Power Rank – Redefining Sports Rankings
Rankings and statistics have always played a crucial role in the field of sports. Not only are rankings used to assess and gauge different teams, but they can also have real economic impacts, for example, in the sports betting market. However, most of us probably only take these rankings for granted without questioning how these rankings were actually assigned. This article talks about a new algorithm for ranking sports teams, called the Power Rank. According to the developer of this ranking system, Ed Feng, the Power Rank algorithm collects only two types of data: the game score and the home field advantage. In theory, this method should provide a more accurate ranking than traditional ranking systems which are often one-dimensional, such as ranking systems that only analyze win-loss record. To give an example of how this algorithm works, the article gave a simple example. In the NFL, suppose that San Francisco defeats Chicago 55-21, Chicago defeats New York 23-20, and New York beats San Francisco 35-32, with each team winning at home. According to the traditional ranking system, all these teams would be equally ranked, since they have the same number of losses and wins; however, the Power Rank system is able to analyze these teams beyond winning and losing teams in each individual game and find out the correlation between games. Given the above information, the Power Rank system is able to resolve the seemingly contradictory results that New York won against San Francisco, despite being beaten by the team Chicago, who got defeated by San Francisco. Using Power Rank, San Francisco would be ranked first, followed by New York and Chicago.
As mentioned in the article, Feng’s Power Rank algorithm was in fact inspired by Google’s PageRank algorithm. Using what I learned in class, I was able to get a much better understanding of how the Power Rank algorithm works. In class, we learned that the primary method in which PageRank sorts webpages is by looking at the number of pages and the quality of pages linking to that page. The greater the number of pages linked to the page, and the better the quality of pages, the more highly valued the page is. The same reasoning can also be applied to understand how the above rankings under the Power Rank algorithm are determined. Using the same NFL example given above, let us analyze the rankings given to San Francisco, Chicago and New York. First, let us compare all the match outcomes. From all of the outcomes, the match between San Francisco and Chicago has the most lopsided win, indicating that San Francisco should be theoretically stronger than Chicago. Under this premise, let us consider the respective match outcomes for Chicago and New York. While Chicago lost to San Francisco and won against New York, New York won against San Francisco and lost to Chicago. Considering the winning outcomes for both teams, the difference in score is the same for Chicago and New York. However, New York’s win against San Francisco is valued more highly than Chicago’s win against New York because while New York beat San Francisco, Chicago was beaten by San Francisco. Also, our inference from the match between San Francisco and Chicago does not provide any information about the strength of New York. Therefore, while we cannot give any extra credits to Chicago for defeating New York, we would naturally give New York more credit for defeating the stronger team that we know so far, San Francisco. Thus, New York is valued and ranked more highly than Chicago. This is analogous to the fact that authorities that are connected by “higher quality” hubs are valued more highly. In order to see the link between the Power Rank algorithm and the PageRank algorithm, let us consider an example where we have two pages with the same number of pages linked to each respective page, where page A is directed by more hubs which point to similar pages, and another page B is directed by hubs which point to very different pages. In this case, it is clear that page A is valued more highly than B because the hubs which point to A form a mutually reinforcing set of hubs, suggesting A is a higher quality page than B. In conclusion, we can see that the sports algorithm Power Rank in fact works in a very similar way that PageRank does. More importantly, this article also sheds light on how the algorithm used in PageRank can also be applied for use in many other fields.