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.