http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0047445
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 Top
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:
© 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:
j.fewell@asu.edu
Introduction Top
Capturing
the interactions among individuals within a group is a central goal of
network analyses. Useful depictions of network structure should provide
information about the networks purpose and functionality. But how do
network attributes relate to functional outcomes at the group and/or
individual levels? A useful context to ask this question is within small
team networks. Teams occur everywhere across the broad array of
biological societies, from cooperatively hunting carnivores to social
insects retrieving prey
[1]–
[4],
and are ubiquitous in human organizations. We define teams as groups of
individuals working collaboratively and in a coordinated manner towards
a common goal be it winning a game, increasing productivity, or
increasing a common good
[5].
Within teams, individuals must coordinate across different roles or
tasks, with their performance outcomes being interdependent
[4]–
[6].
The success of the team is rarely a simple summation of the tools each
individual brings. Instead it must emerge from the dynamic interactions
of the group as a whole
[7].
How can we capture
the relevance of these interactions to team function? Because teams are
dynamic systems, it makes sense to use network analyses to approach this
problem. The game of basketball is based on a series of interactions,
involving a tension between specialization and flexibility; players must
work together to move the ball into the basket while anticipating and
responding to the opposing team. Thus, plays that begin as set
strategies evolve quickly into dynamic interactions
[8].
Unlike many sports, the game does not revolve around a series of dyadic
interactions (eg tennis, baseball) or a summation of individual efforts
(track and field); it is dependent on a connected team network
[9].
The dynamic between
within-group cooperation and conflict, and group versus individual
success, is an inherent feature of both human and biological social
systems. This tension, exemplified in the distribution of shooting
opportunities in a game across players, or by salary dispersion
inequities in a team or organization, is a fundamental issue across
cooperative systems
[6],
[10],
[11].
The dynamic between specialization and flexibility also appears across
systems. In prides of lions, for example, different females assume the
roles of driving or flanking prey
[1].
However, in both contexts individuals must flexibly change positions in
a rapidly changing game. Finally, like almost all cohesive groups,
teams must compete with other teams, and their success/failure is shaped
by their ability to respond to those challenges. Unlike a lion pride or
business organization, however, the success and failure of specific
network interactions for a basketball team can be easily measured
iteratively and in real time, as the team scores points or loses the
ball to a superior defense.
To evaluate
basketball teams as networks, we examined the 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 movement among nodes (including shots to the basket) as
edges. From the iterated offensive 24 second clocks, we recorded
sequences of ball movement of each of the 16 play-off teams across two
games. We used the compiled data to first ask whether we can capture the
game of basketball through a transition network representing the mean
flow of the ball through these sequences of play (a stochastic matrix),
and secondly whether individual teams have specific network signatures.
We then examined how different network metrics may be associated with
variation in actual play strategy. We asked whether teams vary
strategically in centrality of ball distribution, such that some teams
rely more heavily on a key player, such as the point guard, to make
decisions on ball movement. We used degree centrality to compare teams
using this strategy with those in which the ball is distributed more
evenly. We similarly used clustering analyses to examine relative
connectedness among players within teams and to ask whether teams
differentially engaged players across multiple positions. We also asked
whether ball movement rate, measured as path length and path flow rate,
could capture the perceived dichotomy of teams using dominant large
players, usually centers, versus small ball teams that move the ball
quickly across multiple players
[12].
We were interested in
whether network metrics can usefully quantify team decisions about how
to most effectively coordinate players. We examined two network metrics
that we hypothesized might capture different offensive strategies. One
is to move the ball in a way that is unpredictable and thus less
defensible. To measure network unpredictability we calculated team
entropy, applying Shannons entropy to the transition networks as a proxy
for the unpredictability of individual passing behavior among team
players. Another, not mutually exclusive, strategy is to capitalize on
individual expertise by moving the ball towards players with high
probability of shooting success. In a sense, this strategy reflects a
coordinated division of labor between ball distributors early in the
play, transitioning to shooting specialists. We looked for evidence of
this strategy using a metric of uphill/downhill flux, which estimates
the average change in potential shooting percentage as the ball moves
between players in relation to their differential percent shooting
success. Uphill/downhill and team entropy both recognize the need for
coordination within a team, but they emphasize different aspects of
network dynamics; one capitalizes on individual specialization while the
other emphasizes team cohesion.
Methods Top
We
recorded and analyzed transition networks for the 16 teams in televised
games of the 2010 NBA first round play-offs. The sequential ball
movement for each teams offensive plays was recorded across two games
for each pair; games were picked haphazardly a priori, not based on
outcome (analyzed games and outcomes in
Table 1).
For analysis, the five starting players for each team were assigned
position numbers from 1–5, in the order of: (1) Point Guard; (2)
Shooting Guard; (3) Small Forward; (4) Power Forward; (5) Center. All
offensive plays with at least three of the five starters on the floor
were included (player list in
Table S1.
This allowed us to equate positions with specific players within each
team and to use player positions as nodes. Preliminary analyses
indicated that offensive play paths were fairly consistent between the
two games analyzed for the majority of teams, so sequences were pooled.
For
initial analyses, all possible start-of-play (inbounds, rebounds and
steals) and outcomes (successful/failed two point or three point shots,
fouls, shooting fouls with different success outcomes, steals and
turnovers) were recorded as nodes. Data per offensive play generated a
sequential pathway
[9],
[13].
The cumulative paths throughout the game were combined to generate a
weighted graph of ball movement with possession origin, players and
possession outcomes as nodes and ball movement between those nodes as
directed edges.
Although we chose
games haphazardly, the differential in total points in analyzed games
generally reflected outcomes for the play-off round (
Table 1).
The primary exception was the two Atlanta Hawks/Milwaukee Bucks games,
in which the Bucks beat the Hawks in the series, but were defeated by a
mean of 12.5 points during the two focal games. In the analyzed Dallas
Mavericks/San Antonio Spurs games, Dallas won by a mean differential of 6
points, but the Spurs beat the Mavericks in the play-off series by a
mean differential of 0.5; wins were split across the two games analyzed
(Games 5 and 6).
Network Analyses
We generated
weighted graphs from the cumulative transition probabilities. When all
data were analyzed, almost all nodes became connected, making it
difficult to differentiate across graphs. Therefore, we generated a
series of weighted graphs at increasing cut-off weights from the 30th to
70th percentiles (with the 30th percentile graphs highlighting only the
most frequently seen transitions). This allowed us to analyze changes
in network structure as we move from the most likely links between
players to those that were least frequent. We used the entire matrix of
transitions for each team to perform structural network analyses
[12],
[14],
adapted for offensive plays in a basketball game. Metrics included:
path length, path flow rate, degree centrality, clustering coefficient,
individual and team entropy, individual and team flow centrality,
shooting efficiency flux.
Path length
and path flow rate compared the number of passes and the speed of ball
movement involved in team play. Path length simply included the number
of passes between players per play, ignoring inbound and outcome nodes.
Paths included all between-player edges, such that a given player could
be involved twice or more across the path. Path flow rate was calculated
as the number of edges per unit time from inbound to shot clock time at
the end of the play. To calculate degree centrality we used the
weighted graphs from iterated offensive plays across the two games.
However, we aggregated outcome data into two categories of shoot and
other, to reduce weighting bias from multiple outcome nodes. Degree was
first calculated per position as the weighted sum of total out-edges per
player. The relative distributions of player degrees were then
calculated across the graph, such that a homogeneous graph (connectivity
distributed most equally across all players) has zero degree
centrality. For a weighted graph
with weights summing to 1 and a vertex of maximal degree
the degree centrality is then:
(1)
To calculate
team entropy, we first determined individual player entropy. For this
metric we excluded inbound passes because of the strong weight of the
inbound edge. We included outcome, because the possibility of shooting
the ball represents a decision point contributing to uncertainty of ball
movement. As with centrality, outcomes were collapsed into two node
categories of shooting or not shooting. We used Shannons entropy
[15],
, to measure the uncertainty of ball transitions between any player or outcome.
We then
combined player entropies to determine entropy of the whole team. There
are multiple ways to calculate network entropy. One possibility is to
use a simple averaging of player entropies. A second is Markov chain
entropy, which incorporates the conditional probability of any given
player moving the ball to any other player, conditioned on the
probability that the given player has the ball. However, from the
opposing teams perspective, the real uncertainty of team play is the
multiplicity of options across all ball movements rather than just
across players. We thus calculated a whole-network or Team Entropy from
the transition matrix describing ball movement probabilities across the
five players and the two outcome options.
We used individual flow centrality to characterize player/position importance within the ball distribution network
[16].
Individual player flow centrality was calculated as the number of
passing sequences across all plays in which they were one of the nodes,
normalized by the total number of plays. We also calculated a more
restricted flow centrality that included only player appearances as one
of the last three nodes before an outcome. This allowed us to focus on
the set-up phase for a scoring drive and the actual scoring attempt. We
compared this more restricted flow centrality for successful versus
unsuccessful plays; this success/failure ratio was considered as a
measure of the utility of an individual player to team success.
To capture a
teams ability to move the ball towards their better shooters, we
developed a metric we call uphill/downhill flux, defined as the average
change in potential shooting percentage per pass. A team that has a high
positive uphill/downhill flux moves the ball consistently to their
better shooters; a team that with a negative value moves the ball on
average to the weaker shooters. The latter can happen if the ball
distributor (e.g. the Point Guard) is also the best shooter on the team.
Letting
be the shooting percentages for players
and
and
the probability of a pass from player
to player
, we define the uphill/downhill flux as:
(2)
Finally, we
wanted to compare teams in terms of relative player involvement, such
that we can differentiate those teams for which most players are
interconnected from those that rely consistently on a defined subset for
offensive plays. One way to do so is to look for the occurrence of
triangles, or connected 3-node subgraphs within the network. Teams with
higher connectedness will contain more cases in which sets of 3 players
have a link to each other; the maximum number of these triangles in a
group of 5 players is 10. The clustering coefficient measures the number
of triangles in a network as a percentage of all possible triangles.
However, a single evaluation of this metric is again problematic. If we
use all ball movement data, all nodes become connected to all other
nodes, and the clustering coefficient is uniformly high. Additionally,
it is important to remember that the triangles in these networks are
association links and not necessarily sequences of plays. Hence we
decided that the most meaningful measure to characterize the association
structure of the ball movements was to calculate the clustering
coefficients for undirected unweighted graphs across the different
cutoffs of the cumulative weight, beginning with the 30 percentile when
triangles first appear. This allowed us to compare teams with
consistently high clustering to those that showed triangles only when
less frequent links were included.
Results and Discussion Top
The
first question posed by this study was how well a network approach can
capture the game of basketball from a team-level perspective. We
constructed transition networks (i.e. stochastic matrices) as
first-order characterization of team play style for each team
individually and for the pooled set of all observed transitions across
all teams. Because even a single game generates a rich dataset, we
imposed thresholds to clarify the dominant transitions, highlighting
from most to least frequent the minimal set of transitions representing a
particular percentile of all ball movements. At the 60th percentile,
players in all but one network were connected to at least one other
player (the San Antonio Spurs Center was disconnected) and all teams had
an edge to at least one outcome, generally success. This matched the
expectation that these are elite and cohesive teams and gave us a
starting point for comparative analyses (weighted graphs for all teams
across the 30th to 70th percentile thresholds shown in Supplemental
Figures S1 and
S2).
To look at the NBA as a whole, we combined the transition data across all teams in a compiled network (
Figure 1).
As a note, although it is tempting to relate the structure of play to
physical location on the court, it is important to remember that these
data capture passing probabilities independently of spatial information.
In this network, as in an NBA game, the ball moved most frequently from
the inbound pass to the Point Guard and was rebounded either by the
Center or Power Forward. It was primarily distributed from the Point
Guard to other players, with most likely distributions to the Shooting
Guard or Power Forward. Other players generally distributed back to the
Point Guard, with lower weights to edges connecting the Shooting Guard,
Power Forward and Small Forward. The only edge to an outcome at this
weighting was from the Power Forward to a successful shot. This NBA team
thus showed a star-shaped pattern of ball movement controlled centrally
by the Point Guard, with a division of labor across positional roles.
Transitions from other players were most likely to be towards the Point
Guard. The Shooting Guard occupied a secondary leadership role by
creating connections between the Point Guard and the Power Forward who
functioned as the primary shot-taker. The role of the Center was
rebounding and redistribution to the Point Guard.
The
importance of the Point Guard in distributing the ball identifies this
as the primary leadership position in the team network. If we define
leadership as the relative importance of any player or position in the
network, we can capture this quantitatively using individual flow
centrality, or the proportion of paths (offensive plays) involving a
particular node
[16]. We compared flow centrality across positions from all data (ANOVA; F = 42.02; P =
; df = 4, n = 80 (
Table S2); and for the three players contacting the ball before a shot (F = 36.12; P =
).
As expected from the network graphs, the Point Guard position had the
highest mean centrality across all positions and was highest for the
majority of teams (
Figure 2).
Flow centrality was conversely lowest for the Center, with intermediate
and similar values for other positions. Two notable (but unsurprising)
exceptions to this rule were the Cleveland Cavaliers, for which the
Small Forward had high flow centrality, and the Los Angeles Lakers, for
which the flow centrality of the Shooting Guard matched that of the
Point Guard. These deviations match leadership roles within these teams
by LeBron James and Kobe Bryant respectively. It will be interesting to
compare their shifting network roles as their teams have changed; one
moved to a team with an increased number of skilled offensive players
(and the winning team in 2012), and the other’s team recently gained a
new point guard (Steve Nash) known as an offensive strategist.
Team Network Graphs
How do individual teams vary around this centralized model? The star pattern was most exemplified by the Bulls (
Figure 3), who inbound only to the Point Guard at
,
and for which most passes were between the Point Guard and other
players. Their high degree centrality is illustrated by considering that
removing the point guard node would cause all other player nodes to be
completely disconnected. A similar disconnect would happen to five of
the sixteen teams at 60% weighting and nine teams at 50% weighting (
Figure S1 and
S2).
There are trade-offs to a highly centralized team between clarity of
roles and flexibility of response. Lack of player connectedness may
allow the defense to exploit a predictable weakness in the network by
moving defenders off disconnected players to double team.
Deviations from the Point-Guard centered star pattern confirmed known team playing styles (
Figure 3).
In the 2010 Cleveland Cavaliers network the Small Forward was a highly
weighted distributor of the ball, as expected by his high flow
centrality (
Figure 2).
He also shot the ball successfully at an edge weight close to the Power
Forward. Thus the network visualization again picked up Le Bron James
combined skills in ball distribution and shooting. However, perhaps the
most important deviation from a centralized network strategy appeared in
the weighted graphs of the Los Angeles Lakers. Even at low weighting,
their network included multiple between-player edges beyond those
connecting to the Point Guard. One way to analyze the impact of these
additional edges is by quantifying the frequency of triangles within the
network
[17] via a clustering coefficient
[14].
Figure 4
shows the cumulative clustering coefficients of each team from the 30th
to 70th percentile weighting. The Lakers had the highest cumulative
clustering coefficient, primarily because they had high connectedness in
their most frequent plays. In a highly clustered network like the
Lakers, passing decisions are made by multiple players, expanding the
possible paths that must be considered by the opposing team. In the 2010
first round only two other teams showed comparable cumulative
clustering: the Boston Celtics and the San Antonio Spurs. Like the
Lakers, the Celtics - who also reached the finals - built triangles even
at relatively low weighting. The Spurs were unusual in that they had
low connectedness when considering their most dominant edges, but high
clustering when less frequent passes were included in the analysis (i.e.
at the 70th percentile).
The
network concept of triangles as a fully connected subgroups translates
well to the Lakers highly discussed triangle offense. Jackson and Winter
[8]
define the triangle offense as a spatial concept, in which a group of
three players is set up on one side of the court connecting to a
balanced two-man set on the other side. It is designed to distribute
players across the floor so that they can be used interchangeably,
depending on open lanes and defense. In this strategy the Point Guard
becomes less central to the decision process, because all players have
the ability to make decisions about ball distribution depending on
immediate context. Thus the triangle offense can be considered as a
network strategy that can be visualized in the Lakers weighted graph.
Team Network Signatures: Degree Centrality and Entropy
An important
question is whether differences in the weighted team graphs can be
captured more quantitatively by network metrics. As discussed above, a
primary visual distinction in our weighted graphs was between teams
using a central player to distribute the ball, and those moving the ball
across multiple players. Our calculated degree centralities in general
matched our visual networks (
Table 2).
The data were not definitive, however, in whether less centralized
teams had an advantage in the 2010 play-offs. Five of the 8 winning
teams had lower degree centralities than opponents, but overall rankings
of centrality showed no pattern of win/loss.
Like
degree centrality, entropy should be strongly influenced by the extent
to which multiple players distribute the ball. Degree centrality and
team entropy were negatively correlated (Pearson product moment
correlation = −0.6; p<0.003; n = 16), but they captured somewhat
different aspects of ball distribution, because team entropy takes into
account probabilities outside the network topology. Variation in team
entropy was more closely connected to individual team success/failure;
winners in 6 of the 8 first round match-ups had higher team entropy, and
when entropies were ranked from highest to lowest, 5 of the 8 highest
entropies were for winning teams. The play-offs only provide 8
match-ups, too small a sample size to make a statistically meaningful
claim (and it would be a simplistic game that allowed a predictive
single metric). However, our analyses do suggest that these combined
network metrics have value in: (1) capturing variation in team offense,
and (2) supporting the hypothesis that complex and unpredictable ball
distribution pattern is an important component of team strategy. Indeed,
the 2010 Lakers and Celtics teams were arguably built around this
principle. The highest entropies overall were achieved by the Lakers and
Celtics, and the Lakers simultaneously had the lowest degree
centrality. These assertions would be tested by the subsequent play-off
seasons, one in which a team known for its dominant forward was
successful (2011 Dallas Mavericks) and the next in which the winning
team was built around the multi-player model (2012 Miami Heat).
Uphill-downhill Flux and Passing Rate
The Dallas
Mavericks, who lost in the first round in 2010 but won the title in
2011, are an important counter-point. Their strategy was clear; move the
ball consistently to their best shooter. To capture this
quantitatively, we developed a new metric that uses flow flux to compare
individual player flow centrality with calculated shooting percentage
for each player across the two games. Uphill/downhill flux measures the
degree to which teams move the ball towards versus away from players
relative to their differential shooting success (
Figure 5).
High uphill/downhill indicates a different set of priorities in ball
distribution than entropy. It focuses on playing to strengths by
separating the roles of ball distribution and scoring, moving from
distributors to shooters. Unsurprisingly, the 2010 Mavericks had the
highest uphill/downhill flux of all teams in the play-offs. Success in
this strategy was not connected consistently to team success within our
data set. However, it is notable that only three teams had a combination
of both higher uphill/downhill and higher entropy than their opponents.
Two of the three were the Lakers and the Celtics; the third was the
Heat.
Our final team-level metrics were path length and flow rate (speed of ball movement through the path;
Table 3).
Recently, there has been increased interest in small ball teams, which
distribute the ball quickly across players. Small ball has been
hypothesized to allow teams to achieve success beyond what would be
expected based on individual player skill levels. The exemplar small
ball team in past years has been the Phoenix Suns
[18].
However, in 2009–2010 they transitioned away from this approach. We
predicted a correlation between path length and flow rate, such that
some teams distribute the ball quickly and across multiple players, but
surprisingly little variation in path length or ball movement speed
showed in our data.
Player Value
A question in evaluating any organizational network is the relative value of its individual members
[11]. Duch et al.
[16]
used individual flow centrality to show that higher paid players in
soccer teams are in fact strong contributors to ball movement during a
game. We asked a similar question for basketball, by quantifying player
involvement in paths with successful versus unsuccessful outcomes. For
our analyses we used only those sequences with at least 3 of the 5
starting players on the floor. We matched each player to position and
excluded any sequences in which starters clearly rotated into a
different position than assigned. This allowed us to analyze individual
player contribution by position, using flow centrality analyses to
determine the relative frequency by which any player was involved in (1)
all, (2) only successful, and (3) only unsuccessful plays. We used the
ratio of (2) to (3) to determine whether we could quantify player
“value” beyond apparent dominance in the game (
Table 4).
We
found an interesting positional bias in the data, with the Center often
having the highest success/failure ratio. In contrast, Point Guards
tended to have success/failure ratios at or below 1.0. Although the
ratio measure should statistically control for frequency effects, we
suggest this metric might be biased mechanistically by relative player
involvement. The low flow centrality of the most highly utilized
position reflects the argument that high frequency player contributions
become negatively affected by exposure. The nonlinear relationship
between player involvement and success in our metrics may thus
illustrate the price of anarchy
[13],
the expectation that maximizing gain within any given offensive play
can ultimately jeopardize overall game efficiency. If entropy is
valuable, as our data suggest, then moving the ball frequently to a
specific player or position is costly, because it allows the opposition
to adjust their defense accordingly.
Conclusion
We have
presented a network structure analysis of basketball teams in the
context of team coordination and strategy. As a starting point, we
applied network-level metrics to quantitatively measure fundamental
components of team offensive strategy, moving currently available
individual player metrics (examples at NBA.com). The study involved more
than a thousand ball movements and typically more than one hundred
sequences or paths for each team. This dataset allowed us to capture the
game of basketball as a network. Because our team comparisons were
limited to the pairs in the first round of the play-offs, correlations
between game outcome and specific aspects of network structure could not
definitively test the specific hypotheses suggested. Answering the
question of how network dynamics contribute to successful team strategy
will be more complex than a single network variable can capture. We also
expect intransitivity across games and opponents, such that the success
of emphasizing any given strategy is dependent on the behavior of the
opposing team. However our data do suggest that certain metric
combinations, particularly entropy, centrality, and clustering, are
relevant components of team strategy.
One of the
advantages of this beautiful game is the wealth of available data. We
encourage the expansion of both the network toolbox and the datasets
analyzed. Analyses across a season will help determine whether network
structures for a given team are stable or whether they respond flexibly
to different defense strategies. Dissecting network shifts within games
(e.g. the final quarter or as point differentials change) could help
explore game dynamics. Analyses across multiple seasons could track the
development of team cohesion. It would also be extremely useful to
connect network with spatial and temporal models; this may not be
practical with current data acquisition methods, but recent publications
[19] suggest that automated ball tracking in basketball games is becoming more feasible.
Beyond
basketball, this approach may act as a template for evaluating other
small team collaborations. Although the specific network metrics will
vary across the disparate contexts in which teams occur, the general
approach of analyzing network interactions and function is robust
[14].
Teams take multiple approaches to communication and leadership, from
centralized to decentralized, from more rigidly bureaucratic to
flexible, and from assigned roles to emergent. Each of these
organizational strategies corresponds with a specific network model. As
one example, our finding that the more successful teams distributed
decision making about ball movement beyond a centralized leader is
mirrored in models of business team structure. Network assessments
suggest that business teams with mixed leadership roles optimize
performance relative to highly centralized or highly distributed teams
[6].
It would be interesting to see how the network measures used here apply
to other small teams that are tasked differently, such as research
groups organized around innovation, remote military teams on assignment,
or intelligence agencies tasked with pattern recognition. The
application could also be expanded to animal teams in which roles
develop naturally rather than through external assignment, and for which
team success/failure has a direct connection to fitness. For example,
the ontogeny of team coordination is a general phenomenon. In hunting
teams of lions, chimpanzees and wild dogs, new members can require years
of practice to achieve coordination with the group
[1]–
[3].
These discussions highlight the potential of this approach and its
applicability across the broad array of contexts in which cohesive teams
are found.
Supporting Information Top
Figure S1.
Weighted graphs of ball movement for East Coast teams. Red edges represent transition probabilities summing to the percentile indicated in the column header.
(PDF)
Figure S2.
Weighted graphs of ball movement for all West Coast teams. Red edges represent transition probabilities summing to the percentile indicated in the column header.
(PDF)
Table S1.
Starting players and position assignments for the 2010 NBA playoffs, first round. Substitutes are in parentheses.
(PDF)
Table S2.
Player flow centrality.
Flow centrality (FC) is calculated as the proportion of all plays in
which a player was involved. Flow centrality based on outcome is
calculated as the proportion of successful (FC3 S) or failed (FC3 F)
plays in which a player appears as one of the last 3 player possessions
in the sequence.
(PDF)
Acknowledgments Top
We thank Alex
Gutierrez and Mark Goldfarb for their help in data collection and
analysis, and Jon Harrison and an anonymous reviewer for comments on the
manuscript.
Author Contributions Top
Conceived
and designed the experiments: JHF DA. Performed the experiments: JHF JI
AP. Analyzed the data: JHF JI AP DA JSW. Contributed
reagents/materials/analysis tools: JHF DA. Wrote the paper: JHF DA JI
JSW.
References Top
- Stander P (1992) Cooperative hunting in lions: the role of the individual. Behavioral Ecology and Sociobiology. 29(6): 445–454.
Find this article online
- Boesch C (2002) Cooperative hunting roles among Tai chimpanzees. Human Nature 13(1): 27–46.
Find this article online
- Gazda
SK, Connor RC, Edgar RK, Cox F (2005) A division of labour with role
specialization in group–hunting bottlenose dolphins (Tursiops truncatus)
off Cedar Key, Florida. Proceedings of the Royal Society B: Biological
Sciences 272(1559): 135–140.
Find this article online
- Anderson C, Franks NR (2001) Teams in animal societies. Behavioral Ecology 12(5): 534–540.
doi:
10.1093/beheco/12.5.534.
Find this article online
- Zaccaro SJ, Rittman AL, Marks MA (2001) Team leadership. The Leadership Quarterly 12(4): 451–483.
doi:
10.1016/S1048-9843(01)00093-5.
Find this article online
- Mehra
A, Smith BR, Dixon AL, Robertson B (2006) Distributed leadership in
teams: The network of leadership perceptions and team performance. The
Leadership Quarterly 17(3): 232–245.
doi:
10.1016/j.leaqua.2006.02.003.
Find this article online
- Eccles
DW, Tenenbaum G (2004) Why an expert team is more than a team of
experts: A socialcognitive conceptualization of team coordination and
communication in sport. Journal of Sport Exercise Psychology 26(4):
542–560.
Find this article online
- Jackson P, Winter T (2009) Triangle Offense. In: Gandolfi G, editor. NBA coaches playbook. Human Kinetics Publishers p. 89–111.
- Skinner B (2010) The price of anarchy in basketball. Journal of Quantitative Analysis in Sports 6(1).
- Wilson E, Hölldobler B (2009) The Superorganism. New York, NY: WW Norton & Co.
- Kniffin KM (2009) Evolutionary perspectives on salary dispersion within firms. Journal of Bioeconomics 11(1): 23–42.
Find this article online
- Freeman LC (1977) A set of measures of centrality based on betweenness. Sociometry 40: 35–41.
Find this article online
- Oliver D (2004) Basketball on Paper. Potomac Books Inc.
- Newman MEJ (2003) The structure and function of complex networks. SIAM review 45: 167–256.
doi:
10.1137/S003614450342480.
Find this article online
- Shannon C (1948) A mathematical theory of communication. Bell System Technical Journal 27: 379–423.
Find this article online
- Duch
J, Waitzman JS, Amaral LAN (2010) Quantifying the performance of
individual players in a team activity. PloS one 5(6): e10937.
doi:
10.1371/journal.pone.0010937.
Find this article online
- Milo
R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, et al. (2002)
Network motifs: simple building blocks of complex networks. Science
298(5594): 824–827.
doi:
10.1126/science.298.5594.824.
Find this article online
- McCallum J (2006) Seven Seconds or Less. New York City: Touchstone.
- Chen
F, De Vleeschouwer C (2010) Automatic production of personalized
basketball video summaries from multi-sensored data. Proceedings of 2010
IEEE 17th International Conference on Image Processing September 26–29,
2010, Hong Kong.
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