Category: Technical Notes

Like its predecessors the model below was estimated using the “Tobit” method with the endpoints constrained to values of one and sixteen.

The top portion of the table above restates the basic relationship between RPI and seeding, and how that relationship varies by conference.  Again I find that seeding depends directly on RPI, and that mid-major conference members and, even more, major conference members receive a “bonus” when the Tournament Committee decides their seedings.  Those results present this now-familiar graph:

I’ve also reanalyzed the results for conference champions and have determined that only major conference champions receive a seeding bonus of 1.3 seeding ranks.  In other words, a major-conference team that wins its conference championship will be promoted at least one full rank in the seedings.

Finally I address the “favoritism” question in the lower half of the table.  The Committee has awarded teams belonging to the ACC and Big East conferences a bonus of about one third of a rank.  The Committee has also looked especially fondly at two teams over the years, mid-majors Gonzaga and Cincinnati.  That Gonzaga is one of these should not be a surprise to anyone who follows the Tournament. It is one of only five schools, along with Duke, Kansas, MIchigan State, and Wisconsin, to have qualified for the Tournament every year since 2000.  Cincinnati has the second most appearances, twelve, of any team not in a major conference.

On the other side of the ledger, three of the mid-major conferences have fared more poorly in the seedings than the others.  The Committee appeared to view with suspicion teams from the American Athletic, Colonial, and Western Athletic Conferences.  Teams from these conferences are seeded on average about one and a half rankings below what those teams’ performances would predict.  In addition, the Committee has historically marked down teams from Brigham Young University, seeding them nearly two ranks below what their RPI and conference membership would predict.

This table presents the results of three “Tobit” estimations of the effects of RPI and conference membership on seedings in the NCAA Tournament.

The first column reports the results for a model that includes each teams RPI, its conference membership, and “interaction” terms for each combination of RPI and conference so that the slopes can differ across conferences.  RPI has a strong negative relationship with seeding, and that relationship is steeper for mid-major teams, and steeper still for majors.

The second column tests the hypothesis that the slope for majors and mid-majors are the same.  Here I include a variable that measures RPI for all major and mid-major teams together, then include a separate measure for the major conference teams.  If the majors and mid-majors followed the same path, the term for majors only in model (2) should be zero.  Since it is not, I maintain the distinction between majors and mid-majors in model (3).

This is the model where I add in whether a team won a conference championship. Champions from single-bid conferences actually have lower seeds because they are included in the Tournament automatically.  Since many of these are among the weaker teams, a tournament winner from a conference like the Colonial or Ivy receives a worse seeding than an average at-large team at the same RPI.

When we turn our attention to the mid-majors and majors, though, conference champions receive a substantial seeding bonus.  Mid-major champions have better (lower) seedings by a factor of 1.4.  For major champions the effect is a whopping 2.6 ranks.  Given the usual denigration of the conference championships by basketball pundits, these are surprisingly large effects indeed.

Method using program averages for teams with at least two appearances

Ordinary Least Squares applied to 832 team appearances (64 teams x 13 years):

Model 6: OLS, Appearances, 2002-2014 (832 observations)
Dependent variable: seed

             coefficient   std. error   t-ratio   p-value 
  --------------------------------------------------------
  const        36.7650      1.86680      19.69    4.38e-71 ***
  midmaj       29.1555      2.97857       9.788   1.76e-21 ***
  power        29.6810      2.63332      11.27    1.65e-27 ***
  rpi         −42.1049      3.45923     −12.17    1.82e-31 ***
  rpimid      −53.8989      5.23069     −10.30    1.66e-23 ***
  rpipower    −57.5874      4.60477     −12.51    5.46e-33 ***

Mean dependent var   8.500000   S.D. dependent var   4.612545
Sum squared resid    2389.298   S.E. of regression   1.700768
R-squared            0.864859   Adjusted R-squared   0.864041
F(5, 826)            1057.224   P-value(F)           0.000000
Log-likelihood      −1619.405   Akaike criterion     3250.809
Schwarz criterion    3279.152   Hannan-Quinn         3261.677

OLS does not have any special methods to handle “censored” information like seedings.  The coefficients above predict seeds below one and above sixteen.  A better alternative is Tobit with censors at one and sixteen.  This model (with some minor adjustments to the intercept differences) generates the graph in the article.

Tobit, 2002-2014 (n = 831)
Dependent variable: seed

             coefficient   std. error      z      p-value 
  --------------------------------------------------------
  const        49.1581      2.54088      19.35    2.16e-83 ***
  midmaj       18.8101      3.59081       5.238   1.62e-07 ***
  power        25.0724      3.32994       7.529   5.10e-14 ***
  rpi         −64.1098      4.64080     −13.81    2.09e-43 ***
  rpimid      −35.3690      6.31863      −5.598   2.17e-08 ***
  rpipower    −48.6491      5.83366      −8.339   7.47e-17 ***

Chi-square(5)        4401.971   p-value              0.000000
Log-likelihood      −1517.352   Akaike criterion     3048.703
Schwarz criterion    3081.762   Hannan-Quinn         3061.380

sigma = 1.79472 (0.0469158)
Left-censored observations: 52 (seed <= 1) 
Right-censored observations: 51 (seed >= 16)

Estimates from this model show a greater difference between the majors and mid-majors than do the OLS estimates.