We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
“Who's number 1?” is a question asked and analyzed by sports announcers before, during, and sometimes even after a season. “We're number one!” is the cheer athletes chant in the pandemonium of success! In this chapter, we learn to apply linear algebra to sports ranking. We compute mathematical “number 1s” by ranking teams. We'll see how the rankings can assist in predicting future play. We'll apply the methods to two tournaments: March Madness and FIFA World Cup. You can learn more about these in [5, 1, 2].
Soon we'll learn how to compute teams' ratings to determine who is number 1 and also who is number 2, 3, 5, 8 and so forth. Here lies the important distinction between ratings and rankings. A rating is a value assigned to each team from which we can then form a ranking, an ordered list of teams based on a rating method. Solving the linear systems that we will derive produces the ratings. Sorting the ratings in descending order creates a ranked list, from first to last place.
When someone wants to rank teams, a natural rating to start with is winning percentage. This is done by computing each team's ratio of number of games won to the total number of games played. This includes information only about each game's end result and can lead to misleading information. For instance, if Team A only plays one game and they win, then their winning percentage rating would be 1. If Team B plays 20 games and goes undefeated, their winning percentage rating would also be 1. Intuitively, Team B is more impressive since they went undefeated for 20 games, while Team A only won once. But, both teams have the same winning percentage, so this rating system would produce a tie when ranking these two teams.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
