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Sports by the Numbers

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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