Let us today look at a very interesting application of complex networks in identifying the greatest cricket team and captain. We would numerically estimate the success of a team as well as the captain by analysing the network of interaction of competing teams and also the captains.
We will consider all Test matches played between 1877 and 2010 and ODI matches played between 1971 and 2010. The success of a team or captain is decided by the quality of win rather than number of wins alone. We form directed and weighted network of teams and their captain. We apply the diffusion based page rank algorithm on the network to rank the teams. In short we would quantify the success of the teams and their captains.
Networks of Cricket Teams
Three teams A,B and C compete against each other. If A defeats B, a directed link is establised from B to A. The thickness of the link is proportional to the fraction of wins between A and B. Thus considering all the teams a weighted and directed graph if formed. We quantify the relevance of matches with the use of a complex network approach equivalent to the one used for the computation of page rank score.
Mathematically, the process is described by the following set of equations
where wji is the weight of the link and sj(out) is the out strength of a link. pi is the page rank score assigned to team i and represents the fraction of the overall "influence" sitting in the steady state diffusion process on vertex i. q is a control parameter that accounts for the importance of the various terms contributing to the score of the nodes and N is the total number of teams in the network.
|The network of teams in the history of Test cricket (1877−2010)|
The choice of q is set at 0.15 and ranking scheme is run on networks of cricket teams and also on their captains. As expected Australia is identified as the most successful team in both forms of the cricket. Steve Waugh is ranked as the best caption in test format and Ricky Ponting as the best caption in ODI.
|Subgraph of most successfull captions|
The work demonstrates the strength of social network analysis methods in quantifying the success of cricket teams and their captains. The correct assessment of a team's success needs the consideration of entire network of interaction. The Page Rank algorithm takes into account the quality of matches won. For example, a win against a strong team is more important than a win against a weak team. The analysis shows that Page Rank algorithm is effective in finding the most successful team and caption in the history of cricket.
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