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Sports by the Numbers

Category: NCAA Men’s Basketball

How much does seeding matter?

Posted on March 13, 2015October 16, 2015 by Peter Lemieux

On Sunday the NCAA Selection Committee will release this year’s Tournament brackets and create the structure within which the teams will compete.  Teams will be placed in one of sixteen seedings spread across four so-called “regions,” for a total of sixty-four competitors.  How teams are seeded dramatically influences their chances of victory in the Tournament.  Teams seeded sixteenth may dream of becoming the first of their kind win a first-round game against a top-seed, but probably none will do so.  Those top seeds should be feeling optimistic as they begin their paths through the Tournament.  Eight of the past thirteen Tournaments have been won by a top seed.

Here is a comprehensive look at the performance of all 832 competitors, representing 216 schools, that have participated in the thirteen Tournaments between 2002 and 2014. (Play-in games are excluded.)

performance-by-seed2

Of the 156 teams seeded fourteenth or lower, only one has managed to advance to the Sweet Sixteen, along with three others from the ranks of the thirteens.  Teams seeded tenth through twelfth, and those seeded seventh, have fairly similar records.  Just over a fifth of them (22%) survived their two first-round contests and advanced to the Sixteen. When applied to the upcoming Tournament, we should expect to see three teams advance from those four seedings.

If I were a college basketball coach, I would be very disappointed to find my team seeded eighth or ninth.  These teams face each other in the first game, with the survivor usually losing to the one seed in the next round. In terms of advancing to the Sweet Sixteen, the odds are better as a twelve seed than they are as an eight or nine!

While the 8/9 matchup is usually seen as a “pick ’em” choice between equally matched opponents despite the seedings, empirically that has not been the case over the past thirteen Tournaments.  Eight seeds hold a 30-22 edge over teams seeded ninth in first-round games played since 2001 though that margin is not “statistically significant” by conventional standards.

The survival rates for teams rated sixth or higher rise quickly along with their seedings, but it is the top-seeded teams whose performances really stand out.  About a third of the teams seeded first (18 of 52) advanced to the Final Four, and eight of them went on to win one of the thirteen Championships awarded since 2001.  Many of those victories came at the expense of teams seeded second in the semifinals and finals. Only one team seeded second, Connecticut in 2004, has won a Championship since 2001, while three Championships were captured by teams seeded third. Last year’s remarkable victory by Connecticut as a seven seed rounds out the list of Champions between 2002 and 2014.

 

Posted in NCAA Men's Basketball

Them That’s Got Shall Get: Seedings for March Madness

Posted on March 10, 2015March 13, 2015 by Peter Lemieux

In just a few weeks time the Selection Committee for the 2015 Division I Men’s Basketball Tournament, better known as “March Madness,” will be inviting sixty-eight teams to fill a field of sixty-four.  (Eight of the teams play off for four of the sixty-four seedings.)  These seedings matter greatly over the three weeks of the Tournament.  Top seeds win on average four out of five games they play.  Teams seeded seventh win half their games, while teams seeded twelfth win about two out of every five.

Most college basketball fans know that the NCAA considers something called the “RPI,” or “Ratings Performance Index,” as a measure of each team’s strength.  The Selection Committee uses RPI to help decide on at-large bids and seedings.

The RPI adjusts each team’s won-loss record by its “strength of schedule,” the won-loss record of its opponents.  The NCAA also adjusts for the won-loss record of those opponents’ opponents.  The team’s own performance gets only a 25% weight in the RPI.  Its opponents’ record counts 50%, and their opponents records count 25%. These weightings make strength of schedule the primary determinant of RPI.

In principle these adjustments should make RPI a neutral measure of team strength and remove the effects of conference affiliations. Teams playing in “major” conferences like the ACC or Big 12 have higher RPI scores because they play a tougher schedule.  In a world where seedings depended only a team’s innate abilities, it shouldn’t matter which conference that team plays in. The historical data summarized in this chart says otherwise.

seedings

The Selection Committee awards better seedings to teams playing in the major conferences than it awards to schools with identical RPI scores from weaker conferences. In the chart I’ve shown the relationship between seeding and RPI for teams grouped by their type of conference.  At the top are the six “major” conferences — the ACC, Big East, Big 10, Big 12, Pac 12, and SEC.  Next come the eight so-called “mid-major” conferences — Atlantic 10, Colonial Athletic, Conference USA, Horizon League, Missouri Valley, Mountain West, Western Athletic, and West Coast conferences.  The Selection Committee routinely grants multiple Tournament bids to members of both these types of conferences.

The eighteen remaining conferences receive only a single Tournament invitation, the one extended to each conference’s champion.  This policy forever limits teams in these conferences to also-ran status.  Take a team with an RPI of 0.600.  If that school plays for a team in a single-bid conference, the Committee is likely to seed that team eleventh (10.7 according to the model).  Put that same team in a mid-major conference, and it would be awarded an eight seed (7.8).  Playing in a major conference would earn that team a seven (7.1). Both the advantage the majors have over the mid-majors, and the advantage they both have over single-bid schools, widens with RPI.

 

Posted in NCAA Men's Basketball

Technical Appendix: Estimating Seedings from RPI

Posted on February 26, 2015September 9, 2015 by Peter Lemieux

Method using program averages for teams with at least two appearances
seeding-model-estimates

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.

 

 

Posted in NCAA Men's Basketball, Technical Notes

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