March Madness in the Classroom

Calculating Prior Expected Values of the Tournament Teams

Students must estimate the potential returns from each tournament team so they may determine their maximum bid in the auctions. The NCAA basketball tournament invites sixty-four teams to play, so each team can potentially play up to six games.

Sponsorship values are determined by a team’s success in the tournament:

· The thirty-two teams that win their first-round game provide $10,000 in sponsorship value to their apparel company. (The thirty-two teams that initially lose do not provide any value to their sponsoring company.)

· The teams that win their second game to reach the “sweet sixteen” provide an additional $20,000 in sponsorship value ($30,000 total).

· The teams that win their third game to reach the “great eight” provide an additional $25,000 in sponsorship value ($55,000 total).

· The teams that win their fourth game to reach the “final four” provide an additional $50,000 in sponsorship value ($105,000 total).

· The teams that win their fifth game to reach the championship final game provide an additional $75,000 in sponsorship value ($180,000 total).

· The team that wins its sixth game and is crowned the “NCAA champion” provides an additional $100,000 in sponsorship value ($280,000 total).

To calculate the expected value of a particular team in the tournament, one must consider the probability that the team will reach each additional round in the tournament, the probability the team will face a particular opponent in each additional round, and the probability the team will beat each opponent in each round. Conceivably, a team could end up playing any of the other sixty-three teams in the tournament, so one must determine the probability, , that team i will beat opponent j for all possible i and j. We also define the probability, , to represent the probability team i wins round r in the tournament.

The following is an example of the expected sponsorship value of a team identified as Team 1. (The numbers of the other teams in this example do not represent seedings in the tournament. Team 1 plays team 2 in the first round; if team 1 wins it plays the winner of team 3 versus 4 in the second round; if team 1 wins the second round it plays either team 5, 6, 7, or 8 in the third round; etc.)

Expected Value for Team 1 =

where:

Calculating the expected sponsorship value of all sixty-four tournament teams requires students to determine their private estimations of each probability, , that team i will beat opponent j for all possible i and j. This may appear to be a daunting task, yet using a spreadsheet package like Microsoft Excel can significantly ease the process. A spreadsheet is included with these exercise materials that automatically calculates each team’s expected value once students enter every . Instructors may require students to create their own spreadsheet or they may allow students to use the spreadsheet provided here. Before the classroom auction, students may hand in a report from their spreadsheet that indicates their expected values of each team in the tournament.