PageRank and Soccer
https://www.technologyreview.com/s/535861/pagerank-algorithm-reveals-worlds-all-time-top-soccer-team/
The Google PageRank algorithm has been proving its value since its discovery. The PageRank evaluation has been also used to explore complex data structures, primarily things such as web authorities nevertheless today researchers use the algorithm in order to rank scientific papers or even the “World’s All-Time Top Soccer Team” – which is precisely what a group of scientist did. In an article published in the MIT tech Review, on March 13 2015, we are revealed the way in which Verica Lazova and Lasko Basnarkov from the university of Macedonia used PageRank to create an “all-time ranking of the world’s national football teams.”
To understand how they did this we must first understand the algorithm itself. The PageRank update rule follows the concept of continuously updating nodes authorities and dividing their scores. In fact, as referred in the article, PageRank is rather intuitive as you start off with simple voting based on the weight of link endorsement and pooling. When we think of the weight in PageRank we generally think of the number of edges that point to a same node (the endorsement of that node within the graph from other nodes). In the case of web-authority the weight would be the amount of pages that direct you to a same page. From there, you would divide the assigned PageRank equally among its outgoing links.
Lazova and Basnarkov, used the results of the all 20 World Cup tournaments to determine the ranks of the teams. In this case the weight determining the PageRank is the amount of times it beat other highly ranked teams. They considered over 7000 games played between 210 countries. Nodes in this case were teams and links were the games played, the direction of the link would determine the winner of the games (the weight polarity). Take for example the graph below with four teams A B C and D. The link between A to C with a weight of 1/3 and C to A with a weight of 2/3 means that out of 3 match A and C have played between each other A won 2 matches and C won 1. For this example, the final PageRank calculation is 0.333 for A (considering all other games played) and 0.28 for C. They did this with all 210 nodes (teams).
The results were rather expected: Brazil was the top ranked team (“this is unsurprising since it won the tournament 5 times more than any other nation”) then comes Italy, Germany, Netherlands, Argentina, England, Spain, France… A major use for this ranking is that some of these results did not correspond to the FIFA rankings (for example argentina is 4th ranked in FIFA but 5th in PageRank list). Thus PageRank can be used to confirm and introduce new rankings and authorities for different situations