篮球名人堂积分(入选可能性)计算方式
Building the Model For the Hall of Fame problem, I tried to use as many predictor variables as I could think of, but I did not use statistics that have not been kept for most of the NBA's history (e.g., steals). My player pool consisted of players who had played a minimum of 400 NBA games and had been eligible for at least one Hall of Fame election. After trying numerous models, my final model had eight predictor variables:
height (in inches)
last season indicator (1 if 1959-60 or before, 0 otherwise)
NBA points per game
NBA rebounds per game
NBA assists per game
NBA All-Star game selections
NBA MVP award shares
NBA championships won
All of the predictors listed above were significant at the 0.05 level except for NBA MVP award shares, which had a P-value of 0.07. However, every NBA MVP award winner who is eligible for the Hall of Fame has been elected, so I thought it was important to keep that term. Other than height, all of the predictors had positive coefficients. ABA statistics, honors, and championships were not important predictors of Hall of Fame status, which is why I only used NBA statistics in my final model. I don't like ignoring the ABA statistics, but that's what the voters have apparently done. Keep in mind that my goal was not to determine who should be in the Hall of Fame, but rather who is likely to be in the Hall of Fame.
The table below gives the parameter estimates of the coefficients for each of the seven predictors:
height -0.20518
last season indicator 4.21609
NBA points per game 0.45098
NBA rebounds per game 0.37523
NBA assists per game 0.39329
NBA All-Star game selections 0.48684
NBA MVP award shares 3.18416
NBA championships won 1.03335
Example The parameter estimates given in the previous section can be used to obtain the predicted probability of Hall of Fame election for a particular player. I will go through an example using Jo Jo White. Find the values of the eight predictor variables for White, multiply them by the coefficients given in the table above, and find the sum of the products:
height -0.20518 * 75 = -15.3885
last season indicator 4.21609 * 0 = 0
NBA points per game 0.45098 * 17.2031 = 7.7583
NBA rebounds per game 0.37523 * 3.9964 = 1.4996
NBA assists per game 0.39329 * 4.8925 = 1.9242
NBA All-Star game selections 0.48684 * 7 = 3.4079
NBA MVP award shares 3.18416 * 0.0073 = 0.0232
NBA championships won 1.03335 * 2 = 2.0667
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1.2914
To find the predicted probability of Hall of Fame election, do the following:
P(HoF election) = e**1.2914 / (1 + e**1.2914)
= 0.784
Based on Jo Jo White's statistics and accomplishments, the probability that he has been elected to the Hall of Fame is 0.784.