Similarity Scores

Most Similar Seasons

Last modified on June 2, 2006.

The similarity scores were calculated using a method that is basically a hybrid of John Hollinger's similarity scores method in Pro Basketball Forecast, Kevin Pelton's work on Hoopsworld.com, and my own ideas. Let me state up front that this is a work in progress, and any helpful comments you may have would be appreciated.

Below is a list of the thirteen categories I used for the similarity scores:

1. Height (Ht)
2. Minutes per game (MPG)
3. Percentage of team field goals attempted while on the court (Shot%)
4. Percentage of team offensive possessions used while on the court (Poss%)
5. Effective field goal percentage (eFG%)
6. Free throw percentage (FT%)
7. Free throw attempts per field goal attempt (FTA/FGA)
8. Percentage of teammate field goals assisted (AST%)
9. Turnovers per 100 possessions (TOV%)
10. Steals per 100 opponent possessions (STL%)
11. Blocked shots per 100 opponent two-point field goal attempts (BLK%)
12. Percentage of possible offensive rebounds (ORB%)
13. Percentage of possible defensive rebounds (DRB%)

I used a player pool that included all NBA seasons from 1977-78 to the present. Within each season, I found the standardized score (or z score) for each player in each category. League means and standard deviations were calculated in each season for each category using player minutes played as the weights. Although all players were used to determine the league means and standard deviations, similarity scores were only computed using players who played at least 25 percent of possible minutes played in the given season (in most seasons this will be roughly 1000 minutes played).

To obtain the similarity score between two seasons, I did the following:

1. Calculate the absolute difference in the z scores for each category.
2. The penalty for each category is equal to 10 times the absolute difference, with a maximum penalty of 50 points.
3. Find the sum of the penalties, using weights of 4 for Ht; 2 for Min/G, %Shots, and %Poss; 1.5 for eFG% and %Ast; and 1 for all other categories.
4. Subtract the sum above from 1000.

As an example, let me use LeBron James's 2005-06 season and Tracy McGrady's 2004-05 season. Below are their z scores in each of the 15 categories, the absolute differences in their z scores, and the penalties:

                                                         FTA/
                 Ht    MPG  Shot%  Poss%   eFG%    FT%    FGA   AST%   TOV% STL%   BLK%   ORB%   DRB%

    James     0.295  1.644  2.616  2.352  0.553  1.938 -0.018  0.726 -0.800 0.633  0.008 -0.777  0.469
    McGrady   0.279  1.549  2.220  2.335 -0.185  1.419  0.195  0.049 -1.159 1.049 -0.145 -0.810  0.089

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    Abs Diff  0.016  0.095  0.396  0.017  0.738  0.519  0.213  0.677  0.359 0.416  0.153  0.033  0.380
    Penalty   0.160  0.950  3.960  0.170  7.380  5.190  2.130  6.770  3.590 4.160  1.530  0.330  3.800

The weighted sum of the penalties is 52.755. The similarity score for these two seasons is 1000 - 52.755 = 947.245 (this figure actually rounds up to 948 when all of the decimal places are carried). When all player seasons are analyzed, the closest match to James's 2005-06 season is in fact McGrady's 2004-05 season.

On the player pages, similarity scores are presented for each qualifying season. The first list shows the most similar season at the same age. In other words, players are only compared to other players at the same age. The second list shows the most similar season regardless of age. In other words, players are compared to all other qualifying players.

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