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Basketball Teams As Strategic Networks Basketball Teams as Strategic Networks Jennifer H. Fewell1,3*, Dieter Armbruster2,3, John Ingraham2, Alexander Petersen2, James S. Waters1 1 School of Life Sciences, Arizona State University, Tempe, Arizona, United States of America, 2 School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, United States of America, 3 Center for Social Dynamics and Complexity, Arizona State University, Tempe, Arizona, United States of America Abstract We asked how team dynamics can be captured in relation to function by considering games in the first round of the NBA 2010 play-offs as networks. Defining players as nodes and ball movements as links, we analyzed the network properties of degree centrality, clustering, entropy and flow centrality across teams and positions, to characterize the game from a network perspective and to determine whether we can assess differences in team offensive strategy by their network properties. The compiled network structure across teams reflected a fundamental attribute of basketball strategy. They primarily showed a centralized ball distribution pattern with the point guard in a leadership role. However, individual play- off teams showed variation in their relative involvement of other players/positions in ball distribution, reflected quantitatively by differences in clustering and degree centrality. We also characterized two potential alternate offensive strategies by associated variation in network structure: (1) whether teams consistently moved the ball towards their shooting specialists, measured as ‘‘uphill/downhill’’ flux, and (2) whether they distributed the ball in a way that reduced predictability, measured as team entropy. These network metrics quantified different aspects of team strategy, with no single metric wholly predictive of success. However, in the context of the 2010 play-offs, the values of clustering (connectedness across players) and network entropy (unpredictability of ball movement) had the most consistent association with team advancement. Our analyses demonstrate the utility of network approaches in quantifying team strategy and show that testable hypotheses can be evaluated using this approach. These analyses also highlight the richness of basketball networks as a dataset for exploring the relationships between network structure and dynamics with team organization and effectiveness. Citation: Fewell JH, Armbruster D, Ingraham J, Petersen A, Waters JS (2012) Basketball Teams as Strategic Networks. PLoS ONE 7(11): e47445. doi:10.1371/ journal.pone.0047445 Editor: Stefano Boccaletti, Technical University of Madrid, Italy Received June 21, 2012; Accepted September 17, 2012; Published November 6, 2012 Copyright: ß 2012 Fewell 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. Funding: This research was supported by the NSF under Grant No. BECS-1023101 to DA, by a grant from the Volkswagen Foundation under the program on Complex Networks to DA, by an ASU Exemplar award to JHF, and by NSF CSUMS grant No. DMS- 0703587. 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. * E-mail: [email protected] Introduction to move the ball into the basket while anticipating and responding to the opposing team. Thus, plays that begin as set strategies Capturing the interactions among individuals within a group is evolve quickly into dynamic interactions [8]. Unlike many sports, a central goal of network analyses. Useful depictions of network the game does not revolve around a series of dyadic interactions structure should provide information about the networks purpose (eg tennis, baseball) or a summation of individual efforts (track and and functionality. But how do network attributes relate to field); it is dependent on a connected team network [9]. functional outcomes at the group and/or individual levels? A The dynamic between within-group cooperation and conflict, useful context to ask this question is within small team networks. and group versus individual success, is an inherent feature of both Teams occur everywhere across the broad array of biological human and biological social systems. This tension, exemplified in societies, from cooperatively hunting carnivores to social insects the distribution of shooting opportunities in a game across players, retrieving prey [1–4], and are ubiquitous in human organizations. or by salary dispersion inequities in a team or organization, is We define teams as groups of individuals working collaboratively a fundamental issue across cooperative systems [6,10,11]. The and in a coordinated manner towards a common goal be it dynamic between specialization and flexibility also appears across winning a game, increasing productivity, or increasing a common systems. In prides of lions, for example, different females assume good [5]. Within teams, individuals must coordinate across the roles of driving or flanking prey [1]. However, in both contexts different roles or tasks, with their performance outcomes being individuals must flexibly change positions in a rapidly changing interdependent [4–6]. The success of the team is rarely a simple game. Finally, like almost all cohesive groups, teams must compete summation of the tools each individual brings. Instead it must with other teams, and their success/failure is shaped by their emerge from the dynamic interactions of the group as a whole [7]. ability to respond to those challenges. Unlike a lion pride or How can we capture the relevance of these interactions to team business organization, however, the success and failure of specific function? Because teams are dynamic systems, it makes sense to network interactions for a basketball team can be easily measured use network analyses to approach this problem. The game of iteratively and in real time, as the team scores points or loses the basketball is based on a series of interactions, involving a tension ball to a superior defense. between specialization and flexibility; players must work together PLOS ONE | www.plosone.org 1 November 2012 | Volume 7 | Issue 11 | e47445 Basketball Networks To evaluate basketball teams as networks, we examined the Table 1. Analyzed games and outcomes. offensive ball sequences by National Basketball Association (NBA) teams during the first round of the 2010 playoffs. We graphed player positions and inbound/outcomes as nodes, and ball Matchup Games Game Winner Series Winner movement among nodes (including shots to the basket) as edges. From the iterated offensive 24 second clocks, we recorded Bobcats vs. Magic Game 1 Magic Magic sequences of ball movement of each of the 16 play-off teams Bobcats vs. Magic Game 2 Magic Magic across two games. We used the compiled data to first ask whether Cavaliers vs. Bulls Game 2 Cavaliers Cavaliers we can capture the game of basketball through a transition Cavaliers vs. Bulls Game 4 Cavaliers Cavaliers network representing the mean flow of the ball through these Hawks vs. Bucks Game 3 Bucks Hawks sequences of play (a stochastic matrix), and secondly whether Hawks vs. Bucks Game 4 Bucks Hawks individual teams have specific network signatures. We then examined how different network metrics may be associated with Celtics vs. Heat Game 1 Celtics Celtics variation in actual play strategy. We asked whether teams vary Celtics vs. Heat Game 3 Celtics Celtics strategically in centrality of ball distribution, such that some teams Lakers vs. Thunder Game 1 Lakers Lakers rely more heavily on a key player, such as the point guard, to make Lakers vs. Thunder Game 2 Lakers Lakers decisions on ball movement. We used degree centrality to compare Jazz vs. Nuggets Game 1 Nuggets Jazz teams using this strategy with those in which the ball is distributed Jazz vs. Nuggets Game 4 Jazz Jazz more evenly. We similarly used clustering analyses to examine relative connectedness among players within teams and to ask Mavericks vs. Spurs Game 5 Mavericks Spurs whether teams differentially engaged players across multiple Mavericks vs. Spurs Game 6 Spurs Spurs positions. We also asked whether ball movement rate, measured Suns vs. Blazers Game 1 Blazers Suns as path length and path flow rate, could capture the perceived Suns vs. Blazers Game 6 Suns Suns dichotomy of teams using dominant large players, usually centers, versus small ball teams that move the ball quickly across multiple doi:10.1371/journal.pone.0047445.t001 players [12]. We were interested in whether network metrics can usefully between the two games analyzed for the majority of teams, so quantify team decisions about how to most effectively coordinate sequences were pooled. players. We examined two network metrics that we hypothesized For initial analyses, all possible start-of-play (inbounds, re- might capture different offensive strategies. One is to move the ball bounds and steals) and outcomes (successful/failed two point or in a way that is unpredictable and thus less defensible. To measure three point shots, fouls, shooting fouls with different success network unpredictability we calculated team entropy, applying outcomes, steals and turnovers) were recorded as nodes. Data per Shannons entropy to the transition networks as a proxy for the offensive play generated a sequential pathway
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