# Hall of Fame Probability

Explanation ▪ Career
Leaders ▪ Active Leaders

## Introduction

What statistics or accomplishments have the Hall
of Fame voters deemed to be most important? This question can be
answered using a technique called logistic regression. The logistic
regression model is a binary response model where the response is
classified as either a "success" (in this case, being elected to the Hall
of Fame) or a "failure" (not being elected to the Hall of Fame). One or
more predictor variables are selected and the resulting model can be used
to predict the probability of a success given certain values of the
predictor(s).

## 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 seven 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 championships won

All of the predictors listed above were significant at the 0.05 level.
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 <="" span=""> 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 -0.1771
last season indicator 3.1498
NBA points per game 0.3433
NBA rebounds per game 0.4193
NBA assists per game 0.3327
NBA All-Star game selections 0.5626
NBA championships won 0.9151

## 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
seven predictor variables for White, multiply them by the coefficients
given in the table above, and find the sum of the products:

height -0.1771 * 75 = -13.2825
last season indicator 3.1498 * 0 = 0
NBA points per game 0.3433 * 17.2031 = 5.9058
NBA rebounds per game 0.4193 * 3.9964 = 1.6757
NBA assists per game 0.3327 * 4.8925 = 1.6277
NBA All-Star game selections 0.5626 * 7 = 3.9382
NBA championships won 0.9151 * 2 = 1.8302
----------------------------------------------------------
1.6951

To find the predicted probability of Hall of Fame election, do the
following:

P(HoF election) = 1 / (1 + e**(-(1.6951)))
= 0.845

Based on Jo Jo White's statistics and accomplishments, the probability that
he has been elected to the Hall of Fame is 0.845.

## Summary

Hall of Fame probabilities are presented for all players with a minimum of
400 NBA games played. Although it can be risky to make predictions for
active players, you can think of these probabilities as answering the
question "If this player retired today, what is the probability he would
be elected to the Hall of Fame?". The model was built using a pool of 750
players. One method to assess classification accuracy is to compare the
estimated Hall of Fame probability for the case to the actual result. Of
the 750 players, 89 had been elected to the Hall of Fame and 661 had not.
If the player's predicted probability of election was greater than or
equal to 0.5, I predicted that he was in the Hall of Fame. Of the 89
players in the Hall of Fame, 74 were correctly classified (83.1%) and 15
were not (16.9%). Of the 661 players not in the Hall of Fame, 651 were
correctly classified (98.5%) and 10 were not (1.5%). Overall, 725 of the
750 players (96.7%) were correctly classified by the model.