March Madness in the Classroom

Instructor’s Guide

Overview of the March Madness Exercise

Learning Objectives

Description of Classroom Activities

            Class #1 (1 hour) Auction Theory Discussion

Class #2 (1 hour) Calculating Expected Values

Excel Homework Assignment

            Class #3: (1 hour) The March Madness Auctions

            Class #4:  (1 hour)  Follow-up Discussions and Analysis

Online materials for the March Madness Exercise

            The 2005 NCAA Men's Basketball Tournament Expected Values Spreadsheet          

             Managerial Economics Spring 2005 Class Results Spreadsheet

A Variant of the exercise to use in months other than March

Overview of the Exercise

The March Madness in the Classroom exercise simulates the many phenomena associated with auctions of commodities with unknown values.  Oil lease auctions and the Federal Communication Commission’s spectrum auctions are two well-known examples.

You can use the NCAA Tournament as a vehicle to teach auction theory, risk management, and expected values.  The premise is that each of your students will represent a different athletic apparel company vying for the sponsorship rights to the NCAA tournament teams.  Each NCAA team will put their sponsorship rights on the auction block individually.  When a team is on the block, the student with the highest bid will win the rights to that team.  The value of each sponsorship right will be determined by the exposure a team achieves in the NCAA tournament.  The longer a team stays in the tournament, the more valuable the sponsorship.  Before the tournament begins, students will calculate their a priori expected values of each team to determine their valuations in the ensuing auctions.  

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Learning Objectives  

At the conclusion of the exercise, students will: 

·        be able to perform a very intricate calculation of the expected value of each tournament team using spreadsheet software; 

·        understand their attitudes toward risk as they take their risk neutral expected values and convert them into maximum valuations for bidding in auctions; 

·        know how to bid in different auction formats and understand the effects of learning and competition in an open outcry auction;

·        understand risk management and portfolio diversification while buying and selling full or partial sponsorship shares;

·        understand the “winner’s curse”. 

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Class #1 (1 hour) Auction Theory Discussion 

To get the most benefit out of the exercise, an instructor may wish to discuss the following concepts with students before conducting the exercise. 

The Winner’s Curse

The winner of an auction for a commodity with unknown value will most likely be the bidder who has the highest estimated value of the good.  Typically, the winner overestimates the value and then overpays in the auction.  Bidders need to significantly shade their bids to ensure that if they are the highest estimator of value, they do not overpay for a good.  Before the March Madness in the Classroom auction, an instructor may consider discussing the winner’s curse using the popular “Jar of Pennies” auction.  The instructor brings in a jar of pennies and asks students to estimate the number of pennies in the jar.  The instructor then allows students to bid on the jar (using a sealed bid or an open outcry format).  Invariably, the student who wins the auction has overestimated the number of pennies in the jar and spends more than the jar’s value.  Although this instruction should help students bid with more savvy in the March Madness in the Classroom auctions, the “Winner’s Curse” still tends to appear in these auctions as well.    

Bidding Strategies

An instructor may wish to discuss bidding strategies in a first-price open outcry auction, a first-price sealed bid auction, and a second-price sealed bid (Vickrey) auction.  Students should be familiar with how bidding strategies change when bidders’ valuations are common or private and known or unknown.  In the March Madness in the Classroom auctions bidders’ valuations are private and unknown.

Risk Management

The bidders’ estimation of a team’s sponsorship value is based on private beliefs of the probabilities every team will win against every other team in the tournament.  Assuming these probabilities are accurate, a team’s estimation of value is the average payout one may expect if the tournament is played an infinite number of times.  Only a risk neutral bidder can examine this expected value and compare it with a guaranteed payout of the same value.  An instructor may wish to discuss attitudes toward risk before the March Madness in the Classroom auctions to ensure that bidders properly interpret the sponsorship expected values.          

Portfolio Diversification

In the March Madness in the Classroom auctions, individual students will purchase full sponsorship rights to teams in the tournament.  Once the auctions are complete, students may sell these rights in full or partial shares at any time.  Before the auction, students may consider working in a group.  It is up to the instructor to encourage students to do this or to observe whether they do it on their own.  One member of a group may purchase a team and then sell partial shares to the rest of the group after the auction.  This practice may limit the group’s risk and it may keep bid prices lower as there is less competition for sponsorships. 

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 Class #2 (1 hour) Calculating Expected Values

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 in these materials.  Before the classroom auction, students may hand in a report from their spreadsheet that indicates their expected values of each team in the tournament.

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Excel Homework Assignment

Students must create a spreadsheet to estimate the potential returns from each tournament team so they may determine their maximum bid in the auctions.   Students will create an eight-team tournament spreadsheet.  (The NCAA basketball tournament invites sixty-four teams to play, and the 64 team spreadsheet is provided to students in these materials.)

In an eight team tournament, sponsorship values are determined by a team’s success in the tournament: 

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

·        The two teams that win their second game provide an additional $20,000 in sponsorship value ($30,000 total).

·        The team that wins the championship (and the third game) receives an additional $25,000 in sponsorship value ($55,000 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 seven 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.  Team 1 plays team 8 in the first round; if team 1 wins it plays the winner of team 4 versus 5 in the second round; if team 1 wins the second round it plays either team 3, 6, 7, or 2 in the third round.)  

Expected Value for Team 1 =

where:

I have students develop a spreadsheet for an eight team tournament.  The Excel “workbook” must have three sheets:

Sheet 1: Probability Entry Sheet – This sheet will have the probability entry matrix for all eight teams in the tournament.  Your spreadsheet should allow an entry for the probability that Team 8 beats Team 1 (for example), but the probability that Team 1 beats Team 8 should be a calculation.   The only place for data entry in the workbook will be on this sheet – and only have of the probability matrix will be entered – the other half will be automatically calculated.

Sheet 2: Expected Values Sheet – This sheet will first calculate  for each team for each round.  Place teams in rows and each round as a column.  Then place the value of each round at the top of each column and calculate the expected value for each team in the final column.

Sheet 3: Probability of Payoff Sheet – This sheet will calculate the probability of each possible payoff for the eight team tournament.  A team could win $0, $10000, $30000, or $55000.

§         P_i($0) = 1 -

§         P_i($10000) =  -

§         P_i($30000) =  -

§         P_i($55000) =

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 Class #3: (1 hour) The March Madness Auctions

The instructor may choose the type or types of auctions to use to sell the sponsorship rights of all of the 64 tournament teams.  The instructor may choose to sell each of the sponsorships twice - once in a sealed bid auction and then again in an open outcry auction.  The instructor may also choose to auction off half of the teams with an open outcry auction and the other half with a sealed bid auction.  If two separate sponsorship auctions are conducted before the tournament begins, then the instructor can make comparisons between the different auction designs.  Students use their calculations of the expected values of teams to assist with bidding.  The students’ profits are the actual sponsorship value (determined by success in the tournament) minus the bid amount paid to the team in the auction.  The students’ objective is to make the most profit. 

If two different auctions are used, the instructor may wish to proceed in the following manner.  Beginning the Monday morning after the tournament teams are selected, students may enter a sealed bid to purchase sponsorship rights for any team.  The sealed bid auction ends at the start of the open outcry auction (typically held on Wednesday or Thursday morning), so no bidders can learn anything about the valuations of other bidders during the sealed bid auction.  The results of the sealed bid auction are not announced until after the open outcry auction ends.  

The second auction is conducted in an open outcry format and is held during one class period (50-60 minutes).  Students take turns placing a team “on the block” (in any order) by announcing an initial bid for a team still available.  In the open outcry format every student has an opportunity to win the sponsorship contract by being the highest bidder.

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 Class #4:  (1 hour)  Follow-up Discussions and Analysis

The Winner’s Curse

The winner of an auction for a commodity with unknown value will most likely be the bidder who has the highest estimated value of the good.  Typically, the winner overestimates the value and then overpays in the auction.  Bidders need to significantly shade their bids to ensure that if they are the highest estimator of value, they do not overpay.

As an example, The March Madness in the Classroom exercise was conducted at Mount Saint Mary’s University in Emmitsburg, Maryland.  In both auctions (a first-price sealed bid and an open outcry) the winner’s curse was present.  In the open outcry auction, bids totaled $3,939,150 while the total payout was only $1,290,000.  Only five out of twenty-one students made a profit.  The students shaded their bids to some extent in the sealed bid auction, but the bids still totaled $2,511,219.  Only four students in the sealed bid auction made a profit.

Learning and Competition in an Open Outcry Auction

An open outcry auction may generate higher bid prices than a sealed bid auction as bidders have an opportunity to learn the expected valuations of the other bidders.  Competition between bidders may drive prices up further.  Conducting two auctions using different formats (sealed bid versus open outcry) will allow students to experience the differences first hand.   

As an example, The March Madness in the Classroom exercise was conducted at Mount Saint Mary’s University in Emmitsburg, Maryland.  In the open outcry auction, bids totaled $3,939,150 while the bids totaled $2,511,219 in the sealed bid auction.  The difference between the two ($1,427,931) occurred as a result of competition between the students as they bid for sponsorship rights.  For example, Duke University sold its sponsorship rights for $240,000 in the open outcry auction and $148,000 in the sealed bid auction.  Competition drove up the price $92,000.  However, bidders also learned how others students valued Duke as the auction progressed.  The winning bidder in the sealed bid auction had a pre-auction expected value of $157,348.  The winner in the open outcry auction, however, had a pre-auction expected value of $81,256.  In the open outcry auction, the eventual winning bidder learned that another bidder valued Duke at least $76,092 more. 

Learning accounted for bidders raising their maximum valuations $1,046,937 and then competition drove the bid prices up an additional $1,427,931.  Certainly students realized that the open outcry auction format will generate more revenue for a seller with a group of irrationally exuberant bidders.

Bid Price Determination

Using regression analysis instructors and students may use the auction data to determine what factors determine the final bid price.  A team’s past performance and the winning bidder’s valuation of the team are typically important factors.   The analysis may even be used to test whether the “declining price phenomenon” occurred in the auction.  Typically at an auction for multiple goods, the prices of identical goods decline as the auction progresses.  The rational is that potential buyers with higher valuations leave the auction once they have made a purchase.   

As an example, the March Madness in the Classroom exercise was conducted at Mount Saint Mary’s University in Emmitsburg, Maryland.  Students received the Sagarin ratings (a widely accepted computer rating system that the NCAA uses to seed the tournament teams) to represent past performance and students developed expected valuations of all the tournament teams. 

The bid price [OPENPRICE] in the open outcry auction is expected to be a function of [RATING] the Sagarin rating, [VALUATION] the winning bidder’s valuation of the team, and [ORDER #] the order number of the team that indicates when it was auctioned off.  The following is the result of OLS Regression using Microsoft Excel.

With an R-squared of 0.76, the model does a fairly good job of estimating the bid price.  By examining the data, however, one can clearly see that the relationship between the Sagarin rating and the bid price is not linear.  As the Sagarin rating increases, the marginal change in the bid price is increasing as well.  The OLS technique is one that the Managerial Economics students are most familiar with.  It is used for discussion purposes, and the limitations of the model specification are clearly explained. 

The results indicate that the Sagarin rating and the Winning Bidder’s valuation are significant.  According to the model, bidders paid $3,313 more per Sagarin rating point.  Bidders also 45% more than their valuation due to the learning and competition that occurred during the open outcry auction.  The coefficient on [ORDER #] is positive suggesting that prices in the auction increase as the auction progresses.  This might occur as students become worried that they may not initially own any sponsorship rights.  However, the coefficient on [ORDER #] is not statistically significant.

A similar analysis may be conducted using the results of the first-price sealed bid auction.  There is no [ORDER #] in the sealed bid auction, so the bid price [SEALEDPRICE] in the sealed bid auction is expected to be a function of [RATING] and [VALUATION].  The following is the result of OLS Regression using Microsoft Excel.

From the results of this model, it is clear that the students used their valuations to determine their sealed bid price.  The [VALUATION} variable is extremely significant and bidders shaded their bids to 96% of their valuation.  The Sagarin ratings were less important in determining the bid price as [RATING] was not statistically significant. 

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A Variant of the Exercise to use in months other than March

What?  You’d like to have some March Madness all year long?  You can use the March Madness in the Classroom exercise in months other than March! 

An instructor can create a "fantasy tournament" using another sport.  During the fall semester, I use the NFL to create a fantasy tournament with NFL quarterbacks.  This is a 32 quarterback tournament conducted over a period of 5 weeks.  I set up the tournament pairings myself.  The first week, there are sixteen match-ups, and the second week, there will be eight match-ups, etc.  A contest is decided between two quarterbacks by using their statistics from their actual NFL game on a particular Sunday.  (The beauty of the fantasy scoring is that the quarterbacks do not have to actually be playing each other in a real game.)  Students calculate their expected values and participate in an auction to buy sponsorship rights for the quarterbacks in the same manner as the NCAA tournament.

Calculation of Points Scored for Quarterbacks

6 points per touchdown

1 point per carry/rush

1 point per completion

1 point per 10 rushing yards (+3 bonus points if ≥ 100 yards)

1 point per 20 passing yards (+3 bonus points if ≥ 300 yards)

-5 points per interception

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