MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM

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MATHEMATICS BEHIND GOOGLE PAGERANK ALGORITHM ( mathematics-behind-google-pagerank-algorithm )

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CHAPTER VI OTHER APPLICATIONS OF PAGERANK 6.1 NFL Rankings The PageRank algorithm has been applied to other fields as well. Zack, Lamb, and Ball (2012) applied it in an effort to rank NFL teams accurately. Zack et al. (2012) applied what they refer to as the GEM method, which uses the margin of victory between two teams to weigh the link between them. If teams play multiple times, then the sum of points won by is weighted on the outgoing link from each victorious team. By using this method, Zack et al. (2012) build the hyperlink matrix: 1/ ∑nm=1(vim − vjm ) if vi is greater than vj Mij =  (VI.1) 0 otherwise, or if n = 0 Where v is the score from each team in their games, and n is the number of games between teams. Zack et al. (2012) then did the same thing for total yardage, turnovers, and time of possession, with the score rankings noted as GEM 1 and the composite as GEM 2. They compared them using a Kendall rank correlation, defined as τ = (nc − nd)/(n(n − 1)/2), where nc is the number of concordant pairs and nd is the number of discordant pairs in the rankings. After Zack et al. (2012) removed the least-correlated statistic, they found that they achieved a Kendall rating of τ = 0.60. The method Zack et al. (2012) used had room for variability and could be adjusted for use with other sports as well. 28

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