NCAA Basketball Tournament: Predicting Performance

Bobby ZandstraSenior Seminar March 31, 2008

Outline of Project• Introduction and Brief History of the NCAA

Basketball Tournament• The Selection and Seeding of College

Basketball Teams for Postseason Competition

• Identifying the “Dance” Card• Single Elimination Tournament Structure• Probability Models for the NCAA Regional

Basketball Tournaments • Economic Impact from the NCAA

Basketball Tournament• Determining Decision-Making Effectiveness

NCAA Men's Division I Basketball Championship-Quick

Overview• Single-elimination tournament featuring 65

teams representing all Division I Conferences in the nation.

• A "play-in" game determined which of the two lowest seeds will play in the first roundof 64 against a top seed team.

• The Selection Committee (made up of atheletic directors and conference coordinators) seeded the entire field from 1 to 65 within four regionals of 16 teams.

Timeline• 1939 Was the first NCAA Men’s

Tournament.• 1939-1950 8 teams from district

championships.• 1951 16 teams 10 conf. Champs; 6 at large

bids• 1952 final 4 format instead of just

championship• 1954 ~24 teams:15 conf champs; 9 at large

bids• 1975 32 teams qualified

How’s It Setup?• The selection committee is in charge of

setting up 4 regions (east, south, west and midwest).

• There is a tournament in each of these regions, so the teams are seeded 1-16. 1 plays 16; 2 plays 15; etc… The lower the number of the seed the better the team. #1 seed is the best team.

• With this happening the best teams should be playing each other in the later rounds.

• The champions of the regions play in the final four

Who’s In?• A total of 31 teams received automatic bids

for winning their conference tournament championship. Since the Ivy League does not hold a tournament, its regular season champion received the automatic bid.

• This left 34 at-large bids to be decided from the rest of the field by the NCAA Selection Committee. The at-large bids, along withthe seeding for each team in thetournament, was announced on Sunday,March 16.[2]

Selection Sunday-Identifying the “Dance” Card

• The Selection Committee names the teams on the Sunday prior to the beginning ofthe tournament.

• The At-large bids are chosen by the committee with the help of a computer ranking system.

Factors that the Committee Take Into Consideration for the

At-Large Bids

Are Some Criteria Weighted Differently?

• RPI (Rating Percentage Index)• -25% of Team’s Winning Percentage• -50% of its Opponent’s Winning Average• -25% of its Opponent’s Opponent’s Winning

Percentage

• Weighted More• 1. RPI Rank• 2. Conference RPI Rank• 3. Top 25 Wins• 4. Conference Wins-Losses

5 T 50 Wi L

Arrow’s Impossibility Theorem• Published in 1951• Establishes that for two or more voters

declaring their positionings of three or more candidates, no function existsthat, by nondictatorial pairwisecomparisons respecting unanimity,compiles any such positionings intoone.

Arrow’s Impossibility Theorem• Proves that a rational voting system is

logically impossible!• Proposes 5 reasonable, desirable, and

intuitively acceptable conditions that asocial welfare function should satisfy andproves that they are inconsistent. Hence,no welfare function which satisfies all ofthem can exist.

Arrow’s Impossibility Theorem-Applied to NCAA Seeding

• Welfare Function is RPI (3 numbers usedto calculate rating)

• Function Needs to Satisfy Following:• 1. “There will be at least two individuals and

at least three alternatives to be ordered…and requires that he socialwelfare function be defined for all sets ofindividual orderings.”

• 2. “The preference ordering of no individual in the group should have a negative or contrary influence on the social ordering.”

• 3. “If the preference orderings of individualsh d f f th lt ti

1. “There will be at least two individuals and at least three alternatives to be ordered…and requires that he social welfare function be defined for all sets of individual orderings.”

• There must exist at least 3 teams and 2 numbers.• 351 NCAA Basketball Teams

• RPI consisting of 3 numbers for calculations.• Satisfies 1st condition!

2. “The preference ordering of no individual in the group should have a negative or contrary

influence on the social ordering.”

• One number’s preference ordering should have no effect on the overall RPI.

• Single number that is a team’s winning percentage does not have a negative influence on the overall ordering.

• Satisfies 2nd condition!

3. “If the preference orderings of individuals are changed for some of the alternatives, the orderings of the remaining alternatives should be unaffected in the revised social ordering.”

• If one of the numbers used to calculate RPI becomes higher for Team A than for Team B, the order betweeen Team C and TeamD should not be affected in the revised rankings.

• RPI and other methods of ranking DOES NOT satisfy 3rd condition. (Example)

4. “For each pair of alternatives A and B, there must exist at least one set of individual orderings

such that society prefers A to B.”

• Must be possible for the individual numbers that make up the RPI to rank Team Aahead of Team B.

• Satisfies 4th condition!

5. “There is no individual with the power that is he prefers A to B, society does likewise

regardless of other individuals’ orderings.”

• RPI does not work like this since onenumber alone does not rank Team Aahead of Team B in the overall RPI.

• Satisfies 5th condition!

Arrow’s Impossibility Theorem• Conclusion• -“No social welfare function can ever exist,

so there can never be a numerical methodof ranking teams that will be the correctone”

• However, is there a best method?

Revenue and Economic Impact For Host Cities

• Estimated that $2.5 billion Iis bet illegally on the NCAA tournament each year.

• 6-billion dollar (11 year) contract between CBS and NCAA.

Can the NCAA Basketball Tournament Seeding be Used to

Predict Margin of Victory?• -Committee seeds the

teams based upon a consensus of team strength. Attempts for equal strength across regions.

• Only once (1985) has there been no upsetsin the first round of the tournament.

• In 2008, First time all • 1-seeds in each region

advanced to FinalFour.

Data From Past Tournaments

Revenue and Economic Impact For Universities

• The Division I Men's Basketball tournament is the only NCAA championship tournament (officially, the BCS Football Championshipis not an NCAA event) where the NCAAdoes not keep the profits. Instead, themoney from the multi-billion-dollartelevision contract is divided among theDivision I basketball playing schools andconferences as follows: [11]

• 1/6 of the money goes directly to theschools based on how many sports theyplay (one "share" for each sport startingwith 14, which is the minimum needed for

The Perfect Bracket• There are 9,223,372,036,854,775,808

possible brackets. That’s the number nine follow by eighteen zeros. That’s over 9.2 quintillion. Some examples of just how big this number is:

• If everyone on the planet each randomly filled out a bracket, the odds would be over 1.5 BILLION to 1 against anyone having a perfect bracket.

• If all possible brackets were stacked on top of each other (on standard paper) the pile

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