Hall of Fame Probability
Explanation ▪ Career & Active Leaders
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, we tried to use as many predictor variables as we could.
Player awards, sustained effectiveness as measured by appearances on leaderboards, and peak
dominance (measured as a player's peak Win Shares output), all have explanatory value.
Number of championships is a strong predictor, as well, along with the player's height.
Our player pool includes players who have played a minimum of 400 NBA games and were retired by
the end of the 2004-05 season, so that they've had several years to be considered.
We excluded players that spent significant time in the ABA. As well, from the list of current Hall
of Famers we excluded players with fewer than 50 Win Shares. The reasoning here is that the media and
likely voters are more attunded to statistical output, however refined, than they were through the 1980s.
There are players that have been inducted in the past that aren't necessary predictive of future
Players receive points for appearing on leaderboards, receiving 10 points for leading the league in a category and 1 point for finishing 10th. This seems like a fair way to award credit for both black and gray ink. The eligible statistical categories include PTS, TRB, AST, MP, STL, BLK. The list of predictor variables is:
- Height (in.)
- NBA Championships
- NBA Leaderboard Points
- NBA Peak Win Shares
- All-Star Game Selections
Keep in mind that this exercise aims to predict who is likely to be inducted, as a Player, and based solely on NBA accomplishments and statistical output. There are coaches and contributors at all levels of the game, as well as foreign players and WNBA stars that are also worthy of induction.
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. We'll go through an example using Tony Parker following the 2013-14 season. Find the values of the five predictor variables for Parker, multiply them by the coefficients given in the table above, and find the sum of the products:
Int. -0.20303 Height (in.) -0.14203 * 74 = -10.51022 NBA Championships 0.80573 * 4 = 3.22292 NBA Leaderboard Points 0.01594 * 4 = 0.06376 NBA Peak Win Shares 0.41568 * 9.6 = 3.99053 NBA All-Star Game Selections 1.02443 * 6 = 6.14658 --------------------------------------------------------------- 2.71054
To find the predicted probability of Hall of Fame election, do the following:
P(HoF election) = 1 / (1 + exp(-(2.71054))) = 93.8%
Based on Tony Parker's statistics and accomplishments, the probability that he will be elected to the Hall of Fame, as it stands now, is 93.8%
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?".