This paper describes the applications of network methods for understanding interaction within members of sport teams.We analyze the interaction of batsmen in International Cricket matches. We generate batting partnership network (BPN) for different teams and determine the exact values of clustering coefficient, average degree, average shortest path length of the networks and compare them with the Erdös-Rényi model. We observe that the networks display small-world behavior. We find that most connected batsman is not necessarily the most central and most central players are not necessarily the one with high batting averages. We study the community structure of the BPNs and identify each player's role based on inter-community and intra-community links. We observe that Sir DG Bradman, regarded as the best batsman in Cricket history does not occupy the central position in the network − the so-called connector hub. We extend our analysis to quantify the performance, relative importance and effect of removing a player from the team, based on different centrality scores.Keywords: Complex network; Small world behavior; Centrality scores; Cricket.
IntroductionIn recent years there has been an increase in study of activities involving team sports. Time series analysis have been applied to football [1,2], baseball [3,4], basketball [5,6,7] and soccer [8,9]. Again, a model-free approach was developed to extract the outcome of a soccer match [10]. The study of complex networks have attracted a lot of research interests in the recent years [11,12]. A salient feature of such complex networks is that they display small-world behavior [13]. The tools of complex network analysis have previously been applied to sports. Such as a network approach was developed to quantify the performance of individual players in soccer [14] and football [15]. Network analysis tools have been applied to football [16], Brazilian soccer players [17], Asian Go players [18]. Successful and un-successful performance in water polo have been quantified using a network-based approach [19]. Head-to-head matchups between Major League Baseball pitchers and batters was studied as a bipartite network [20]. More recently a network-based approach was developed to rank US college football teams [21] The complex features of numerous social systems are embedded in the inherent connectivity among system components [11,19]. Social network analysis (SNA) allow researchers to explore the intra-group and inter-group relations between players, thus providing an informal relation between various players. Such an analysis provides insight about the pattern of interaction among players and how it affects the success of a team. This article points out that topological relations between players need to be explored in order to better understand individuals who play for their teams. SNA is well suited to investigate the complex relations between team members [24]. Such an approach to cricket at the microscopic level, form a basis of elucidating the individual importance and impact...