Baseball paradox Most baseball hitters perform differently against right-handed and left-handed pitching. Consider two players, Joe and Moe, both of whom bat right-handed. The table below records their performance against right-handed and left-handed pitchers:

(a) Use these data to make a two-way table of player (Joe or Moe) versus outcome (hit or no hit).
(b) Show that Simpson’s paradox holds: one player has a higher overall batting average, but the other player hits better against both left-handed and right-handed pitching.
(c) The manager doesn’t believe that one player can hit better against both left-handers and right-handers yet have a lower overall batting average. Explain in
simple language why this happens to Joe and Moe.