Batting Averages

David Justice and Derek Jeter were professional baseball players. In 1997 they had the following conversation:

David: Did you know that in both 1995 and 1996 I had better batting averages than you?

Derek: No way, my batting average over the last two years was definitely higher than yours!

It turned out that both of them were right. How is it possible?

This is the so called Simpson’s paradox. The reason it occurred is that during 1996 both players had high averages and Derek Jeter had many more hits than David Justice. In 1996 both players had low averages and David Justice had many more hits than Derek Jeter. You can see their official statistics below.

Player199519961995-1996
Derek Jeter12/48 (.250)183/582 (.314)
195/630 (.310)
David Justice104/411 (.253)45/140 (.321)149/551 (.270)
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We do not know where this puzzle originated from. If you have any information, please let us know via email.

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