Relating PageRank and Football Rankings
Recorded by IEEE Spectrum’s Steven Cherry, Cherry interviewed two academics who were apart of a group of mathematicians who compared ranking football teams and Google’s PageRank. The two “have more in common than you might think”. The group’s research was posted in an issue of the Society for Industrial and Applied Mathematics’ Journal of Scientific Computing. In their research, they compared the algorithms used to rank football teams, namely the Colley method and Massey method, to Google’s PageRank algorithm.
One of the problems with Google’s PageRank algorithms, as introduced in this interview was the variability it has for rather specific searches. For example JC Penney was ranked number one for the search terms “dresses” and “living room furniture” until google slightly tweaked their algorithm and JC Penny dropped all the way to below 50. The research group explains this may be due to the “power”nature of google’s PageRank algorithm or more explicitly, if one graphs the rating of googles pages, the PageRank follows a power rule. As one of the research members Tim Chartier put it “highest-ranked Web page, for instance, if we’re talking Web pages, has a very high rating. But then very quickly as you move along to those lower-rated Web pages, those all have a very small page rank, which means they have a very small rating and they’re very close to each other.” This would explain why a small change in the system would cause some rankings to drastically shift, especially those with small PageRank. The researchers believed that the Colley and Massey method did a better job at eliminating this but did not really go into much detail. However, it is still notable that Google’s PageRank algorithm does a better job overall at ranking pages consistently than did the Colley or Massey methods (as to be expected) and vice-versa for football rankings.
As it turns out, the researchers explained that the Colley method seems to be the underlying model that PageRank is built on, which is cool because this is what is used to rank football teams. The similarities of these two ranking systems is interesting. Just like the rating of a webpage depends on the rating of all the page’s that are pointing to it, football rankings depend on the ranking of those teams that you win and lose to. A win in football can be considered like “a link from one page to another” in some sense.
This topic obviously relates to our class discussion of PageRank, as we discussed in decent detail of how google’s PageRank algorithm worked by relating one pages rank to another, or, how the article put it “you actually share your page rank”. The article discusses a way to raise your page rank is to have other high ranking, high quality, pages point to you. Or, in the sports equivalent, to rise in rank you win against other high quality teams. As discussed in class this is a very interdependent system, which we simplify for our understanding, but it is basically like a linear system in that each page rank depends on another. It is refreshing to see PageRank and other ranking algorithms applied outside of the class context, as these thing do show themselves in the “real world” quite often, as should be expected.
http://spectrum.ieee.org/podcast/at-work/innovation/football-rankings-versus-googles-pagerank