The following list summarizes shooting percentage in the 2001–2002 season in the National Basketball Association by Brent Barry and Shaquille O’Neal.
2-point shots
• Brent Barry: 58.8% (237/403)
• Shaquille O’Neal: 58.0% (712/1228)
3-point shots
• Brent Barry: 42.4% (164/387)
• Shaquille O’Neal: 0% (0/1)
Overall
• Brent Barry: 50.8% (401/790)
• Shaquille O’Neal: 57.9% (712/1229)
a. Treating the type of shot as a control variable, whether a shot is made as the response variable, and the player as the explanatory variable, explain how these results illustrate Simpson’s paradox.
b. Explain how O’Neal could have the higher overall percentage, even though he made a lower percentage of each type of shot.