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Statistics

The batter with the higher average each year, but not overall

confoundingsimpsons-paradoxcausal-inference

Two baseball players are compared on batting average (hits divided by at-bats) over two seasons.

  • Season 1: Player X gets 4 hits in 10 at-bats (.400); Player Y gets 35 hits in 100 at-bats (.350).
  • Season 2: Player X gets 25 hits in 100 at-bats (.250); Player Y gets 2 hits in 10 at-bats (.200).

Combining both seasons, X batted 29 for 110 (.264) and Y batted 37 for 110 (.336), so Y has the better combined average.

Which player was the better hitter, and why does the combined average disagree?

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