The Use of PageRank as a Ranking Algorithm for Soccer Teams
In this paper written by Verica Lazova and Lasko Basnarkov of Cyril and Methodius University, the PageRank algorithm is used as a way to rank national soccer teams relative to their performance compared to other nations in the world cup. In their data analysis, they took historical results from over 7000 world cup games from 210 countries over the past 80 years, thus giving a broad dataset to base their historical rankings. In order to give weighing functions between the two soccer teams/vertices, one edge is drawn from one vertex to another if edge A loses to edge B, and if the opposite were to occur, the direction of the edge would be flipped. Through this generation, the teams that would generally tend to win the majority of their games will end up having a very large in-degree in addition to the fact that the teams that beat other good teams will benefit more heavily from that.
The use of PageRank as a way to rank competitors in a sport differs heavily from the way that it was originally intended, which was to to classify the importance of a page based on how it performs relative to other pages, and then in the case of something like a Google search engine, be able to rank them based on the results that are obtained. However, in the case of other ranking algorithms, the numbers obtained from the PageRank algorithm are not incredibly useful in comparing the difference in skill between the other two, or if there was a difference in PageRank in the two teams, what the probability of victory for one team would be relative to another team. One other popular ranking algorithm that is widely used in Elo, and with this system, there is a finite probability for win percentage for people with different Elo ratings. For example, if one person/team were to have 100 more Elo points than another player, they would have a 64% chance of beating them and if they were to have aa 200 point discrepancy they would have a 76% chance of beating them. With PageRank, the values obtained from the continual steps provide no additional knowledge for these types of categories.
While having some flaws with respect to individual performance and the use of comparing two teams under means that aren’t directly having a higher or lower PageRank, the concept of using PageRank as a means to compare teams with wins and losses as the way to measure out-degree and in-degree puts an interesting spin on techniques that can be used to rank different features that aren’t just search relevance. It would probably be worthwhile to obtain more research about the use of PageRank in other such fields that require rankings based on relevance to competitors and a means to apply directions to the competitors, such as through wins and losses.
Sources:
http://arxiv.org/abs/1503.01331
https://en.wikipedia.org/wiki/Elo_rating_system