Answer: The NCAA basketball tournament begins with 64

Chapter 14, Problem 14.46

(choose chapter or problem)

The NCAA basketball tournament begins with 64 teams that are apportioned into four regional tournaments, each involving 16 teams. The 16 teams in each region are then ranked (seeded) from 1 to 16. During the 12-year period from 1991 to 2002, the top-ranked team won its regional tournament 22 times, the second-ranked team won 10 times, the third-ranked team won 5 times, and the remaining 11 regional tournaments were won by teams ranked lower than 3. Let Pij denote the probability that the team ranked i in its region is victorious in its game against the team ranked j. Once the Pijs are available, it is possible to compute the probability that any particular seed wins its regional tournament (a complicated calculation because the number of outcomes in the sample space is quite large). The paper Probability Models for the NCAA Regional Basketball Tournaments (The American Statistician, 1991: 3538) proposed several different models for the Pijs. a. One model postulated Pij .5 (i j) with 1/32 (from which P16,1 , P16,2 2, etc.). Based on this, P(seed #1 wins) .27477, P(seed #2 wins) .20834, and P(seed #3 wins) .15429. Does this model appear to provide a good fit to the data? b. A more sophisticated model has game probabilities Pij .5 .2813625 (zi zj ), where the zs are measures of relative strengths related to standard normal percentiles (percentiles for successive highly seeded teams are closer together than is the case for teams seeded lower, and .2813625 ensures that the range of probabilities is the same as for the model in part (a)). The resulting probabilities of seeds 1, 2, or 3 winning their regional tournaments are .45883, .18813, and .11032, respectively. Assess the fit of this model.

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back