## PageRank in Soccer

http://www.technologyreview.

http://arxiv.org/pdf/1206.

Another real-life example of the advantages of the PageRank system, which we have used to give web pages ranks based on the number of other web pages that they link to, can be seen in a map of players on a soccer field. Pena and Touchette apply properties of web networks to analyze the relationships among soccer players during a game. To model a soccer team using PageRank, we would treat each player as a node, and any successful pass between two players increases the weighting of that edge between the player nodes. Now, each player’s rank would be determined in the same way that we determine ranks using the Basic PageRank Update Rule, and the players with the highest rank value would be those through whom the ball is most likely to circulate.

So, to optimize gameplay, it would be the best strategy of a coach to place the most skilled players in locations where their ranks could be optimally matched to their position. When designing plays in preparation for a competition, it is also important to strategically respond to the way opposing players may place themselves; that is, where edges may be formed or possible at any point during the game. It would definitely be interesting to simulate gameplay based on the instincts of players to move to locations where there are gaps in the field (and where there are edges between nodes in our graph simulation), to figure out what the best player-placing strategy would be. Not only is this a good example of PageRank, but it also provides a more complex problem and graph that can be further investigated using some of the game theory strategies that we have discussed so far this semester.

As seen in the diagrams of the formations of the Netherlands and Spain teams in the attached articles, Spain had many more passes during the game and coincidentally won. Will the team with the most edges, and therefore the most passes, always win? Using PageRank to analyze this data, would Italy decide that more edges could have won them the game? Although this question seems simple, the best layout for any given team would depend on the skill depth of its players. A team with many strong players would want each player to have relatively equal ranks, while a team with a single strongest link would want a layout that permits one player with a higher pass frequency than the others: one significantly higher-ranked node. Would it also be beneficial to keep track of transfers from one team to another? If we could keep track of which ball-stealer has the most incoming edges from the other team and which has the most outgoing edges to the other team, we would know our strongest and weakest links in terms of stealing the ball from the other team and losing it due to errors. Using networking strategy to model a soccer game provides many ways to answer these questions and strategize for games to come.