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

Question

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?

Accepted Answer

Player X hit better. X beat Y in Season 1 (.400 versus .350) and again in Season 2 (.250 versus .200). In each season, X had the higher average. The combined figure flips it, a textbook Simpson's paradox driven by a confounder. The confounder is when the at-bats happened. Season 2 was a harder hitting environment: both players' averages fell. Crucially, the two players piled up their at-bats in opposite seasons. X took most of his at-bats (100 of 110) in the low-average Season 2, while Y took most of his (100 of 110) in the higher-average Season 1. So Y's combined average is inflated by a fav…

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

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