Introduction Basketball Research Paper

Abstract

The purpose of our research was to investigate the relative frequencies of different types of basketball shots (above head, hook shot, layup, dunk, tip-in), some details about their technical execution (one-legged, two-legged, drive, cut, …), and shot success in different levels of basketball competitions. We analysed video footage and categorized 5024 basketball shots from 40 basketball games and 5 different levels of competitive basketball (National Basketball Association (NBA), Euroleague, Slovenian 1st Division, and two Youth basketball competitions). Statistical analysis with hierarchical multinomial logistic regression models reveals that there are substantial differences between competitions. However, most differences decrease or disappear entirely after we adjust for differences in situations that arise in different competitions (shot location, player type, and attacks in transition). Differences after adjustment are mostly between the Senior and Youth competitions: more shots executed jumping or standing on one leg, more uncategorised shot types, and more dribbling or cutting to the basket in the Youth competitions, which can all be attributed to lesser technical and physical ability of developing basketball players. The two discernible differences within the Senior competitions are that, in the NBA, dunks are more frequent and hook shots are less frequent compared to European basketball, which can be attributed to better athleticism of NBA players. The effect situational variables have on shot types and shot success are found to be very similar for all competitions.

Citation: Erčulj F, Štrumbelj E (2015) Basketball Shot Types and Shot Success in Different Levels of Competitive Basketball. PLoS ONE 10(6): e0128885. https://doi.org/10.1371/journal.pone.0128885

Academic Editor: Dante R. Chialvo, National Scientific and Technical Research Council (CONICET)., ARGENTINA

Received: February 13, 2015; Accepted: May 2, 2015; Published: June 3, 2015

Copyright: © 2015 Erčulj, Štrumbelj. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Data Availability: All relevant data are within the paper and its Supporting Information files.

Funding: The authors have no support or funding to report.

Competing interests: The authors have declared that no competing interests exist.

Introduction

The non-free-throw basketball shot (or field goal) is the primary way of scoring and one of the most frequent and important technical elements in competitive basketball [1]. Players shoot using different techniques, the choice of which is influenced by several factors, such as distance, angle, player type, etc … In order to be an effective basketball shooter, a player must be trained in choosing the appropriate technique and executing it. And, because practice time is limited, the techniques that have to be utilized more frequently in competition should be practised more frequently as well.

Therefore, as a first step towards improving the quality of the basketball training process, we require a better understanding of which basketball shot techniques are executed more frequently in competition and in which situations. Furthermore, we want to understand how large the differences between age groups and levels of competition are, in particular, between Youth and Senior level or between European basketball and the National Basketball Association (NBA). In such cases we would expect that major differences in athleticism (especially between youth and senior basketball) and overall technical ability, would also have an effect on shot type selection and technique.

While there has been some work on the technical elements of dribbling and passing [2, 3], related work on understanding the basketball shot is based only on officially recorded statistics (shot success and, sometimes, shot location) [2, 4–12]. Game statistics provide us with only limited insight and no information about the technical aspects of the shots. The few properties with respect to the basketball shot that have been explicitly analysed and supported by empirical research are that more successful teams, on average, have fewer three-point attempts and a higher shooting percentage [2, 5, 9] and that guards attempt more shots from long range than centres, especially three-point shots [10, 11]. A very often researched related topic is the hot hand phenomenon (see [13] and references therein).

The lack of directly related work is understandable, because data on the technical execution of basketball shots are not readily available. In recent years, there have been substantial advancements in automated player and ball tracking. Technology implemented in the NBA, is capable of (semi-)automated recognition of such technical elements as shot type and defensive spacing, and these data are already being used in research [13, 14]. For other technical aspects and basketball competitions other than the NBA, researchers currently have no choice but to manually collect the data by visually inspecting games.

In order to gain more insight into basketball shooting in competition, we visually inspected all non-free-throw shots in 40 competitive basketball games from 5 different levels of competition for a total of 5024 basketball shots. For each shot, we recorded several technical features, the situation in which the shot was executed, and whether or not the shot was successful.

Our primary goal was to estimate the relative frequencies of different technical features of the basketball shot and how these frequencies compare across different levels of competition. Furthermore, we examined whether substantial differences in frequency between competitions are due to differences in shot selection or because some situations arise more frequently in some competitions.

Methods

Target variables of interest

We focused on the following technical features of a basketball shot:

  • Shot type We divided shots into the following 5 basic shot-type categories:
    • above head: Shooting the ball above the head, looking from under the ball towards the rim. This shot type is the most often used shot-type when shooting from distance, but can also be utilized when near the basket. The most typical example of an above head shot is the jump shot. S1 Video
    • hook shot: Shooting the ball turned approximately perpendicular to the basket using the arm facing away from the basket in a sweeping motion, extending the shoulder movement and bending the wrist. Note that half-hook shots (approximately facing the basket) were also categorized as hook shots. S2 Video
    • layup: A one-handed shot made by holding the ball from below and releasing it after an upwards motion of the arm. Typically executed near the basket and jumping from one leg. Sometimes executed by bouncing the ball off the backboard. S3 Video
    • tip-in: Shooting the ball by tipping a rebound into the basket. This type of shot is entirely executed mid-air. S4 Video
    • dunk: Shooting the ball down through the basket with the hands above the rim. This technique is limited to players of sufficient height and/or vertical jump. S5 Video
    Shots that did not fit into these 5 types were left uncategorised and labelled as other shot types.
  • Leg position Shots can be executed standing on (or jumping from) a single leg (one-legged) or both legs (two-legged). S6 and S7 Videos
  • Movement Most shots are executed from a stationary position (no movement), some are executed after moving towards the basket, which we split into two subcategories: (a) direct unopposed drive (penetration) straight to the basket (drive) S3 and S6 Videos and (b) dribbling towards the basket, beating the defender, or being passed the ball while running towards the basket (dribble or cut). S8 and S9 Videos

The following situational variables that might influence shot type selection in a given situation were also recorded:

  • Player type We categorized players using the three major player-types: guard (G), forward (F), and center (C). These player-types have different roles in competitive basketball [15] and they have different morphological (anthropometric) dimensions [11] and motor skills/potential [15, 16]. These differences lead to differences in basketball shooting. One of the main differences is that guards play farther from the basket and more often shoot from distance [10, 17]. Centres on the other hand, play closer to the basket and, due to this and their morphological characteristics, more often execute the dunk or tip-in.
  • Location The location of the shot on the basketball court with respect to the basket substantially influences shot type selection. We decomposed shot locations into distance (in meters) and absolute angle (in degrees) components (see Fig 1). That is, we do not distinguish between the left- and right-hand side.
  • Transition This feature indicates that the shot was made during a transitional attack (fast breaks, secondary breaks, …). That is, while the defending team was still in transition from attacking to defending and not all 5 of their players were in their appropriate defensive positions.
We were also interested in Shot success: made or missed.

Data acquisition

We analysed games from 5 different levels of competition (3 Senior and 2 Youth competitions):

  • NBA The National Basketball Association (NBA) is the strongest men’s Senior club basketball competition. It features the best and most paid basketball players from all around the World.
  • EURO The Euroleague is the top-tier of inter-European men’s Senior club basketball. It features the top clubs from the best European national leagues and therefore the some of the best senior men’s basketball players in Europe and the World.
  • SLO1 The top-tier Slovenian national league ranks in terms of team and player quality in the mid-range of European national competitions. It features Slovenian and foreign Senior players, the majority of whom are professional basketball players, but are not good enough to compete at the international level
  • U16 and U14 The Under-16 and Under-14 Slovenian boys Youth competitions feature the best young Slovenian basketball players. These players are still in the process developing both physically and in terms of basketball knowledge and expertise.

We analysed one full round of the NBA Playoffs and one full round of the Euroleague regular season. The choice of NBA Playoffs instead of the Regular season was deliberate. Due to a very large number of regular-season games in the NBA and a very packed schedule, not all games of the regular season are fully competitive. This is especially true towards the end of the season, when some teams have no motivation to win or even motivation to lose in order to finish lower and earn a better position in the next-year’s player draft. For SLO1, two full rounds of games were analysed. A broader sample was not possible for U16 and U14, because youth basketball games are typically not videotaped. We focused on the final tournament, where the top 4 teams in that season play. For a detailed list of games for each competition see S1 Text.

Every game was analysed by an expert (all experts had playing and coaching experience and were instructed beforehand on how to categorize shots to ensure consistency) who recorded all features of interest for every non-free-throw basketball shot in that game. Every game was analysed by a single expert and every expert analysed several games. For each expert, the aggregate of all games analysed by that expert was re-checked for consistency by another expert and no inconsistencies were found.

For NBA, EURO, and SLO1 games, television broadcast footage was used. For U14 and U16 games, tournament organizers official game footage was used. The data are summarized in Table 1. The complete data set is available for download S1 Dataset.

Statistical analysis

The main objective is to estimating the relative frequencies of outcomes for the following variables: shot type, leg position, movement, and shot success. In addition, we want to compare these estimates across different competitions and to examine if anything changes when relative frequencies are adjusted with situation-based covariates. The features of interest are all categorical variables. We model each of them separately using a Bayesian hierarchical multinomial logistic regression model.

The multinomial model is a natural choice given the categorical variables. We opt for a hierarchical model to facilitate partial pooling. That is, we want to allow the base rates and situational-covariate coefficients to vary across competitions, but we expect them to be similar. Partial pooling also alleviates the problem of comparisons [18].

Let our target variable have r different categories y1, …, yr and let Yi,j be its value for the i–th shot of the j–th competition. We model the probabilities as and for the reference category The model βl,jXi,j in the exponent is composed of m independent variables and the constant term. We put hierarchical priors on every coefficient: where n is the number of different competitions. We give the hyper-parameters μ and σ2, weakly-informative priors N(0,1000) and InverseGamma(10−4,10−4), respectively.

When modelling shot type, leg position, and movement variables, we used angle, location, player type, and transition as independent variables. For shot success, we used all of these seven variables. Some of the independent variables are nominal and we use dummy coding to enter each of them into the regression as q−1 binary independent variables, where q is the number of categories of that nominal variable. Reference categories for nominal variables are (when dummy-coded or when they are the target variable): above head shot type, one-legged, no drive, no transition, missed, and forward player type.

We’ll refer to the above model as Model 3. It is the most general model used in this research, but in most cases, we will use two simplifications:

  • Model 2 is obtained from Model 3 by assuming that the effect of the covariates are the same across all competitions. That is, all competitions have a common set of independent variable coefficients β. Each competition still has its own base rates β0.
  • Model 1 is a further simplification, where we assume that situational-covariates have no effect on the outcome. That is, we only use β0 coefficients, so Model 1 is equivalent to estimating the relative frequencies for each competition separately.

Model fitting, evaluation, and reporting.

All models were coded and estimated using the Stan software for Bayesian inference [19]. For each model, we ran a 5000 adaptation iterations and 5000 sampling iterations. Trace plots and convergence diagnostics values did not show any indication of non-convergence. Assuming convergence, Monte Carlo standard errors of all reported values were less than 0.001. The out-of-sample predictive performance of each model for each outcome was estimated using the Widely Applicable Information Criterion (WAIC) [20]. All reported posterior point estimates are means and all confidence intervals cover 95% and are based on the 0.025—0.975 quantile interval.

Results

The results are split into two parts. In the first part we report the estimates of the relative frequencies of the variables of interest and compare them across competitions. We report two sets of estimates:

  1. Estimates using Model 1. These estimates can be used to compare the raw relative frequencies across competitions. They could be used to compare the underlying shot type selection process only if we could assume that all competitions have the same distribution of situations that arise (this is clearly not true; for example, different distance distributions; see Table 1) or that the situation in which the shot was made does not influence the choice of technique or shot success (again, most likely not true).
  2. Estimates adjusted for situational variables. These were obtained by fitting Model 2, computing the posterior predictive distributions, and estimating the mean relative frequencies. The Euroleague was used as the common denominator. That is, for each competition, we predicted the relative frequencies for the case where the distribution of situations was as is in the Euroleague.

In the second part, we investigate loosening the assumption that the effect of situational variables is the same for all competitions and allowing for competition-specific but related coefficients (Model 3). In particular, how this improves predictive accuracy.

Relative frequency estimates

Shot type.

Overall, the most frequently observed shot type is the above head shot, followed by the layup (see Fig 2). The layup and uncategorised (other) shots are more frequent in Youth basketball competitions, while above head, dunks, tip-ins, and hook shots are less frequent. The only discernible difference between the three Senior competitions is that the hook shot is less common in the NBA, compared to the two European basketball competitions. Adjusting for differences in situations that arise increases the difference in relative frequency of dunks between NBA and other senior competitions and removes the large differences in relative frequencies of above head shots and layups between the Youth and Senior competitions.

Leg position.

In senior competitions, approximately four fifths of all shots are attempted standing on or jumping with both legs (see Fig 3). In Youth competitions, this number is about 10% lower, which could be attributed to Youth basketball players using the layup more. However, the differences, although smaller, persist even after adjustment. There are no discernible differences within the Youth or Senior competitions.

Movement.

Most shots are attempted from stationary situations, approximately one quarter after the player dribbles or cuts through the defence, and only a small fraction of situations arise where the player takes a direct drive to the basket (see Fig 4). Similar to Leg position, the only substantial differences in Movement variable relative frequencies are between the Youth competitions and the Senior competitions: there are more dribbles and/or cuts to the basket in Youth basketball. After adjustment, these differences decrease, but remain.

Shot success.

There are no discernible differences between competitions in terms of overall shot success (see Fig 5). Adjusting the estimates results in a decrease in the estimated shot success for the Youth competitions, which is what we would expect, given that the average distance is much lower in Youth competitions. However, the overall variability of the success of a basketball shot (basically, a coin flip) prevents us from making a more accurate comparison across competitions.

Fundamental differences between competitions

Table 2 compares the three models’ predictive accuracies. As we would expect, taking into account the situational variables substantially improves predictive accuracy. That is, Models 2 and 3 are substantially more accurate predictors that Model 1.

Model 2 assumes that situational variables have an effect on the target variables but that their effect (coefficients β) is the same across all competitions. Model 3 generalizes model two and allows competition-specific coefficients. However, the differences between using Model 3 and Model 2 in terms of predictive accuracy are not large. The only non-negligible difference is for Shot type, where most of the differences can be explained by the fact that Youth basketball players, especially U14, do not (can not) dunk or tip the ball in.

Our main objective was to estimate the (adjusted) relative frequencies, so we will not interpret individual coefficients. We only note that all estimated coefficients are in agreement with what we would expect from practical experience. Estimated coefficients with interpretations are provided for all Models 2 S2 Text. We opt not to report Model 3 coefficients, because these models are not substantially better than their corresponding Model 2. Furthermore, competition-specific coefficients are difficult to interpret.

Discussion

As far as the investigated shot variables are concerned, all three Senior basketball competitions are surprisingly similar. NBA and Euroleague teams and players are superior to Slovenian Division 1 teams and players, so the lack of substantial statistical dissimilarities implies that players’ defensive and offensive abilities scale similarly if we move up or down in level of competition.

There are two discernible differences within the Senior competitions. First, in the NBA dunks are more frequent, and second, hook shots are less frequent compared to European basketball. Both can be, at least partially, attributed to better athleticism of NBA players, who are able to execute the more high-percentage dunk in more situations. However, the hook shot is a shot that is not only very difficult to block but also very difficult to alter (that is, it is also very difficult for the defender to interfere with this type of shot enough to cause the shooter to deviate from his typical execution of the shot and subsequently decreasing the likelihood of scoring) [21]. The hook shot has always played a role in basketball, especially for centres, so a lower relative frequency of this shot can also be partially explained by, at least in this respect, inferior technique of today’s NBA centres. Our results confirm the popular belief that the hook shot is disappearing from the NBA. Those that still utilize the shot in the NBA are typically European centres playing in the NBA (for example, Marc Gasol).

There are no discernible differences between U14 and U16, but U16 are in all observed variables more similar to the Senior competitions than U14, which is expected and can be attributed to their superior physical, tactical, and technical knowledge. The largest differences are between the Youth and the Senior competitions, but most of them can be explained with situational variables, in particular that the average Youth basketball shot is much closer to the basket. In the observed Youth games, more shots are executed jumping or standing on one leg (as opposed to two legs) and there is more dribbling or cutting to the basket. Shots near the basket are more successful. Allowing more such shots implies less effective 1-on-1 defending and closing down. While this might be effective in Youth basketball, it is not in Senior basketball, so during the transition from Youth to Senior level emphasis should be put on two-legged long-range above-head shots. Also, there are more uncategorised shot types (especially in U14), which can be attributed to the fact that these players are still developing proper technique and tactics.

We gain little in terms of predictive accuracy by allowing for competition-specific effects of situational variables. That is, while individual competitions may have different base preferences for shot types and technique, the effects of situational variables on shot selection appear to be consistent across all competitions. While this was not our main objective, the fitted statistical models also allowed us to estimate relative effectiveness of individual shot types and the effects of distance, transition, player type, etc… (see S2 Text for details). All results agree with expert knowledge.

We collected a substantial amount of data, however, they are still insufficient to illuminate more subtle differences between competitions, if they exist. More data would be needed for a more precise analysis, for shot success in particular. With the collected data, we could not analyse temporal aspects of the game. In particular, the connection between game pace (number of shots attempted in a unit time period, which also depends on how successful teams are at offensive rebounding), shots success, and shot selection. It is possible that differences in game pace or its in-game variability could explain some of the remaining differences in shot selection and shot success. However, we would require temporal data, including time left on the shot clock when the shot was attempted.

A little under 10% of all shots were left uncategorised (other). Some of these shots were unconventional shots made at the end of each quarter from a large distance as time was running out, however, a more detailed categorization of the remaining shots is necessary. Two important variables that have an effect on basketball shooting, but were not included in our study, are type of defence (man-to-man, zone) and the amount of pressure put on the shooter by the defence. We aim to address these issues as part of further work.

Acknowledgments

The authors would like to thank Uroš Godler, Samo Plevnik, Jure Puš, and Luka Strle for their assistance with data acquisition and Luka Dobovičnik for basketball shot demonstration.

Author Contributions

Conceived and designed the experiments: FE EŠ. Performed the experiments: FE EŠ. Analyzed the data: FE EŠ. Wrote the paper: FE EŠ.

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Citation: Sampaio J, McGarry T, Calleja-González J, Jiménez Sáiz S, Schelling i del Alcázar X, Balciunas M (2015) Exploring Game Performance in the National Basketball Association Using Player Tracking Data. PLoS ONE 10(7): e0132894. https://doi.org/10.1371/journal.pone.0132894

Editor: José César Perales, Universidad de Granada, SPAIN

Received: February 14, 2015; Accepted: June 22, 2015; Published: July 14, 2015

Copyright: © 2015 Sampaio et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Data Availability: Data are publicly available from the NBA website (http://stats.nba.com).

Funding: This study was supported by the Portuguese foundation for science and technology (PEst-OE/SAU/UI4045/2015). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

The National Basketball Association (NBA) from the United States of America is the most competitive basketball league in the world, with a competition period in regular season comprising 82 games spanning approximately 24 weeks. The coaching staff must prepare and oversee the training loads on players throughout the entirety of the competition period, a complex process that places a great amount of physiological stress on the athletes [1]. This process also requires managing the significant differences in work demands introduced by position-specific game behaviors and player status (e.g., starting vs non-starting players), as well as adjusting throughout the season to several changing unpredictable constraints such as player injuries. Thus, the ongoing planning and monitoring of practice sessions and game performance is critical for optimizing the decisions on individual training loads taken by coaching staff.

While each player responds individually to the stress of practice and competition [2], there remains a clear need to use updated sports performance models to inform starting points for player preparation. One of the most common methods of monitoring sports performance is using game-related statistics to evaluate technical and tactical behavior, as well as the efficiency of players and teams throughout the season. Research reporting these variables frequently uses data from European league games but not from the NBA. This study using NBA data serves somewhat to address this imbalance. Performance variables represent duality of the performer and the environment in order to understand how players engage with others by detecting affordances [3]. For example, the assists are likely a result of affordances to the ball carrier created by open teammates. In fact, perception-action coupling indicates that information drives movement and movement drives information available for players to pick up [4]. In this sense, game-related statistics can provide insight on both perception and action of the players. In addition, they may provide a measure of co-adaptation, in the way that players function as part of a larger system (the team) co-adapting to small but important changes in each others structure and function [5].

Basketball performance depends primarily on shooting 2-point field-goals and on securing defensive rebounds [6–8]. In close contested games, however, fouls and free-throws exhibit increased importance for determining game outcome than for lesser contested games [8, 9]. Other remaining game statistics such as offensive rebounds, turnovers, steals and assists are not reported consistently as discriminating performance variables for winning and losing. When contrasting the best and worst teams, the best performance variables for long term success are related to assists, steals and blocks, denoting the importance of passing skills and of defensive skills along outside and inside court positions [10]. Research from NBA data likewise reported winning game outcomes to be related to better offensive efficiency, specifically points scored in the third quarter, as well as the defensive variables of fouls and steals [11]. Thus, as expected, the results suggest that both offensive and defensive variables are important for winning games.

These descriptions are informative on a team-level basis, however, a need exists to undertake player-level analysis in order to better understand what performance variables most discriminate elite players from other players. In the NBA context, this aim can be accomplished by contrasting game performances from the awarded players that comprise the first, second and third NBA team (all-stars) with the performance statistics of the other players. The all-star players from these three teams are selected from a voting conducted by a panel of sportswriters and broadcasters [12]. The players receive five points for a first team vote, three points for a second team vote, and one point for a third team vote. At the end, and accounting for playing positions, the five players with the highest point totals make the first team, the next five make the second team, and the remaining five the third team.

One of the most recent advances in assessing basketball performance is player-tracking technology [13, 14]. This technology uses computer vision systems designed with algorithms capable of measuring the positions of players with a sampling rate around 25 frames per second [15]. Of course, kinematic variables such as distance, velocity or acceleration may be derived from these data, and sampling frequencies might improve in future [16]. Currently, the tracking technology is being used with data obtained from notational analysis providing combined information about sports performance; for example, by analyzing the distance covered by players when the team is attacking and when the same team is defending. Research in basketball using positional-derived variables however is limited at present to small samples of young basketball players examining physical demands [17], effects of defensive pressure on movement behavior [18], and how tactical performances are affected by activity workload [19].

These new tracking data open up possibilities that advance understanding of game performance by embracing a more holistic approach to analyzing sports behavior. For example, movement patterns (kinematics) from tracking data complement variables from the physiological (e.g., work rate), technical (e.g., actions) and tactical (e.g., individual/team behavioural patterns) domains leading to a more complete description and understanding of sports behavior in its entirety. As noted, an issue to address in this study using the large amounts of tracking data at hand concerns different basketball game performance profiles for different players and teams. That is, to categorize individual player performances into like groupings for use as baseline reference for the future development and preparation of players. The aim of the present study then is twofold: (i) to compare basketball game performances from the all-star and non all-star players, and (ii) to identify and describe the different basketball game performance profiles based on different game roles in the NBA.

Regarding the first aim, it was hypothesized that all-star players will outperform the non all-stars in game statistics. Therefore, the player performances on an actions-by-minute of play basis were compared, in aim of identifying performance variables that discriminate between the two separate groups of players. It is expected that all-star players should outperform the non all-star players in their performance statistics, particularly in scoring and passing related variables, as these important variables are thought to place higher demands on anticipatory processes [20–22]. In the second aim it was hypothesized that player performance profiles will present similarities and dissimilarities that can be used to identify different groups of players based on playing position. This aim is accomplished by using actions-per-game, in order to identify different groups of player performances, regardless of minutes of play in the games, thereby identifying those performance variables that discriminate between different player groupings.

Finally, it is important to describe the data within these performance-based groupings according to the players (all-star vs. non all-star) and playing positions. For example, some groups might have strong presence from all-star players and other groups might comprise both all-star and non all-star players from specific positions. This information can be useful when used in planning representative tasks in practice sessions, thereby fine-tuning playing behaviors in competition by using representative tasks in training [23, 24]. In fact, players are often divided in practice into smaller groups according to specific positions as well as their playing standard. Non-starting players, for example, lack the same amount of playing time as starting players, and this competitive playing deficit likely affects their responses to competition throughout the season [21, 25]. It follows that a detailed description of these different performance profiles using available objective measures would serve as an appropriate performance baseline for optimizing practice planning and, ultimately, for improving game performance.

Methods

Sample and variables

Archival data were obtained from open-access official NBA records for 1230 games played during the 2013–2014 regular season (available at http://stats.nba.com, these records contained both non-tracking and tracking data). A total of 30 teams played 82 games between October 29, 2013 and April 16, 2014. The gathered database had records of game performances from 548 players. The cases of player transfer between teams were counted as two different records.

The variables analyzed included the points per game, minutes played and the following game actions, as defined by the NBA and the company responsible for the player tracking process (SportsVU, Northbrook, IL, USA):

  • Pull-up shots: any jump shot outside 10 feet where a player took one or more dribbles before shooting. Gathered variables include pull-up points per game (PPG) or minute (PPM), field-goal percentage (FG%) and 3-point field-goal percentage (3FG%).
  • Catch and shoot: any jump shot outside of 10 feet where a player possessed the ball for two seconds or less and took no dribbles. Gathered variables include catch and shoot PPG or PPM, FG% and 3FG%.
  • Close shots: any jump shot taken by a player on any touch that starts within 12 feet of the basket, excluding drives. Gathered variables include close PPG or PPM and FG%.
  • Drives: any touch that starts at least 20 feet of the hoop and is dribbled within 10 feet of the hoop and excludes fast breaks. Gathered variables include drives PPG or PPM and FG%.
  • Passing-variables: the total number of passes a player makes and the scoring opportunities that come from those passes, whether they lead directly to a teammate scoring a basket (assists) or free throw (free-throw assists), or if they set up an assist for another teammate (secondary assists). Gathered variables also include total assists opportunities and total points created by assists.
  • Touches-variables: the number of times a player touches and possesses the ball (touches per game), where those touches occur on the court (front, close or elbow), how long the player possessed the ball (time of possession), and the number of points per touch or per half-court touch. Gathered variables also include blocks, steals and the opponent field goals made at the rim while being defended.
  • Speed and distance: variables that measure the distance covered (expressed in miles) and the average speed of all movements (expressed in miles per hour) by a player while attacking or defending.
  • Rebounds: the number of rebounds secured (rebounds), the times when the player was within the vicinity (3.5 feet) of a rebound (chances), the number of rebounds a player recovers compared to the number of rebounding chances available (percentage chances) as well as if the rebound was uncontested by an opponent (uncontested). These variables were gathered either for defensive and offensive rebounds.
  • Free-throw percentage: the number of free-throws made divided by the number of free-throws attempted.

Video footage from the entire court was unavailable making assessment of the NBA tracking data impossible. The NBA non-tracking data (e.g., assists, steals or defensive rebounds) however was assessed for reliability as follows. Two games were selected at random and analyzed conjointly through systematic observation by two experts. The minimum Cohen’s κ value for all variables exceeded 0.91 demonstrating high inter-rater reliability [26] between the NBA non-tracking data and the two experts.

Data analysis

Variables expressed as counts per game were divided by average minutes played. Records were screened for univariate outliers (cases outside the range Mean ± 3SD) and distribution tested, together with advised assumptions for each following inferential analysis [27]. To identify which variables best predict the player category (i.e., all-star vs. non all-star), the performance per minute of play was analyzed using a descriptive discriminant analysis. Structure coefficients greater than |0.30| were interpreted as meaningful contributors for discriminating between the two groups [27]. Validation of discriminant models was conducted using the leave-one-out method of cross-validation [28]. Also, a k-means cluster analysis was performed on the entire sample with the aim of creating and describing maximal different groups of game performance profiles. The cubic clustering criterion, together with Monte Carlo simulations, was used to identify the optimal number of clusters, thereby avoiding using subjective criteria. This statistical technique requires that all cases have no missing values in any of the variables introduced in the model; there were a total of 339 cases meeting this condition (62%). Afterwards, a descriptive discriminant analysis was performed to identify which of the variables best predicts the playing clusters.

One-way independent measures ANOVA was used to compare the variables not selected in the discriminant models (i.e., points scored per game and minutes played). Tukey post-hoc homogeneous subsets were used to describe post-hoc results. Statistical significance was set at 0.05 and calculations were performed using JMP statistics software package (release 11.0, SAS Institute, Cary, NC, USA) and SPSS software (release 22.0, SPSS Inc., Chicago, IL).

Results

Comparing all-star and non all-star players

The means and standard deviations from the variables according to the all-star vs. non all-star categories are presented in Table 1. The most important variables for differentiating all-star and non all-star performances per minute of play were identified using discriminant analysis. The obtained function was statistically significant (p≤0.001) with a canonical correlation of 0.59 (Λ = 0.65) and reclassification of 97.2%. The structure coefficients (SC) from the function reflected emphasis on elbow touches (SC = 0.43), defensive rebounds (SC = 0.35), close touches (SC = 0.34), close points (SC = 0.33), pull-up points (SC = 0.33) and speed in defense (SC = -0.33) (see Table 1). There were six cases misclassified (60.0% accuracy) in the all-star group and seven cases misclassified (97.8% accuracy) in the non all-star group, therefore, the obtained mathematical model shows high accuracy in classifying the players into their original groups.

Figs 1 and 2 present the distribution from the discriminant scores in each group of players. The all-star players presented higher mean scores when compared to non all-star players (3.04±1.45 and -0.13±0.87, respectively).

Describing different game performance profiles

The cubic clustering criterion (CCC) along with Monte Carlo simulations was used to identify the optimal number of clusters. The largest value (CCC = 252.6) was obtained for a model of seven clusters. Therefore, a k-means cluster analysis was performed to create and describe seven maximal different groups of performance profiles per game. The means and standard deviations from the variables according to the cluster solutions are presented in Table 2. The discriminant analysis revealed four statistically significant functions (p≤.001), however, the first two yielded a total of 94.7% from the total variance, with canonical correlations of 0.98 and 0.88, respectively. The reclassification of the cases in the original groups was very high (96.2%).

The structure coefficients from the functions are presented in Table 2. The first function had stronger emphasis on total distance covered in offense (SC = 0.83) and defense (SC = 0.80), whereas the second function was emphasized by performance obtained in passing-related variables (see Table 2).

Table 3 presents the differences between clusters in points scored per game, minutes played and distance from each case (player) to cluster centroid. The clusters 2 and 4 had more playing minutes and points per game. The clusters 1 and 5 were the most homogeneous, as identified in smaller distances to group centroid. In addition, player distributions in the seven clusters were contrasted against player category, presence in the NBA first team, and specific court position of players. The all-star players were grouped in clusters 2, 3 and 4. The NBA first team was grouped in clusters 2 and 4.

Fig 3 presents the territorial map from the cases and created clusters within the space from the first and second discriminant functions. Players from clusters 4 and 2 exhibited better overall performances, however, players from cluster 6 also performed well in variables related to function 2.

Discussion

This study aimed to compare game performances of all-star and non all-star basketball players and to identify and describe different basketball game performance profiles in the NBA. In general terms, key performance indicators were identified that discriminate all-star players from non all-stars and, also, the different groupings of performance profiles in competition.

Comparing all-star and non all-star players

As expected, all-star players outperformed non all-star players in performance statistics, particularly in defensive rebounds, close touches and close points, pull-up points and assists. (Note. These results may be confounded in that the distinction between all-star and non all-star players is determined by sportswriters and broadcasters. This said, discrimination between these prejudged player groups is reflected in some game performance variables as reported in this study.)

Noted previously, the variables obtained from the tracking systems allow use of court locations for better understanding several game statistics. Therefore, these results increase knowledge of basketball game behavior by identifying key performance variables and by reducing prior emphasis on the importance of distance covered and velocity. The reclassification obtained was very high and hence affirms accuracy of the mathematical model.

The close touches and points were identified as key variables, suggesting that all-star players performed consistently better than non all-star players within 12 feet of the basket. These court locations are highly concentrated with teammates and opponents with frequent physical contact between players. These complex actions require high anticipatory skills [29] and all-star players outperform non all-stars in producing these complex skills under extreme adverse conditions [20–22]. Also, related with these findings, all-star players demonstrated the ability to score pull-up points, again showing how well these players perceive environmental information and adapt their behavior accordingly [30, 31], as they strive to reach a better position from which to score (oftentimes using one or more dribble actions before shooting, for example). Several studies from basketball [32], football [33] and futsal [34] analyzing space-time dynamics of player dyads inform how the formation of playing patterns are influenced by scoring targets (i.e., baskets and goals). This higher ability to perceive the environment requires a developed attention span [35, 36], perhaps evidenced in the higher number of assists given that assists constitute passes to a teammate leading directly to a subsequent field goal.

The distance covered and average speeds were not discriminant variables between the all-star and non all-star players. Until the availability of recent technology, getting reliable time motion data in basketball games has been difficult to acquire and, as such, low accuracy in the measures reported and/or small sample sizes have been a concern since early times [37]. The present results however provide measures of distance and velocity from an entire NBA season that are considered reliable [13, 14], despite the 25 Hz sampling frequency limitation [16]. Although discriminant analysis only emphasized velocity in defense, there seems to be a tendency for all-star players to cover slightly shorter distances at lower average velocities. This might be important in that it is consistent with previous observations on the enhanced attunement of players to perceive affordances [38, 39]. Thus, all-star players may well make less mistakes when deciding when and where to run in both offense and defense, possibly taking shorter paths to reach their destinations. These fewer mistakes in a game might well result in lower distances covered by these players. In addition, these considerations might also suggest that all-star players are more efficient, having less energy demands placed on them during a game. In fact, research suggests that motor efficiency achieved through intensive training, leads to improved perception, focus, anticipation, planning and fast responses [40]. The finding of lower defensive velocities for all-star players may reinforce this observation, but might also suggest that these players might be focusing their efforts more on offensive performances, as they are more complex and depend more upon their high level expertise [22, 41].

Describing different game performance profiles

The results reported different performance profiles for different player groupings. There were seven different groups identified by the analysis, obtaining very high reclassifications of the cases (96.2%). These groupings, based on total distance covered in the season and performance per game, might be used in developing specific playing profiles that, taking into consideration the influence of individual differences and functional variability, may serve as baseline to facilitate optimizing practice planning and game performance.

The clusters 2, 3 and 4 performed best at discriminant variables from function 1 (78.3% of total variance) and they contained all of the all-star players. These players participated in more than 30 minutes per game and scored many points per game (from 12.8±3.4 to 17.8±6.3). As an effect of these higher playing times, the most discriminant variables of this function were the distances covered either in defense or offense. Other discriminant variables included participation in offense (touches and front court touches) and passing-related variables (passes, assists, secondary assists, assists opportunities and points created by assists). There are also unique traits from each cluster that could be used to optimize the training process. For example, due to their high playing times in game competition, players from cluster 2 are likely high conditioned players, however, they should also give the most concern for coaches when planning recovery time between games [42]. Conversely, players from cluster 4 comprised all guards or shooting guards with extremely high values from time of possession, touches per game or passing-related variables. This is key information for coaches to optimize representative task designs that enable players to perceive adequate environmental information and to subsequently act accordingly [25, 30, 43]. Finally, players from cluster 3 demonstrated less possession time and touches, despite the higher minutes of play, which suggests a predominant defensive role for these players. The defensive tasks are particularly related to player fitness variables as high-level defensive performances seem to require higher energy demands [44] and these kind of tasks are therefore particularly related to player fitness variables.

In addition, the worst performance variables in function 1 belong to players from cluster 1, as they exhibited lower playing times (12.6±5.0) distributed equally on playing position. In fact, the most unclear player positions (and missing values), in reference to players that can play in several different positions, were grouped in this cluster. Therefore, these results might be suggesting a profile of an all-round player that can be used in a game to serve multiple purposes, or a profile of a very specialized player (e.g. in shooting or rebounding). Together with workload compensation of reduced playing time, coaching staffs can modify the tasks to optimize the performance produced by these all-round players or specialists.

When adding the results from the second discriminant analysis function, clusters 4 and 6 emerge as active performers in the analyzed variables, such as time in possession, touches, passing, pull-up points and drives per game. These results confirm the guards profile (in cluster 4) identified previously, and also for players in cluster 6. In fact, there is an important requirement to adjust the tasks required of these players in order to fine-tune the environmental information necessary for information pick-up in game play [30, 45]. From the same perspective, players from cluster 3, identified as defensive-related, demonstrate less activity in these variables, consistent with their roles in the game.

Conclusions

In summary, this study provided analysis of an NBA regular season using player-tracking variables and notation data. It was found that all-star players performed consistently better than non all-star players within 12 feet of the basket, possibly a result of optimized attention processes that are key for perceiving the required appropriate environmental information for action production. In addition, different groupings were identified based on playing performance, particularly in relation to the roles of scoring, passing, defensive and all-round duties. These findings can be used to optimize preparation for individual player groupings and, ultimately, improve game performances of the players and teams.

Acknowledgments

This study was part of a project registered at the Portuguese Foundation for Science (FCT, PEst-OE/SAU/UI4045/2015).

Author Contributions

Conceived and designed the experiments: JS TM. Performed the experiments: JS TM JC SJ XS MB. Analyzed the data: JS TM. Contributed reagents/materials/analysis tools: JS TM. Wrote the paper: JS TM JC SJ XS MB.

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