Overview | Rankings and ratings can have considerable, and serious, implications. How do we determine that a student, team, school, teacher or policy is better than another? And what does “better” mean? In this lesson, students explore the use of quantitative ratings by examining how Division I college basketball teams are ranked, and how specific mathematical decisions can have significant consequences.
Materials | Computers with Internet access; Simple Spreadsheet software (optional)
Warm-up | Tell students to pair up and work with their partners to answer the following questions:
How can we determine the top student in school? Would you use a single variable, like grade point average? Or would you create a ranking system based on multiple variables, like G.P.A. and standardized test scores, activity participation and perhaps other factors? How might you begin to create a fair composite ranking system using quantifiable measures?
Let the pairs work for about 10 minutes to construct working systems that they believe would produce a “fair” student ranking. Then invite the pairs to share their ideas, and compare and contrast the methodologies and criteria the various groups put forth.
Discuss the pairs’ ideas using some or all of the following questions: Are all of the proposed categories equally important? Or should G.P.A. count more than, say, sports participation? Should we consider which classes a student has taken? Are some classes harder than others? How do we decide? Is it fair to use attendance as a criterion? What if a student were ill for an extended period? What other factors should be taken into account when creating a ranking system?
Explore the notion that deciding what quantities to use in a ranking, and how to weigh each of those quantities, makes a big difference in the ultimate rankings. For example, there might be different “top students” as determined by, say, the parent-teacher association and various academic departments; the school “scholar athlete” may well be a different person from the valedictorian.
Explain that in order to understand what these rankings really mean, one must understand the mathematical formulas that are used to create them. Tell the class that they will now explore these ideas using the Ratings Percentage Index (R.P.I.), the standard ranking system in N.C.A.A. basketball, as our example.
Related | In the FiveThirtyEight blog post “In N.C.A.A. Tournament, Overachievers Often Disappoint,” Nate Silver looks at the numbers behind March Madness, specifically the Associated Press preseason poll:
