterior probabilities. At each stage, we compare three different changepoint models to the constant success rate model using the bivariate binary data. The proposed method is applied to analyze real sports datasets on baseball and basketball players as illustration. Extensive simulation studies are performed to demonstrate the usefulness of the proposed methodologies.
The identification of disease clusters in space or space–time is of vital importance for public health policy and action. In the case of methicillin‐resistant Staphylococcus aureus (MRSA), it is particularly important to distinguish between community and health care‐associated infections, and to identify reservoirs of infection. 832 cases of MRSA in the West Midlands (UK) were tested for clustering and evidence of community transmission, after being geo‐located to the centroids of UK unit postcodes (postal areas roughly equivalent to Zip+4 zip code areas). An age‐stratified analysis was also carried out at the coarser spatial resolution of UK Census Output Areas. Stochastic simulation and kernel density estimation were combined to identify significant local clusters of MRSA (p
Basketball coaches at all levels use shot charts to study shot lo- cations and outcomes for their own teams as well as upcoming opponents. Shot charts are simple plots of the location and result of each shot taken during a game. Although shot chart data are rapidly increasing in richness and availability, most coaches still use them purely as descriptive summaries. However, a team's ability to defend a certain player could potentially be improved by using shot data to make inferences about the player's tenden- cies and abilities. This article develops hierarchical spatial mod- els for shot-chart data, which allow for spatially varying effects of covariates. Our spatial models permit differential smoothing of the fitted surface in two spatial directions, which naturally correspond to polar coordinates: distance to the basket and an- gle from the line connecting the two baskets. We illustrate our approach using the 2003-2004 shot chart data for Minnesota Timberwolves guard Sam Cassell.
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