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Some Examples of Simpson's Paradox in Basketball Statistics

If you are wondering just what Simpson's Paradox is, the column I wrote for the Daily Kent Stater will step you through one example in detail.

All data comes from the Kent State Athletics' web pages. The season box scores list the data for total field goals and three-pointers. Subtract to find the numbers for two-pointers. Instances of Simpson's Paradox in the field goal shooting percentages appear to be rather common. I have been able to find at least one in each data set I've checked. I've included just a few examples here. The interested reader should pull out her calculator and look for more for herself!

  1. Here is the example from the Stater column:

    Kent State Men's Basketball: 2000-2001 Conference Games Only (18 games)
      Trevor Huffman Bryan Bedford
      Made Attempted Average Made Attempted Average
    Two-pointers 57 127 0.449 13 30 0.433
    Three-pointers 35 100 0.350 0 1 0.000
    All field goals 92 227 0.405 13 31 0.419

    The Lurking Variable: The more difficult 3-pointers made up a much higher percentage of Huffman's attempts than Bedford's. Thus, when the two categories are combined for the field-goal shooting percentage, the harder shots are weighted more in Huffman's total than in Bedford's.

      Trevor Huffman Bryan Bedford
    Percentage of FG Attempts
    which are 3-Pointers    		 44% 3%

  2. Here is an example from 2000-2001 women's statistics:

    Kent State Women's Basketball: 2000-2001 All Games
      Morgan O'Hara Lisa Wube
      Made Attempted Average Made Attempted Average
    Two-pointers 20 40 0.500 44 95 0.463
    Three-pointers 8 32 0.250 3 19 0.158
    All field goals 28 72 0.389 47 114 0.412

    Here again, O'Hara attempted a higher percentage of three-pointers than did Wube.

      Morgan O'Hara Lisa Wube
    Percentage of FG Attempts
    which are 3-Pointers    		 29% 6%

  3. Here is an intriguing example from 2001-2002 men's statistics through the MAC tournament (so not including the NCAA tournament games). Note how close their all-field-goal percentages are! Not surprisingly, this paradox didn't last through even the the first round of the NCAA tourney.

    Kent State Men's Basketball: 2001-2002 games through the MAC tournament
      Andrew Mitchell Demetric Shaw
      Made Attempted Average Made Attempted Average
    Two-pointers 109 230 0.4739 63 134 0.4701
    Three-pointers 61 159 0.3836 17 49 0.3469
    All field goals 170 389 0.4370 80 183 0.4372

      Andrew Mitchell Demetric Shaw
    Percentage of FG Attempts
    which are 3-Pointers    		 41% 27%

  4. This example is from the women's 2002-2003 season.

    Kent State Women's Basketball
    2002-2003 All Games
      Jamie Rubis Lindsay Shearer
      Made Attempts Average Made Attempts Average
    Two-pointers 119 234 0.509 86 170 0.506
    Three-pointers 36 97 0.371 5 21 0.238
    All field goals 155 331 0.468 91 191 0.476

      Jamie Rubis Lindsay Shearer
    Percentage of FG Attempts
    which are 3-Pointers    		 29% 11%

  5. And here is one from the men's 2002-2003 season. Note that Wilkins shot from beyond the three-point arc 75% of the time!

    Kent State Men's Basketball:
    2002-2003 Conference Games Only
      Anthony Wilkins Antonio Gates
      Made Attempts Average Made Attempts Average
    Two-pointers 31 56 0.554 216 440 0.491
    Three-pointers 67 171 0.392 15 43 0.349
    All field goals 98 227 0.432 231 483 0.478

      Anthony Wilkins Antonio Gates
    Percentage of FG Attempts
    which are 3-Pointers    		 75% 9%